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Figure 527mtop distributions fortt default sample and systematic variations
59 Crosschecks 133
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59 Crosschecks
Alternative methods to extractmtop from its distribution (Figure 518) have been attempted The goalis to test the robustness of the template method explained above
591 Mini-template method
This section explains a simplified template method to extract the mtop The goal is to perform thefit of the mtop distribution (Figure 529) using the function given in Section 57 but with as many freeparameters as possible The idea is to avoid possible MC malfunctions7 as for example different jetenergy resolution
In the current implementation all the parameters are left free exceptλ which took the same parametriza-tion as in the template method andǫ which takes its constant value Hereafter this method andtheirresults will be labelled asmini-template The linearity of the mini-template has been also studied and theresults are shown in Appendix O
When fitting the combined distribution with the mini-template technique the extracted top-quark massvalue is
mtop = 17418plusmn 050 (stat)plusmn 042 (JSF) GeV
the error quotes the statistics plus the jet scale factor uncertainties All fit parameters split by channel canbe consulted in Table 59
Themtop value obtained with the template and mini-template methodsare just above 1 standard devia-tion from each other Moreover it is worth to compare the fitted value forσ in the mini-template method(1074plusmn 034 (stat) GeV) with its counterpart in the template fit (1123plusmn 009 (stat) GeV) Theσ values
7It is already proven that the JES is different between data and MC as shown in Table 53
134 5 Top-quark mass measurement with the Globalχ2
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Figure 529 Distribution of themtop parameter after the Globalχ2 fit using theminiminus templatemethodUpper right presents the results in thee+ jets channel and upper left in themicro + jets one Bottom plotthe distributions of thee+ jets andmicro + jets are added together The real data distribution has beenfitted(drawn as a solid gray line) to a lower tail exponential distribution with resolution model (for the correctcombinations drawn as green dashed line) plus a Novosibisrk function (to account for the combinatorialbackground drawn as a red dashed line) All the contributions to the irreducible physics background areadded together (blue area)
59 Crosschecks 135
Parameter ℓ + jets e+ jets micro + jetsmtop 17418plusmn 050 17354plusmn 084 17418plusmn 063σ (GeV) 1074plusmn 034 1051plusmn 055 1096plusmn 044λ 427plusmn 006 430plusmn 009 417plusmn 007microbkg (GeV) 15834plusmn 151 16303plusmn 280 15737plusmn 189σbkg (GeV) 2265plusmn 068 2381plusmn 115 2239plusmn 088Λbkg 041plusmn 005 026plusmn 008 044plusmn 006
Table 59 Parameter values extracted with the mini-template method fit The fraction of combinatorialevents has been fixed to 546 in both methods The errors onlyaccount for the statistical uncertainty ofthe fit
obtained from the two fits are 14 standard deviations away from each other Although that difference isnot significant yet it may suggest a slightly different jet energy resolution in data and MC
The systematic uncertainties for the mini-template methodhave been also computed Table 510 quotesthe results for each individual systematic source and also for the total systematic uncertainty These un-certainties were evaluated following the same prescription given in Section 58 Notice that the JERsystematic uncertainty one of the dominant errors for the template method has been considerably re-duced This could be understood since the mini-template leaves theσ as a free parameter and thereforeit can absorb the impact of the JER as already highlited in theparagraph above Nonetheless the finalsystematic uncertainty was found to be larger than in the template method
Table 510 Systematic errors of themtop analysis with the mini-template methodSource of error Error (GeV)
Method Calibration 021Signal MC generator 049Hadronization model 104Underlying event 019Color reconection 005ISR amp FSR (signal only) 038Proton PDFs 004Irreducible physics background 005Jet Energy Scale (JES) 073b-tagged Jet Energy Scale (bJES) 087Jet energy resolution 009Jet reconstruction efficiency 009b-tagging efficiency 054Lepton Energy Scale 011Missing transverse energy 002Pile-up 011
Total systematic uncertainty 176
This method represents an attempt to understand the shape ofthemtop distribution with a minimal MCinput If for some reason data and MC had different behaviour the template will irremediable bias themtop measurement By contrast the mini-template method could avoid this kind of problems
136 5 Top-quark mass measurement with the Globalχ2
592 Histogram comparison
Themtop distribution extracted from data has been compared with those extracted fromtt MC samplesat differentmtop generated points These histograms have been contrasted with the expected hypothesesthat both represent identical distributions The Chi2TestX ROOT [135] routine has been used to performthis cross-check
The test has been done for signal events only Therefore the physics background contribution has beensubtracted from the data histogram Theχ2nDoF values for eachtt MC samples compared with data canbe seen in Figure 530 The results for the electron muon andcombined channel have been separatelyfitted with a parabolic function in order to obtain their minima The final values reported below agreewith the templatemtop result within their uncertainties
mtop(emicro + jets) = 1731plusmn 04 GeV
mtop(e+ jets) = 1735plusmn 07 GeV
mtop(micro + jets) = 1731plusmn 04 GeV
The aim of using this method has only been a cross-check and the systematic uncertainties have notbeen evaluated
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Figure 530 Parabolic function describing theχ2nDoF versus generatedmtop for electron muon andcombined channel
510 Conclusions of themtop measurement 137
510 Conclusions of themtop measurement
The top-quark mass has been measured using 47 fbminus1 of data collected by ATLAS during the 7 TeVLHC run of 2011
The measurement has been performed in thett rarr ℓ + jets channel (ℓ was either an electron or amuon) In order to get an enriched sample different requirements were imposed First of all the standardtt selection was applied In addition only those events with two b-tagged jets were kept Moreoverthe hadronically decayingW boson reconstruction introduced several cuts to remove most of the com-binatorial background while keeping enough statistics After this selection the physics background wasconsiderable reduced The W boson allowed for an in-situ calibration of the jet energy as well as todetermine a global jet energy scale factor
For each event themtop is evaluated with the Globalχ2 kinematics fit This method exploits the fullkinematics in the global rest frame of each top quark (including the estimation of thepνz) Finally themtop distribution was fitted using a template method In this template the correct jet combinations arecast to a lower tail exponential with resolution model probability density function The combinatorialbackground is described with a Novosibirsk distribution The physics background contribution to thett rarr ℓ + jets of the final sample is about 5
The extracted value formtop is
mtop = 17322plusmn 032 (stat)plusmn 042 (JSF)plusmn 167 (syst) GeV
where the errors are presented separately for the statistics the jet energy scale factor and systematic con-tributions Its precision is limited by the systematic uncertainties of the analysis The main contributorsare the uncertainty due to the hadronization model (081 GeV) jet energy resolution (087 GeV) and theb-tagged jet energy scale (076 GeV) The result of this analysis is compatible with the recent ATLASand CMS combination [14]
An alternative template fit where many of the parameters that describe themtop probability distributionfunction were left free was also attempted This mini-template approach could be used to detect data-MCmismatch effects blinded for the template method In addition a cross-check based on aχ2 histogramcomparison has been also performed and the obtained resultsare compatible with themtop value fromthe template method
138 5 Top-quark mass measurement with the Globalχ2
C
6Conclusions
This thesis is divided in two parts one related with the alignment of the ATLAS Inner Detector trackingsystem and other with the measurement of the top-quark massBoth topics are connected by the Globalχ2
fitting method
In order to measure the properties of the particles with highaccuracy the ID detector is composedby devices with high intrinsic resolution If by any chance the position of the modules in the detectoris known with worse precision than their intrinsic resolution this may introduce a distortion in the re-constructed trajectory of the particles or at least degradethe tracking resolution The alignment is theresponsible of determining the location of each module withhigh precision and avoiding therefore anybias in the physics results My contribution in the ID alignment has been mainly related with the develop-ing and commissioning of the Globalχ2 algorithm During the commissioning of the detector differentalignment exercises were performed for preparing the Globalχ2 algorithm the CSC exercise allowed towork under realistic detector conditions whilst the FDR exercises were used for integrating and runningthe ID alignment software within the ATLAS data taking chain In addition special studies were contin-uously done for maintaining the weak modes under control Atthe same time the ATLAS detector wascollecting million of cosmic rays which were used to align the modules with real data The alignmentwith cosmic rays provided a large residual improvement for the barrel region producing therefore a gooddetector description for the first LHC collisions Subsequently the data collected during the pilot runswas used for performing the first ID alignment with real collisions Here not only the residuals but alsophysics observable distributions were used to monitor the detector geometry and therefore obtain a moreaccurate ID alignment (specially in the end-cap region) The Inner Detector alignment achieved with thework presented in this thesis was crucial for fixing the basisof the ID alignment getting a good initial IDperformance and leading to the first ATLAS physic paper [104]
The physics analysis part of this thesis is focused on measuring the top-quark mass with the Globalχ2
method This measurement is important since the top quark isthe heaviest fundamental constituent ofthe SM and may be a handle to discover new physics phenomena BSM The analysis used the 47 fbminus1 ofdata collected by ATLAS during the 7 TeV LHC run of 2011 in order to obtain amtop measurement withreal data This measurement has been performed in thett rarr ℓ+ jets channel with twob-tagged jets in theevent This topology contains aW boson decaying hadronically which is used to determine the global jetenergy scale factor for this kind of events This factor helps to reduce the impact of the Jet Energy Scaleuncertainty in the final measurement For each event themtop is evaluated from a Globalχ2 fit whichexploits the full kinematics in the global rest frame of eachtop Finally themtop distribution has beenextracted using a template method and the obtainedmtop value is
mtop = 17322plusmn 032 (stat)plusmn 042 (JSF)plusmn 167 (syst) GeV
The total uncertainty is dominated by the systematic contribution The result of this analysis is com-patible with the recent ATLAS and CMS combination [14]
139
140 6 Conclusions
C
7Resum
El Model Estandard (SM) de la fısica de partıcules es la teoria que descriu els constituents fonamentalsde la materia i les seves interaccions Aquest model ha sigut una de les teories cientıfiques amb mesexit construıdes fins ara degut tant al seu poder descriptiu com tambe predictiu Per exemple aquestmodel permete postular lprimeexistencia dels bosonsWplusmn i Z0 i del quarktop abans de la seva confirmacioexperimental Malgrat que en general aquest model funciona extremadament be hi ha certs problemesteorics i observacions experimentals que no poden ser correctament explicats Davant dprimeaquest fet sprimehandesenvolupat extensions del SM aixı com tambe noves teories
Actualment la fısica dprimealtes energies sprimeestudia principalment mitjancant els acceleradors de partıculesEl Gran colmiddotlisionador dprimehadrons (LHC) [40] situat al CERN [41] es lprimeaccelerador mes potent que tenimavui en dia Aquesta maquina ha sigut dissenyada per fer xocar feixos de protons a una energia de 14 TeVen centre de masses En lprimeanell colmiddotlisionador hi ha instalmiddotlats quatre detectors que permeten estudiar ianalitzar tota la fısica que es produeix al LHC ATLAS [44] acutees un detector de proposit general construıtper realitzar tant mesures de precisio com recerca de nova fısica Aquest gran detector esta format perdiferents subsistemes els quals sprimeencarreguen de mesurar les propietats de les partıcules Generalmentdespres del muntatge i instalmiddotlacio del detector la localitzacio de cadascun dels seusmoduls de deteccioes coneix amb una precisio molt pitjor que la seua propia resolucio intrınseca Lprimealineament sprimeencarregadprimeobtenir la posicio i orientacio real de cadascuna drsquoaquestes estructures Un bon alineament permet unabona reconstruccio de les trajectories de les partıcules i evita un biaix dels resultats fısics Dprimeentre totesles partıcules produıdes en les colmiddotlisions del LHC el quarktop degut a les seves propietats (gran massa idesintegracio rapida) es de gran importancia en la validacio de models teorics i tambe en el descobrimentde nova fısica mes enlla del SM
71 El model estandard
El SM intenta explicar tots els fenomens fısics mitjancant un grup reduıt de partıcules i les seves inter-accions Avui en dia les partıcules elementals i com a talssense estructura interna es poden classificaren tres grups leptons quarks i bosons Els leptons i els quarks son fermions partıcules dprimeespın 12 men-tre que els bosons partıcules mediadores de les forces son partıcules dprimeespın enter Aquestes partıculesinteraccionen a traves de quatre forces fonamentals la forca electromagnetica que es la responsable demantenir els electrons lligats als atoms la forca debil que es lprimeencarregada de la desintegracio radioac-tiva dprimealguns nuclis la forca forta la qual mante els protons i neutrons en el nucli i finalment la forcagravitatoria Actualment el SM nomes descriu tres dprimeaquestes quatre forces pero hi ha noves teories queintenten explicar la unificacio de totes elles
El SM es pot escriure com una teoria gauge local basada en el grup de simetriaS U(3)C otimes S U(2)L otimes
141
142 7 Resum
U(1)Y on S U(3)C representen la interaccio fortaS U(2)L la debil i U(1)Y lrsquoelectromagnetica El la-grangia del SM descriu la mecanica i la cinematica de les partıcules fonamentals i de les seves interac-cions La inclusio dels termes de massa dels bosonsWplusmn i Z0 viola automaticament la invariancia gaugelocal Aquest problema es resol mitjancant la ruptura espontania de simetria (mecanisme de Higgs) elqual genera massa per als bosonsWplusmn i Z0 mentre que mante el foto i el gluo com partıcules de massanulmiddotla Aquest mecanisme introdueix una nova partıcula fonamental el boso de Higgs Recentmenten els experiments ATLAS i CMS del LHC sprimeha descobert una partıcula amb una massa de 126 GeV ipropietats compatibles amb les del Higgs del SM [6] Aquest descobriment es el resultat dprimeun gran esforcteoric i experimental per entendre quin es el mecanisme que dona massa a les partıcules
La majoria de les observacions experimentals realitzades fins al moment presenten un bon accord ambles prediccions del SM No obstant hi ha alguns problemes pendents com per exemple com sprimeunifiquenles forces com es resol el problema de la jerarquia que es lamateria fosca com es genera lprimeasimetriamateria-antimateria etc Una de les teories mes populars per resoldre aquests problemes es la super-simetria Aquesta teoria incorpora partıcules supersim`etriques amb propietats similars a les del modelestandard pero amb diferent espın Dprimeacord amb la versio mes comuna dprimeaquesta teoria la desintegraciodprimeuna partıcula supersimetrica produeix almenys una altrapartıcula supersimetrica en lprimeestat final i lesmes lleugeres son estables Aixı doncs en cas dprimeexistir deuria haver un espectre de superpartıcules de-tectables al LHC Totes les noves teories deuen ser validades experimentalment i es acı on el quarktopjuga un paper fonamental
Fısica del quark top
El quarktop fou descobert lprimeany 1995 en lprimeaccelerador Tevatron en Chicago (USA) El seu descobri-ment fou un gran exit per al model estandard perque confirma lprimeexistencia de la parella dprimeisospın del quarkbellesa (quarkb) En els colmiddotlisionadors hadronics el quarktop es produeix principalment a traves de lainteraccio forta i es desintegra rapidament sense hadronitzar (casi exclusivament a traves det rarr Wb)Segons el SM el quarktopes un fermio amb carrega electrica de 23 la carrega de lprimeelectro i es transformasota el grup de colorS U(3)C Durant el primer perıode de funcioament del LHC ATLAS ha recollit mesde 6 milions de parellestt Aquesta gran quantitat de dades ha servit per mesurar les propietats del quarktop amb una alta precisio (seccio eficac [15 16] carrega electrica [20] asimetria de carrega [23] espın[24] acoblaments estranys [25 26] ressonancies [29]) A mes a mes tambe sprimeha mesurat la seva massa(mtop) [14] la qual es important per ser un dels parametres fonamentals de la teoria aixı com tambe pertenir una alta sensibilitat a la fısica mes enlla del SM
La massa del quarktop depen de lprimeesquema de renormalitzacio i per tant nomes te sentit dintre dprimeunmodel teoric Aquesta no es una propietat exclusiva de la massa del quarktop sino comuna a totsels parametre del model estandard (masses i constants dprimeacoblament) En contraposicio a les massesdels leptons la definicio de massa dprimeun quark te algunes limitacions intrınseques ja que els quarks sonpartıcules amb color i no apareixen en estats asımptoticament lliures Hi ha diferents definicions de massala massa pol (definida en lprimeesquema de renormalitzacioon-shellon sprimeassumeix que la massa de la partıculacorrespon al pol del propagador) i la massarunning(massa definida en lprimeesquema de renormalitzacio demınima sostraccio (MS) on els parametres del lagrangia esdevenen dependents delprimeescala dprimeenergies a laqual es treballa) Experimentalment malgrat no estar teoricament ben definida tambe sprimeutilitza la massacinematica que correspon a la massa invariant dels productes de la desintegracio del quarktop La majoriade les analisis que utilitzen la massa cinematica empren un metode de patrons (template method) Aixıdoncs el parametremtop mesurat correspon a la massa generada en el Monte-Carlo (MC)la qual sprimeesperaque diferisca aproximadament de la massa pol en un GeV [32 33]
72 Lprimeaccelerador LHC i el detector ATLAS 143
72 Lprimeaccelerador LHC i el detector ATLAS
El LHC amb un perımetre de 27 Km i situat a 100 m sota la superfıcie del CERN es lprimeaccelerador departıcules mes gran del mon Aquest potent accelerador guia dos feixos de protons (tambe pot treballaramb ions de plom) en direccions oposades i els fa colmiddotlidir en els punts de lprimeanell on estan instalmiddotlats elsdetectors Lprimealta lluminositat de disseny del LHC (L = 1034 cmminus2 sminus1) permet estudiar processos fısicsinteressants malgrat tenir una seccio eficac menuda Per estudiar la fısica del LHC hi ha 4 grans exper-iments ATLAS CMS [45] LHCb [46] i ALICE [47] ATLAS i CMS sacuteon dos detectors de propositgeneral els quals permeten realitzar un estudi ampli de totala fısica que es produeix tant mesures deprecisio com nova fısica Lprimeexistencia de dos detector de caracterıstiques similarses necessari per com-provar i verificar els descobriments realitzats El LHCb esun espectrometre dissenyat per a estudiar lafısica del quarkb i ALICE es un detector construıt per treballar principalment amb ions de plom i estudiarles propietats del plasma de quarks i gluons
El detector de partıcules ATLAS
El detector ATLAS pesa 33 tones i te 45 m de llarg i 22 m dprimealt Esta format per diferents subdetectorsinstalmiddotlats al voltant del tub del feix En general tots presenten lamateixa estructura capes concentriquesal voltant del tub en la zona central (zona barril) i discs perpendiculars al feix en la zona de baix anglecap endavant i cap a darrere (zonaforward o backward) Aquesta estructura proporciona una coberturahermetica i facilita una reconstruccio completa de cada esdeveniments La Figura 71 mostra un dibuixesquematic de la geometria del detector ATLAS esta format per tres subdetectors cadascun dels qualsconstruıt per desenrotllar una determinada funcio
bull Detector intern (ID) es el detector responsable de la reconstruccio de les trajectories de lespartıcules la mesura del seu moment i la reconstruccio dels vertexs primaris i secundaris Aquestdetector format per detectors de silici i tubs de deriva esta envoltat per un solenoide que genera uncamp magnetic de 2 T i corba les trajectories de les partıcules carregades
bull Calorımetres son els detectors encarregats de la mesura de lprimeenergia de les partıcules El calorımetreelectromagnetic amb una geometria dprimeacordio mesura lprimeenergia dels electrons positrons i fotonsTot seguit tenim el calorımetre hadronic format per teules espurnejadores que mesuren lprimeenergiadepositada pels hadrons
bull Espectrometre de muonsaquest detector sprimeencarrega principalment de la identificacio i mesuradel moment dels muonsEs el detector mes extern dprimeATLAS i es combina amb un sistema detoroides que generen el camp magnetic necessari per corbarla trajectoria dels muons
Tambe cal comentar lprimeimportancia del sistema detrigger que sprimeencarrega dprimeidentificar i seleccionar elsesdeveniments interessants produıts en les colmiddotlisions Mitjancant tres nivells de seleccio aquest sistemaredueixen en un factor 105 el nombre dprimeesdeveniments que cal emmagatzemar
Per ultim la distribucio de dades dprimeATLAS basada en tecnologies grid ha estat dissenyada per co-brir les necessitats de la colmiddotlaboracio Basicament aquest model permet guardar accedir i analmiddotlitzarrapidament la gran quantitat de dades que genera el LHC
Gracies al bon funcionament del LHC i ATLAS els quals han treballat amb una alta eficiencia deproduccio i recolmiddotleccio sprimeha aconseguit una lluminositat integrada de 265f bminus1 en la primera etapa de
144 7 Resum
presa de dades (RunI)
Figura 71 Dibuix esquematic de la geometria del detectorATLAS
El Detector Intern
El ID es el detector mes intern del sistema de reconstruccio de traces dprimeATLAS Aquest detector ambuna geometria cilındrica al voltant del feix de 7 m de longitud i un diametre de 23 m esta compost pertres subdetectors el detector de Pıxels el detector de micro-bandes (SCT) i el detector de tubs de deriva(TRT)
El principal objectiu del detector de Pıxels es determinar el parametre dprimeimpacte de la trajectoria de lespartıcules i reconstruir els vertexs primaris i secundaris Aquest detector esta format per 1744 moduls depıxels de silici (amb una grandaria de 50micromtimes400microm) distribuıts en tres capes concentriques al voltantdel feix i tres discs perpendiculars al feix en les zones end-cap Aquest geometria produeix com a mınimtres mesures (hits) per traca La resolucio intrınseca del detector es de 10 microm en la direccio mes precisadel modul (rφ) i 115microm en la direccio perpendicular
LprimeSCT sprimeencarrega de la mesura del moment de les partıcules Els seus moduls estan formats per dosdetectors de micro-bandes (distancia entre bandes de 80microm) pegats esquena amb esquena i rotats 40 mradun respecte a lprimealtre El SCT esta format per 4088 modules instalmiddotlats en 4 capes cilındriques al voltantdel feix i nou discs perpendiculars en cada end-cap La geometria del SCT proporciona com a mınim 4hits per traca La resolucio intrınseca dprimeaquest detector es de 17microm en la direccio rφ (perpendicular a lesbandes) i de 580microm en la direccio de les bandes
El TRT sprimeencarrega de la identificacio de les partıcules i tambe interve en la mesura del moment Aquestdetector produeix en mitja 30 hits per traca Esta formatsim300000 tubs de deriva amb un diametre de 4mm i una longitud variable depenent de la zona del detector La seva resolucio intrınseca es de 130micromen la direccio perpendicular al fil del tub de deriva
73 Alineament del Detector Intern dprimeATLAS 145
73 Alineament del Detector Intern dprimeATLAS
El ID es un ingredient crucial en les analisis de fısica jaque molts del algoritmes de reconstrucciodprimeobjectes utilitzen la seva informacio (traces vertex identificacio de partıcules) Les prestacions dprime
aquest detector es poden veure compromeses per una incorrecta descripcio del camp magnetic desconei-xement del material i per suposat dprimeun alineament erroni Els desalineaments dels moduls degraden lareconstruccio de les trajectories de les partıcules cosa que afecta inevitablement als resultats de fısicaPer assolir els objectius dprimeATLAS l primealineament del ID no deu introduir una degradacio dels par`ametres deles traces en mes dprimeun 20 de la seva resolucio intrınseca Els estudis realitzats amb mostres simuladesexigeixen una resolucio de 7microm per als pıxels 12microm per al SCT (ambdos en la direccio rφ) i 170microm peral TRT No obstant hi ha escenaris mes ambiciosos que requereixen coneixer les constants dprimealineamentamb una precisio de lprimeordre del micrometre en el planol transvers del detector
Lprimealgoritme Globalχ2 sprimeha utilitzat per a alinear el sistema de silici del ID Aquestsistema consta de5832 moduls (1744 del Pıxel i 4088 del SCT) Cadascuna dprimeaquestes estructures te 6 graus de llibertattres translacions (TX TY TZ) i tres rotacions (RX RY RZ) Aixı doncs el repte de lprimealineament esdeterminarsim35000 graus de llibertat amb la precisio requerida
L prime algoritme dprimealineament Globalχ2
Els algoritmes dprimealineament utilitzen les trajectories de les partıculesper estudiar les deformacions deldetector Idealment en un detector perfectament alineatla posicio delhit deu coincidir amb la posicio dela traca extrapolada Per altra banda en un detector desalineat aquests punts son diferents La distanciaentre ambdues posicions sprimeanomena residu i esta definida com
r = (mminus e (π a)) middot u (71)
one(π a) representa la posicio de la traca extrapolada en el detector i depen dels parametres de les traces(π) i dels dprimealineament (a) m dona la posicio delhit i u es un vector unitari que indica la direccio demesura
Dintre del software dprimeATLAS sprimehan testejat diferents algoritmes dprimealineament
bull Robust [77] es un metode iteratiu que utilitza els residus calculats a les zones de solapamentAquests residus permeten correlacionar la posicio dels m`oduls dintre drsquounstaveo ring i identificarmes facilment les deformacions radials Aquest algoritmenomes permet alinear les direccions messensibles (coordenades x i y locals)
bull Localχ2 [78] i Globalχ2 [79] son algoritmes iteratius basats en la minimitzacio drsquounχ2 ElGlobalχ2 utilitza residus definits dintre de la superficie planar del detector Per altra banda laimplementacio del Localχ2 utilitza residus en tres dimensions (DOCA) Les diferencies del for-malisme matematica entre els dos algoritmes srsquoexplica mes endavant
Lprimealgoritme Globalχ2 calcula les constants dprimealineament a partir de la minimitzacio del seguentχ2
χ2 =sum
t
r (π a)T Vminus1 r (π a) (72)
on r(πa) son els residus i V la matriu de covariancies Aquesta matriu conte principalment les incerteseso erros dels hits Si no tenim en compte les correlacions entre els moduls la matriu V es diagonal Per
146 7 Resum
contra si sprimeinclou la dispersio Coulombiana (MCS) o qualsevol altre efecte que connecte diferents modulssprimeomplin els termes fora de la diagonal
El χ2 te un mınim per a la geometria real Aixı doncs per trobarla posicio correcta dels moduls esminimitza lprimeEquacio 72 respecte a les constants dprimealineament
dχ2
da= 0 minusrarr
sum
t
(
drt(π a)da
)T
Vminus1rt (π a) = 0 (73)
Els residus poden calcular-se per a un conjunt de parametres inicials (r0=r(π0a0)) i poden ser introduıtsen el formalisme del Globalχ2 mitjancant un desenvolupament en serie al voltant dprimeaquests valors
r = r(π0 a0) +
[
partrpartπ
dπda+partrparta
]
δa (74)
La clau del Globalχ2 es considerar que els parametres de les traces depenen delsparametres dprimealineamenti per tant la derivada deπ respecte aa no es nulmiddotla Aco pot ser facilment entes ja que la posicio delsmoduls (donada per les constants dprimealineament) sprimeutilitza en la reconstruccio de les trajectories i per tanten la determinacio dels parametres de les traces Degut a lprimeaproximacio lineal utilitzada el metode ne-cessitara iterar abans de convergir al resultat correcteIntroduint lprimeequacio anterior en lrsquoEquacio 73 idespres dprimealguns calculs sprimeobte la solmiddotlucio general per a les constants dprimealineament
δa = minus
sum
t
(
partrt
parta
)T
Wtpartrt
parta
minus1
sum
t
(
partrt
parta
)T
Wt rt
(75)
En una notacio mes compacta podem identificar el primer terme de la part dreta de lprimeigualtat com unamatriu simetrica (M) amb una dimensio igual al nombre de graus de llibertat que estem alineant i el segonterme com un vector amb el mateix nombre de components
M =sum
t
(
partrt
parta
)T
Wt
(
partrt
parta
)
ν =sum
t
(
partrt
parta
)T
Wtrt (76)
De manera simplificada lprimeequacio 75 es pot escriure com
Mδa + ν = 0 minusrarr δa = minusMminus1ν (77)
Per obtenir les constants dprimealineament necessitem invertir la matriuM Lprimeestructura dprimeaquesta matriudepen de lprimealgoritme dprimealineament amb el que treballem
bull Localχ2 aquest algoritme es pot considerar un cas particular del Globalχ2 on la dependenciadels parametres de les traces respecte als parametres dprimealineament es considera nulmiddotla (dπda=0 enlprimeequacio 74) Aquesta aproximacio calcula els parametres de les traces sense tenir en compte lesseves correlacions El resultat es una matriu diagonal de blocs 6times6 perque nomes els graus de llib-ertat dintre de cada estructura estan correlacionats Aquesta matriu pot diagonalitzar-se facilmentja que la majoria dels elements son zero
73 Alineament del Detector Intern dprimeATLAS 147
bull Globalχ2 aquest algoritme calcula la derivada dels parametres de les traces respecte als parametresdprimealineament Aquest fet introdueix una correlacio entre estructures i ompli els termes fora de ladiagonal A mes a mes aquesta aproximacio permet incloure restriccions en els parametres de lestraces i dprimealineament produint dprimeaquesta manera una matriu totalment poblada
La inversio de la matriuM esdeve un problema quan alineem els moduls de manera individual (sim35000graus de llibertat) La dificultat no nomes radica en lprimeemmagatzemament dprimeuna matriu enorme sino tambeen el gran nombre dprimeoperacions que han dprimeexecutar-se per trobar la solmiddotlucio de tots els graus de llibertatdel sistema Sprimehan realitzat molts estudis per determinar i millorar la tecnica dprimeinversio de la matriuEs possible obtenir la matriu inversa a traves del metode de diagonalitzacio que converteix una matriuquadrada simetrica en una matriu diagonal que conte la mateixa informacio Aixı doncs la matriu es potescriure com
M = Bminus1MdB Md = [diag(λi)] (78)
n Md es la matriu diagonal iB la matriu canvi de base Els elements de la diagonal (λi) de la matriuMd sprimeanomenen valors propis oeigenvaluesi apareixen en la diagonal ordenats de manera ascendentλ1 λ2 λN Per altra banda els vectors propis oeigenvectorsson les files de la matriu canvi de baseEstos valors i vectors propis representen els moviments delsistema en la nova base
El formalisme del Globalχ2 permet introduir termes per constrenyir els parmetres de les traces (util-itzant la posicio del feix la posicio dels vertex primaris o la reconstruccio invariant drsquoalgunes masses)com tambe els parmetres dprimealineament (utilitzant informacio mesurada en la fase dprimeinstalmiddotlacio del sis-tema de lasers del SCT) La inclusio dprimeaquests termes modifica lprimeestructura interna tant de la matriucom del vector dprimealinemanet
Weak modes
Els weak modeses defineixen com deformacions del detector que mantenen invariant elχ2 de lestraces Lprimealgoritme Globalχ2 no els pot eliminar completament ja que no poden ser detectades mitjancantlprimeanalisi dels residus Estes deformacions poden ser font dprimeerrors sistematics en la geometria del detectori comprometre el bon funcionament del ID
Aquestes deformacions poden dividir-se en dos grups
bull Moviments globals la posicio absoluta del ID dintre dprimeATLAS no ve fixada per lprimealineament ambtraces Per tal de controlar aquesta posicio necessitem incloure referencies externes al sistemaLprimeestudi dels valors i vectors propis indica quins son els moviments menys restringits del sistemai permet eliminar-los En general el sistema presenta sis moviments globals tres translacions itres rotacions Per altra banda lprimeus de diferents colmiddotleccions de traces configuracions etc potmodificareliminar aquests modes globals
bull Deformacions del detector sprimehan realitzat estudis amb mostres simulades per tal dprimeidentificaraquelles deformacions del detector que no modifiquen elχ2 i tenen un gran impacte en els resultatsfısics (Figura 44 del Capıtol 4) El Globalχ2 pot incloure restriccions en els parametres de lestraces aixı com tambe en els parametres dprimealineament per tal de dirigir lprimealgoritme cap al mınimcorrecte i evitar que apareguen aquests tipus de deformacions en la geometria final
148 7 Resum
Lprimeestrategia dprimealineament sprimeha dissenyat per eliminar elsweak modes Sprimehan desenrotllat diferentstecniques per poder controlar aquest tipus de deformacions durant la presa de dades reals A mes sprimehaestudiat que la combinacio de diferents topologies pot mitigar lprimeimpacte dprimeaquellsweak modesque no soncomuns a totes les mostres Per aixo lprimealineament del ID sprimeha realitzat utilitzant raigs cosmics i colmiddotlisionsal mateix temps
Nivells dprimealineament
Dprimeacord amb la construccio i el muntatge del detector sprimehan definit diferents nivells dprimealineament quepermeten determinar la posicio de les estructures mes grans (corregint moviments colmiddotlectius dels moduls)com tambe de les mes petites (moduls individuals) Aquests nivells son
bull Nivell 1 (L1) alinea el Pıxel sencer com una estructura i divideix el SCT en tres parts (un barril idos end-caps)
bull Nivell 2 (L2) corregeix la posicio de cada una de les capes idels discs del detector
bull Nivell 3 (L3) determina la posicio de cada modul individual
A mes dprimeaquests nivells sprimehan definit nivells intermedis que permeten corregir desalineaments in-troduıts durant la fase de construccio del detector Per exemple els pıxels es montaren en tires de13 moduls (ladders) i foren instalmiddotlats en estructures semi-cilindriques (half-shells) les quals porterior-ment foren ensamblades de dos en dos per formar les capes completes Per tant aquestes estructuresmecaniques utilitzades en la construccio del detector foren definides com nous nivells drsquoalineament isprimealinearen de manera independent Per altra banda les rodesdel SCT (rings) tambe foren alineades perseparat
Desenvolupament i validacio de lprimealgoritme Globalχ2
Previament a lprimearribada de les colmiddotlisions es realitzaren molts estudis per comprovar i validar el correctefuncionament dels algoritmes dprimealineament Alguns dels exercicis mes rellevants foren
Analisi de la matriu dprimealineamentQuan resolem lprimealineament del detector intern amb el Globalχ2 es pot utilitzar la diagonalitzacio dela matriu per identificar els moviments globals del sistema menys constrets (els quals estan associats avalors propis nuls) La grandaria dels valors propis depen de la configuracio del sistema (si sprimeutilitzenrestriccions en els parametres de les traces o dprimealineament) aixı com tambe de la topologia de les tracesutilitzades (raigs cosmics colmiddotlisions) Per tal dprimeidentificar i eliminar els modes globals de cada sis-tema sprimeanalitzaren les matrius dels escenaris dprimealineament mes utitzats alineament del detector de silicialineament del detector de silici amb la posicio del feix fixada alineament del detector de silici util-itzant la posicio del feix i el TRT en la reconstruccio de les traces i alineament de tot el detector in-tern amb la posicio del feix fixada Lprimeestudi es realitza a nivell 1 i a nivell 2 Els resultats obtingutspermeteren coneixer el nombre de moviments globals de cadascun dprimeaquests escenaris (Taula 42 delCapıtol 4) Aquests modes foren eliminats de la matriu i no computaren per a lprimeobtencio de les constantsdprimealineament evitant dprimeaquesta manera una possible deformacio en la descripciogeometrica del detectorque podria produir un biaix en els parametres de les traces
73 Alineament del Detector Intern dprimeATLAS 149
CSCLprimeexercici dprimealineament CSC (sigles del nom en anglesComputing System Commissioning) permeteper primera vegada treballar amb una geometria distorsionada del detector La geometria inicial esgenera dprimeacord amb la posicio dels moduls mesurada en la fase dprimeinstalmiddotlacio Sobre aquestes posicionssprimeinclogueren desalineaments aleatoris per a cadascun dels moduls aixı com tambe deformacions sis-tematiques (rotacio de les capes del SCT) Aquest exercici fou realment important ja que permete trebal-lar amb una geometria mes similar a la real i comprovar el comportament dels algoritmes dprimealineamentfront a deformacions aleatories i sistematiques del detector
FDREls exercicis FDR (de les sigles en angles deFull Dress Rehearsal) serviren per comprovar el correc-te funcionament de la cadena dprimeadquisicio de dades dprimeATLAS Dintre dprimeaquesta cadena el calibratge ilprimealineament del detector intern deu realitzar-se en menys de24 hores La cadena dprimealineament integradaen el software dprimeATLAS te diferents passes reconstruccio de la posicio del feix alineament dels detectorsde silici i el TRT (primer per separat i despres un respecte alprimealtre) i reconstruccio de la posicio del feixamb la nova geometria Aquestes constants foren validades amb el monitor oficial dprimeATLAS i en casde millorar la geometria inicial introduides a la base de dades per ser utilitzades en posteriors reproces-sats Els exercicis FDR es repetiren al llarg de lprimeetapa de preparacio del detector per tal de dissenyar icomprovar lprimeautomatitzacio de la cadena dprimealineament i el seu correcte funcionament
Restriccio dels moviments dels discs del detector SCTLa convergencia de lprimealgoritme Globalχ2 sprimeestudia utilitzant mostres simulades El Globalχ2 treballa ambuna geometria perfecta (no inclou cap distorsio del detector) i realitza unes quantes iteracions per analitzarla grandaria i la tendencia de les constants dprimealineament En principi les constants dprimealineament deurienser nulmiddotles ja que partim dprimeuna geometria perfectament alineada No obstant sprimeobserva una divergenciade la posicio dels discs del SCT en la direccio Z (paralmiddotlela al feix) Despres dprimealguns estudis detallatslprimeexpansio dels discs sprimeidentifica com unweak mode Per tal de controlar-la es desenvoluparen diferentstecniques
bull Restriccio relativa dels discs del SCT lprimeevolucio de les constants dprimealineament per als discs del SCTmostrava un comportament divergent molt mes pronunciat per als discs externs que interns Aixıdoncs es fixa la posicio dels discs externs respecte als interns utilitzant les distancies mesuradesdurant la instalmiddotlacio del detector i sprimealinearen nomes els discs mes proxims a la zona barril
bull SMC (de les sigles en angles deSoft Mode Cut) aquesta tecnica introdueix un factor de penalitzacioen la matriu dprimealineament que desfavoreix grans moviments dels moduls
El comportament de les constants dprimealineament fou estudiat utilitzant ambdues estrategiesEls resultatsmostraren que malgrat la reduccio dels desplacaments dels discs utilitzant la primera tecnica no obtenienles correccions correctes Aixı doncs sprimeescollı la tecnica de SMC per a fixar els graus de llibertat delsdiscs del SCT menys constrets
Alineament del detector intern amb dades reals
El detector ATLAS ha estat prenent dades des del 2008 Durantlprimeetapa de calibratge i comprovaciodel funcionament del detector es recolliren milions de raigs cosmics Aquestes dades foren utilitzades
150 7 Resum
per obtenir la geometria inicial del detector Seguidamentarribaren les primeres colmiddotlisions les qualssprimeutilitzaren per corregir la posicio dels moduls sobretot en la zona end-cap Des dprimealeshores el con-tinu funcionament del LHC ha permes recollir una gran quantitat de dades que han sigut utilitzades permillorar la descripcio geometrica del detector intern demanera continuada
Raigs cosmics
Els esdeveniments de cosmics tenen una caracterıstica molt interessant connecten la part de dalt i debaix del detector establint una bona correlacio entre ambdues regions Per contra la ilmiddotluminacio deldetector no es uniforme ja que les parts situades al voltantdeφ=90 i φ=270 estan mes poblades que lesregions situades enφ=0 i φ=180 les quals estan practicament desertes
Els cosmics recolmiddotlectats durant el 2008 i el 2009 sprimeempraren per obtenir el primer alineament del IDamb dades reals Lprimeestrategia dprimealineament utilitzada intenta corregir la majoria de les deformacions deldetector Primer sprimealinearen les grans estructures (L1) seguidament els nivells intermedis (capes discsanellsladders) i finalment la posicio de cada modul individual Deguta lprimeestadıstica nomes sprimealinearenels graus de llibertat mes sensiblesTX TY TZ i RZ Durant lprimealineament de L3 es van detectar defor-macions sistematiques dintre dprimealgunsladdersdel detector de Pıxels Concretament aquestes estructurespresentaren una forma arquejada en la direccioTX minus RZ i enTZ
La Figura 72 mostra els mapes de residus per a una de les capesdel SCT abans (esquerra) i despres(dreta) de lprimealineament Cada quadre representa un modul del SCT i el color indica el tamany dels residusen eixe modul Lprimeestudi i correccio dprimeaquestes deformacions permete obtenir un bona reconstruccio deles primeres colmiddotlisions del LHC
etaring-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
phis
tave
0
5
10
15
20
25
30
Res
(m
m)
-01
-008
-006
-004
-002
0
002
004
006
008
01Res (mm)
SCT Barrel L0 residuals Before Alignment
etaring-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
phis
tave
0
5
10
15
20
25
30
Res
(m
m)
-005
-004
-003
-002
-001
0
001
002
003
004
005Res (mm)
SCT Barrel L0 residuals After Alignment
Figura 72 Mapa de residus per a la capa mes interna del SCT abans (esquerra) i despres (dreta) delprimealineament amb raigs cosmics
Colmiddotlisions
En Novembre del 2009 arribaren les primeres colmiddotlisions del LHC La reconstruccio dprimeaquests esde-veniments mostra un alineament acceptable de la zona barril mentre que la zonaforward exhibı alguns
73 Alineament del Detector Intern dprimeATLAS 151
problemes Els desalineaments en els end-caps degut principalment a la impossibilitat dprimealinear-los ambraigs cosmics foren rapidament corregits amb les dades recolmiddotlectades durant les dos primeres setmanesUna vegada millorada lprimeeficiencia de reconstruccio dels end-caps es realitza unalineament complet deldetector (zona barril i zonaforward) Aquest exercici dprimealineament utilitza no nomes les distribucions deresidus sino tambe distribucions dprimeobservables fısics que permeteren monitoritzar la geometria del de-tector i corregirevitar lprimeaparicio deweak modes A mes sprimeimposa una restriccio en la localitzacio del feixque permete fixar la posicio del ID dintre dprimeATLAS aixı com tambe millorar la resolucio del parametredprimeimpacte transversal La Figura 73 mostra la distribucio de residus per al barril i end-cap del SCT abans(negre) i despres (roig) de lprimealineament Lprimeamplada de les distribucions dels end-caps de 70microm abans ide 17microm despres dprimealinear mostra la millora considerable de lprimealineament en aquesta zona
mm-004 -002 000 002 004
000
005
010
015
020
025 Cosmic
Collision09_09SCT residual (Barrel)
mm-020 -015 -010 -005 -000 005 010 015 020
000
005
010
015
020
025
030
035
040
045Cosmic
Collision09_09SCT residual (End-Cap)
Figura 73 Distribucio de residus del SCT per a la zona barril (esquerra) i end-cap (dreta) abans (negre)i despres (roig) de lprimealinemanet amb colmiddotlisions
En resum lprimealineament del detector intern amb els primers 7microbminus1 de colmiddotlisions corregı els desalinea-ments de la zonaforward i millora lprimealineament de la zona barril Aquest exercici permete reconstruir elsposteriors esdeveniments de manera molt mes eficient
Millores t ecniques de lprimealineament
Lprimealineament del detector Intern dprimeATLAS ha estat millorant-se contınuament Despres de lprimealineamentdel ID amb les primeres colmiddotlisions sprimehan anat desenvolupant noves tecniques per obtenir una descripciomes acurada de la geometria del detector Algunes dprimeaquestes tecniques son
bull Combinacio de cosmics i colmiddotlisions paralmiddotlelament a les colmiddotlisions sprimehan recolmiddotlectat raigs comicsAquest fet ha permes no tant sols augmentar lprimeestadıstica de les dades sino tambe treballar ambdiferents topologies reconstruıdes sota les mateixes condicions dprimeoperacio i geometria del detector
bull Estudi de les deformacions internes dels pıxels en la fase de construccio del detectors de pıxelses realitzaren estudis de qualitat de cadascun dels modulsque mostraren algunes deformacionsinternes Aquestes distorsions sprimehan introduıt en la geometria del ID i han sigut corregides perlprimealineament
152 7 Resum
bull Millora de l prime alineament del TRT sprimeha implementat elsoftwarenecessari per corregir la posiciodels fils del TRT Lprimealineament dprimeaquestes estructures en la direccio mes sensible ha permacutees corregirdeformacions sistematiques del detector
bull Alineament dels detectorRun a Run lprimealineament de cadaRunper separat permet corregir idetectar mes rapidament els canvis en la geometria del detector Sprimeha observat un canvi notableen les constants dprimealineament despres dprimealgunes incidencies en lprimeoperacio del detector com araconectar o desconectar lprimealt voltatge el sistema de refredament el camp magetic etc
bull Analmiddotlisi de la reconstruccio del moment de les partıcules la correcta reconstruccio del momentde les partıcules es molt important per a les analmiddotlisis de fısica Aixı doncs sprimeha estudiat els possi-bles biaixos drsquoaquest parametre degut a les distorsions enla geometria del detector i les tecniquesper resoldreprimels Basicament tenim dos metodes un basat en la reconstruccio de la massa invariantde partıcules conegudes (Z rarr micro+microminus) i altre basat en la comparacio de la informacio del ID i elcalorımetre (Ep) Tots dos metodes permeten corregir i validar la geometria del detector
74 Mesura de la massa del quarktop
El quarktop es la partıcula mes massiva del SM En lprimeactualitat la seva massa sprimeha mesurat amb unaalta precisio tant en Tevatron (mtop=1732plusmn09 GeV) [13] com en el LHC (mtop=1732plusmn10 GeV) [108]
En aquesta tesi sprimeha mesurat la massa del quarktop amb les colmiddotlisions del LHC a 7 TeV (lluminositatintegrada de 47f bminus1) El metode utilitzat reconstrueix completament la cinematica de lprimeesdevenimenti calcula lamtop a partir dels productes de la seva desintegracio Lprimeanalisi sprimeha realitzat en el canal deℓ + jets (ℓ = e micro) Aquest canal esta caracteritzat per la presencia dprimeun boso W que es desintegra enlepto i neutrı mentre que lprimealtre ho fa hadronicament Aixı doncs lprimeestat final presenta un lepto aıllat doslight-jets dosbminus jetsque emanen directament de la desintegracio deltop (trarrWb) i energia transversalfaltant (Emiss
T ) Una vegada sprimehan identificat i reconstruıt tots aquest objectes sprimeintrodueixen a lprimeajust delGlobalχ2 Aquest metode te un primer fit (o fit intern) que calcula elsparametres locals (pνz) i un segonfit (o fit global) que determina la massa del quarktop Finalment la distribucio de lamtop obtinguda ambels resultats del Globalχ2 es fita amb untemplate methodi dprimeaquesta manera sprimeextrau el valor de la massa
Dades reals i mostres simulades
Aquesta analisi ha utilitzat les dades de colmiddotlisions de protons a una energia de 7 TeV en centre demasses recollides per ATLAS durant lprimeany 2011
Per altra banda les mostres simulades sprimeutilitzen per validar lprimeanalisi La mostra de referencia dett sprimehagenerat amb el programa P [118] amb una massa de 1725 GeV normalitzada a una seccio eficacde 1668 pb La funcio de distribucio de partons (pdf) utilitzada en la simulacio es CT10 La cascadade partons i els processos subjacents produıts en una colmiddotlisio (underlying event) sprimehan modelitzat ambP [119] Perugia 2011C A mes a mes de la mostra de referencia sprimehan produıt altres mostres de MCamb les mateixes caracterstiques pero amb diferents masses de generacio de 165 GeV fins 180 GeV
Hi ha esdeveniments que malgrat no sertt deixen en el detector una signatura molt similar Aquestsprocessos anomenats fons fısic han sigut simulats per tal dprimeestimar la seva contribucio en la mesurafinal demtop Les mostres desingle-topsprimehan generat amb P+P PC2011C per al canals s
74 Mesura de la massa del quarktop 153
i Wt mentre que el canal t utilitza AMC [122] +P Els processos dibosonics (ZZWWZW)sprimehan produıt utilitzant H [123] Els processos de ZW associats a jets han sigut generats ambA+HJ Totes aquestes mostres inclouen multiples interaccionsper a cada encreuamentde feixos (pile-up) per tal dprimeimitar les condicions reals del detector
Seleccio estandard del quark top
Totes les analisis dprimeATLAS relacionades amb el quarktop apliquen una mateixa seleccio estandardAquesta seleccio consisteix en una serie de talls basats en la qualitat dels esdeveniments i propietats delsobjectes reconstruıts que permeten obtenir una mostra enriquida en processostt rarr ℓ + jets
bull Lprimeesdeveniment deu passar el trigger del lepto aıllat
bull Els esdeveniments deuen tenir nomes un lepto aıllat ambpT gt25 GeV
bull Es requereix un vertex amb mes de 4 traces per tal de rebutjar processos de raigs cosmics
bull Almenys 4 jets ambpT gt25 GeV i |η| lt25
bull Sprimeexigeix una bona qualitat dels jets reconstruıts Sprimeeliminen jets relacionats amb zones sorollosesdel detector o processos del feix (beam gas beam halo)
bull Es seleccionen nomes jets originats en el proces principal i no degut a efectes depile-up
bull Sprimeimposa un tall en laEmissT i la mw per reduir la contribucio del fons de multi-jets
bull Lprimeesdeveniment deu tenir almenys 1 jet identificat com ab (a partir dprimeara els jets identificats com ab sprimeanomenaran directamentb-jets)
La taula 71 resumeix lprimeestadıstica obtinguda per a la senyal i cadascun dels fonsEl factor de senyalsobre fons (SB) es de lprimeordre de 3 Els principals fons sonsingle top QCD multi-jet i Z+jets Les figures55 56 i 57 del Capıtol 5 mostren la comparacio de dades iMC dprimealguns observables importants per alcanale+ jets imicro + jets
Process e+ jets micro + jets
tt signal 17000plusmn 1900 28000plusmn 3100Single top 1399plusmn 73 2310plusmn 120WWZZWZ 469plusmn 14 747plusmn 24Z+jets 4695plusmn 91 453plusmn 12W+jets (data) 2340plusmn 450 5000plusmn 1100QCD (data) 890plusmn 450 1820plusmn 910Background 5150plusmn 730 9700plusmn 1400Signal+Background 22100plusmn 2000 37700plusmn 3400Data 21965 37700
Taula 71 Estadıstica de dades i MC despres de la selecciacuteo estadard La senyal i els fons fısics esperatscorresponen a una lluminositat integrada de 47f bminus1 La incertesa inclou els seguents errors estadısticefficiencia deb-tagging normalitzacio dett lluminositat i normalitzacio de QCD i W+jets
154 7 Resum
Cinematica dels esdevenimentstt en el canalℓ + jets
Per tal dprimeobtenir la massa del quark top en cada esdeveniment necessitem
bull Reconstruir el boso W que es desintegra hadronicament a partir dels seus jets lleugers (Wrarr qq)A mes a mes la presencia del W pot ser utilitzada per establir una relacio entre lprimeescala dprimeenergiesdels jets en dades i en MC
bull Estimar lapz del neutrı (assumint que laEmissT correspon al moment transvers del neutrı) per recon-
struir el W leptonic
bull Associar elsb-jetsa la part leptonica o hadronica de lprimeesdeveniment
Un dels reptes de lprimeanalisi es la correcta identificacio dels objectes En les mostres simulades podemaccedir a la informacio vertadera i per tant comprovar que la reconstruccio i associacio sprimeha realitzatcorrectament Quan els objectes reconstruıts no son correctament associats al seu parell vertader parlemde fons combinatorial Aixı doncs els esdeveniments de lprimeanalisi poden dividir-se segons les seves ca-racterıstiques en esdevenimentstt correctament associats (correct) esdevenimentstt on lprimeassociacio hafallat (combinatorial background) i fons fısic irreductible (physics background)
Seleccio del W hadronic
Lprimeobjectiu dprimeaquesta seccio es seleccionar dprimeentre totes les possibles combinacions el parell de jetsassociats al W hadronic La parella de jets seleccionada deu complir les seguents condicions
bull Cap dels jets deu ser unb-jet
bull El moment transvers del jet mes energetic de la parella deuser major de 40 GeV i el del segon jetmajor de 30 GeV
bull La distancia radial entre els dos jets∆R( j1 j2) lt 3
bull La massa invariant reconstruıda deu estar dintre de la finestra de masses|mj j minus MPDGW | lt 15 GeV
Per tal dprimeagilitzar lprimeanalisi i ja que la seleccio final requereix dosb-jets sprimeeliminen tambe tots aquellsesdeveniments que no compleixin aquesta condicio
Calibratge in-situ
El calibratge in-situ es realitza amb una doble finalitat seleccionar el parell de jets correcte i corregirlprimeescala dprimeenergies dels jets tant per a dades com per a MC Per a cadascundel parells de jets seleccionatscalculem el seguentχ2
χ2(α1 α2) =
(E j1(1minus α1)
σE j1
)2
+
(E j2(1minus α2)
σE j2
)2
+
mj j (α1 α2) minus MPDGW
ΓPDGW oplus σE j1 oplus σE j2
2
(79)
74 Mesura de la massa del quarktop 155
on E12 i σ12 son lprimeenergia del jet i la seva incertesaα1 i α2 son els parametres del fit m(α1 α2)representa la massa invariant del parell que testem iΓPDG
W es lprimeamplada del boso W tabulada en el PDGLprimeenergia dels jets seleccionats sprimeescala amb els factors de calibratgeα1 i α2
Si un esdeveniments te mes dprimeun parell de jets viable sprimeescull el de menysχ2 A mes a mes nomes elsesdeveniments amb unχ2 menor de 20 sprimeutilitzen per a la posterior analisi Lprimeeficiencia i la puresa de lamostra despres dprimeaquesta seleccio correspon al 14 i 54 respectivament
Per a dades reals sprimeutilitza el mateix procediment Cal notar que la contribucio dels fons de processosfısics despres de la seleccio del W hadronic es redueix considerablement (essent un 7 del total) LaFigura 74 mostra la distribucio de la massa invariant del parell de jets (mj j ) en el canale+ jets imicro + jets
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Figura 74 Massa invariant del parell de jets associat al boso W hadronic per a dades i MC en el canale+ jets (esquerra) imicro + jets (dreta)
La figura anterior mostra que la distribucio demj j obtesa amb dades i MC no pica per al mateix valorAquesta diferencia (associada a una escala dprimeenergies diferent per als jets de les dades i del MC) necessitacorregir-se per no introduir un biaix en la mesura final demtop Per tal de corregir aquesta diferencia esdefineix el seguent factorαJS F = MPDG
W M j j Els valors obtinguts poden consultar-se en la Taula 53 delCapıtol 5 Aquest factor es calcula utilitzant tota la mostra i sprimeaplica a tots els jets que intervenen en elcalcul de lamtop
Neutrı pz i EmissT
Per reconstruir el W leptonic necessitem estimar lapz del neutrı Lprimeingredient essencial es exigir que lamassa invariant del lepto i el neutrı siga la massa del bosacuteo W El desenvolupament matematic es troba enlprimeApendix K En general aquesta equacio proporciona dos solucions per a lapz i nprimehem dprimeescollir una Noobstant el 35 de les vegades lprimeequacio no te una solucio real En aquests casos es realitza un reescalat dela Emiss
T per trobar almenys una solucio real La tecnica de reescalat ha sigut validada comparant laEmissT
reconstruıda i la vertadera (informacio MC) Les distribucions de lprimeApendix K mostren que el reescalates apropiat la qual cosa permetet treballar amb tota lprimeestadıstica
156 7 Resum
Seleccio delsb-jets
En aquesta seccio sprimeexigeix que els dosb-jetsseleccionats anteriorment tinguen unpT gt30 GeV Encas contrari lprimeesdeveniment no sprimeutilitzara en lprimeanalisi
b-jet i seleccio de la pz del neutrı
Per escollir lapz del neutrı i associar elsb-jetsa la part hadronica i leptonica de lprimeesdeveniment sprimeutilitzael seguent criteri
ε = |mhadt minusmlep
t | + 10(sum
∆Rhad+sum
∆Rlep)
(710)
on mhadt i mlep
t designen la massa invariant de la part hadronica i leptonica isum
∆Rhad isum
∆Rlep descriuen ladistancia dels objectes dintre dels triplets Despres dprimeaquesta seleccio la puresa de la mostra es del 54
Algoritme Globalχ2 per a la mesura de lamtop
En lprimeactual implementacio del fit Globalχ2 els observables utilitzats exploten la informacio de lprimeesdevenimenten el centre de masses de cada quarktop
bull Cinematica dels dos cossos (trarrWb) lprimeenergia i el moment del boso W i del quarkb en el centrede masses depenen de les seves masses aixı com tambe demtop (parametre del fit) Aquestes mag-nituds es calculen en el centre de masses i es transporten al sistema de laboratori on es comparenamb les magnituds mesurades directament pel detector
bull Conservacio de moment la suma del moment dels productes de la desintegracio del quark topen el seu centre de masses deu ser nulmiddotla Aixı doncs els objectes reconstruıts en el sistema dereferencia de laboratori son traslladats al sistema en repos on es calcula la suma de moments isprimeexigeix que siga nulmiddotla
La llista de residus i les seves incerteses es poden veure en la Taula 72 Tambe es mostra la dependenciade cada residu amb el parametre local o global Per tal dprimeeliminar esdeveniments divergents o amb unamala reconstruccio sprimeaplica un tall en elχ2 (χ2 lt20) La distribucio final de la massa del quark top en elcanal combinat pot veureprimes en la Figura 75 El fons fısic sprimeha reduıt fins a unsim5 de lprimeestadıstica total
Obtencio de la massa deltop amb el metode de patrons
Com sprimeha explicat anteriorment per a cada esdeveniment que entraal fit del Globalχ2 obtenim unvalor de pz i de mtop Aquestes distribucions tenen diferents contribucions esdeveniments correctesfons combinatorial i fons fısic Utilitzant la informaciacuteo del MC es possible separar cadascuna dprimeaquestescontribucions i analitzar el seu impacte en la forma final de la distribucio
La distribucio demtop obtinguda nomes amb les combinacions correctes (Figura 520 del Capıtol 5)presenta les seguents propietats es una distribucio quasi Gaussiana amb caiguda asimetrica per la dreta iesquerra i a mes no pica en el seu valor nominal (mtop=1725 GeV) sino a un valor inferior Per descriurecorrectament les caracterıstiques dprimeaquesta distribucio sprimeha utilitzat una Gaussiana convolucionada amb
74 Mesura de la massa del quarktop 157
Taula 72 Llista de residus incerteses i dependencia ambels parametres local i globalResidual Expresion Uncertainty pνz mtop
r1 mWℓminus MPDG
W σEℓ oplus σEmissToplus ΓPDG
W
radic
r2 ErecoWhminus Etest
WhσE j1oplus σE j2
radic
r3 ErecoWlminus Etest
WlσEℓ oplus σEmiss
T
radic radic
r4 Ereco
bhminus Etest
bhσEhad
jb
radic
r5 Ereco
blminus Etest
blσElep
jb
radic radic
r6 cos(
angle(~p ⋆had ~ptop)
) ∣∣∣∣~p ⋆
j1+ ~p⋆j2 + ~p
⋆bh
∣∣∣∣ σE j1
oplus σE j2oplus σEhad
jb
radic
r7 cos(
angle(~p ⋆lep ~ptop)
) ∣∣∣∣~p ⋆ℓ+ ~p⋆ν + ~p
⋆bℓ
∣∣∣∣ σEℓ oplus σEmiss
Toplus σElep
jb
radic radic
]2[GeVctopm100 150 200 250 300 350 400
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Single TopW+jetsWWZZWZZ+jetsQCDuncertainty
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Figura 75 Distribucio del parametremtop obtingut amb el Globalχ2 per al canal combinat Les dadesreals es comparen amb el MC
una distribucio exponencial amb caiguda negativa Per altra banda la contribucio del fons combinatorial(distribucio roja de la Figura 519) esta ben descrita peruna funcio Novosibirsk Aixı doncs la distribuciofinal sprimeobte de la suma de ambdues funcions i te 7 parametres
bull m0 es la massa de lprimeobjecte a mesurar
bull λ caiguda negativa del pic de la distribucio
bull σ resolucio experimental enm0
bull microbkg valor mes probable de la distribucio de fons combinatorial
158 7 Resum
bull σbkg amplada de la distribucio de fons combinatorial
bull Λbkg caiguda de la distribucio de fons combinatorial
bull ǫ fraccio dprimeesdeveniments correctes
El metode de patrons utilitza les mostres de MC generades per a diferents masses del quarktopLprimeanalisis es repeteix per a cada una dprimeaquestes mostres i la distribucio final es fita amb la funcioan-teriorment comentada En cada fitm0 es fixa a la massa de generacio i sprimeextrauen la resta de parametresEsta tecnica permet calcular la dependencia de cadascundel parametres en funcio de la massa de gen-eracio La figura 521 del capıtol 5 mostra les distribucions dels parametres per al canal combinat Podemexpressar cada parametre de la distribucio com una combinacio lineal dem0 per exemple el parametreλes pot escriure com
λ(m) = λ1725 + λs∆m (711)
Dprimeigual manera es parametritzen tota la resta Aixı doncs quan obtenim la distribucio de dades finals lacomparem amb el model donat per la parametritzacio i obtenim la massa del quarktop La distribucio 76mostra la distribucio demtop fitada La funcio blava representa el fons fısic la roja elfons combinatoriali la verda les combinacions bones El valor obtes demtop amb dades reals es
mtop = 17322plusmn 032 (stat)plusmn 042 (JSF) GeV
on lprimeerror correspon a la suma de lprimeerror estadıstic i lprimeerror associat a lprimeescala dprimeenergies del jets (JSF)
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Figura 76 Distribiucio del parametremtop obtingut amb el Globalχ2 amb dades La distribucio mostrael resultat del fit per al canal combinat
75 Conclusions 159
Errors sistematics
Els errors sistematics sprimehan avaluat seguint les prescripcions oficials del grup deltop Cada una de lesvariacions sistematiques sprimeaplica a la mostra i es repeteix lprimeanalisi la preseleccio el calcul del JSF i el fitGlobalχ2 La distribucio final de MC sprimeutilitza per generar 500 pseudo-experiments Utilitzant el metodede patrons sprimeobtenen 500 mesures demtop amb les quals sprimeompli un histograma La distribucio resultantsprimeajusta a una Gaussiana i la mitja sprimeagafa com a valormtop de la mostra modificada Generalment lprimeerrorsistematic es calcula com la diferencia entre el valor de la mostra de referencia i la mostra on sprimeha aplicatla variacio La taula 73 mostra els resultats dels errors sistematic avaluats en aquesta analisi aixı comtambe la combinacio total
Taula 73 Errors sistematics demtop obtesos amb el metode de patronsFont dprimeerror Error (GeV)
Metode de Calibracio 017Generador de MC 017Model dprimehadronitzacio 081Underlying event 009Color reconection 024Radiacio dprimeestat inicial i final 005pdf 007Fons fısic irreductible 003Escala dprimeenergies dels jets (JES) 059Escala dprimeenergies delsb-jets (bJES) 076Resolucio de lprimeenergia dels jets 087Eficiencia de reconstruccio de jets 009Efficiencia deb-tagging 054Escala dprimeenergies dels leptons 005Energia transversa faltant 002Pile-up 002
Incertesa sistematica final 167
75 Conclusions
Aquesta tesi esta dividida en dos parts la primera relacionada amb lprimealineament del detector interndprimeATLAS i la segona amb la mesura de la massa del quarktop Tots dos temes estan connectats perlprimealgoritme Globalχ2
Per mesurar les propietats de les partıcules amb una alta precisio el ID esta format per unitats dedeteccio amb resolucions intrınseques molt menudes Normalment la localitzacio dprimeaquests dispositiuses coneix amb una resolucio pitjor que la propia resoluciacuteo intrınseca i aco pot produir una distorsio de latrajectoria de les partıcules Lprimealineament es el responsable de la determinacio de la posicio i orientaciode cada modul amb la precisio requerida Durant lprimeetapa dprimeinstalmiddotlacio i comprovacio del detector serealitzaren diferents exercicis per tal de preparar el sistema dprimealineament per a lprimearribada de les dades realslprimeexercici CSC permete treballar sota condicions reals del detector el FDR sprimeutilitza per automatitzar lacadena dprimealineament i integrar-la dintre de la cadena de presa de dades dprimeATLAS A mes a mes sprimeha
160 7 Resum
desenvolupat un treball continu per a lprimeestudi i correccio delsweak modesdel detector En paralmiddotlel a totsaquests exercicis ATLAS estigue prenent dades de raigs cosmics els qual sprimeutilitzaren per determinar lageometria real del detector Finalment arribaren les primeres collisions i amb elles es torna a alinear eldetector En aquest exercise dprimealineament no nomes es monitoritzaren les distribucions de residus sinotambe les distribucions dprimeobservables fısics per tal dprimeevitar i eliminar els possiblesweak modes Acopermete obtenir un alineament molt mes precıs del detector (millora notable en els end-caps) El treballpresentat en aquesta tesi servı per fixar les bases de lprimealineament del detector intern obtenir una descripcioacurada de la seva geometria i contribuir de manera significativa als primeres articles de fısica publicatsper ATLAS
La segona part de la tesi descriu lprimeanalisi realitzada per mesurar la massa del quarktop El quarktop esuna de les partıcules fonamentals de la materia i la seva gran massa li confereix propietats importants en lafısica mes enlla del model estandard Per tant es important obtenir una mesura precisa de la seva massaAquesta analmiddotlisi ha utilitzat 47 f bminus1 de dades de colmiddotlisions a 7 TeV en centre de masses recolmiddotlectadesper ATLAS en el 2011 Lprimeanalisi sprimeha realitzat en el canal deℓ + jetsamb esdeveniments que tenen dosb-jets Esta topologia conte un W que es desintegra hadronicament i sprimeutilitza per obtenir un factor decorreccio de lprimeescala dprimeenergies dels jets (JSF) Amb el metode dprimeajust Globalχ2 sprimeobte una mesura demtop per a cada esdeveniment Finalment la distribucio demtop es fita utilitzant el metode de patrons isrsquoobte el resultat final
mtop = 17322plusmn 032 (stat)plusmn 042 (JSF)plusmn 167 (syst) GeV
La incertesa de la mesura esta dominada per la contribuciode lprimeerror sistematic Els resultats dprimeaquestaanalisi son compatibles en els recents resultats dprimeATLAS i CMS
Appendices
161
A
ALepton and Quark masses
The SM is a renormalizable field theory meaning that definitepredictions for observables can be madebeyond the tree level The predictions are made collecting all possible loop diagrams up to a certain levelalthough unfortunately many of these higher contributionsare often ultraviolet divergent1 The regu-larization method [136] which is a purely mathematical procedure is used to treat the divergent termsOnce the divergent integrals have been made manageable therenormalization process [136] subtractstheir divergent parts The way the divergences are treated affects the computation of the finite part of theparameters of the theory the couplings and the masses Therefore any statement about the quantitiesmust be made within a theoretical framework
For an observable particle such as theeminus the definition of its physical mass corresponds to the positionof the pole in the propagator The computation of its mass needs to include the self-interaction termswhich takes into account the contribution of the photon loopto the electron propagator Some of thesediagrams are shown in the Figure A1
Figure A1 Self-energy contributions to the electron propagator at one and two loops Thep andk arethe four-momentum vector of the electron and photon respectively
The propagator of the electronS(p) = 1pminusm will have a new contribution due to the higher order loop
correctionsΣ(p)
iSprime(p) =i
pminusmminus Σ(p)(A1)
The pole of the propagator is notm anymore but rather the loop corrected mass mrsquo=m+Σ(p) TheΣ(p) is the self-energy contribution to the electron mass Its calculation at one loop is logarithmicallydivergent so a regularization and a renormalization scheme have to be introduced There are differentrenormalization methods depending on how the divergences are subtracted out One of the common ap-proaches is the on-shell scheme which assumes that the renormalized mass is the pole of the propagatorAnother used technique is the modified minimal subtraction scheme (MS) Here the renormalized pa-rameters are energy dependent and commonly called running parameters The running mass is not thepole mass but reflects the dynamics contribution of the mass to a given process The relation between the
1Ultraviolet divergences in the loop corrections usually stem from the high momentum limit of the loop integral
163
164 A Lepton and Quark masses
pole mass and the running mass can be calculated as a perturbative series of the coupling constantsαQ2
Table A1 shows the electron and top-quark masses calculated with both methods on-shell scheme(Mlq) andMS renormalization scheme at different energies (mc (c-quark mass)mW andmtop) The elec-tron exhibits small differences between both masses (O(10minus2) MeV) The effects of the renormalitzationin QED are almost negligible due to the small value ofαe [4] Detailed calculations have shown that afterfour loop corrections the value of the mass converges and higher orders do not have any additional con-tribution On the other hand the quarks exhibit a different behaviour since they are always confined intohadrons The QCD coupling constant (αs) increases when decreasing the energy so the quark pole massis affected by infrared divergences3 giving a non negligible contribution for higher order corrections Thetop-quark mass in different schemes can differ up to 10 GeV and that is way the mass of the quarks hasto be always given within a certain renormalization scheme
Energy Scale (micro) me(micro) (MeV) mtop(micro) (GeV)
mc(mc) 0495536319plusmn0000000043 3848+228204
MW 0486845675plusmn0000000042 1738plusmn30mtop(mtop) 0485289396plusmn0000000042 1629plusmn28
Mlq 0510998918plusmn0000000044 1725plusmn27
Table A1 Running electron and top-quark masses at different energiesmicro = mc micro = MW andmicro = mtop
and their pole massesMlq The values shown in the table are taken from [137] where the masses for allleptons and quarks are reported
2αQ symbol refers QCD coupling (αs) as well as QED coupling (αe)3Infrared divergencies are generated by massless particlesinvolved in the loop quantum corrections at low momentum
A
B
Globalχ2 fit with a track param-eter constraint
Theχ2 equation including a track parameter constraint looks as follows
χ2 =sum
t
rt(π a)TVminus1rt(π a) + R(π)TSminus1R(π) (B1)
The second term which only depends on the track parametersrepresents the track constraint TheR(π)vector acts as the track parameter residuals and S is a kind ofcovariance matrix that keeps the toler-ances As always the goal is the minimization of the totalχ2 with respect to the alignment parametersTherefore
dχ2
da= 0 minusrarr
sum
t
(
drt(π a)da
)T
Vminus1rt(π a) +sum
t
(
dRt(π)da
)T
Sminus1Rt(π) = 0 (B2)
Track fit
In order to find the solution for the track parameters the minimization of theχ2 with respect to thetrack parameters needs to be calculated
dχ2
dπ= 0 minusrarr
(
drt(π a)dπ
)T
Vminus1rt(π a) +
(
dRt(π)dπ
)T
Sminus1Rt(π) = 0 (B3)
The track-hit residuals are computed for an initial set of alignment parameters (π0) which enter in theGlobalχ2 expression via Taylor expansion (as in Equation 48) The second derivatives are consideredequal to zero Inserting these expanded residuals in Equation B3 and identifyingEt = partrtpartπ |π=π0 andZt = partRtpartπ |π=π0 one obtains the track parameter corrections
δπ = minus(ETt Vminus1Et + ZT
t Sminus1Zt)minus1(ETt Vminus1rt (π0 a) + ZT
t Sminus1Rt(π0)) (B4)
Alignment parameters fit
Once the track parameters have been calculated (π = π0 + δπ) the alignment parameters must be com-puted by minimizing theχ2 (Equation B2) The key of the Globalχ2 lies in the total residual derivatives
165
166 B Globalχ2 fit with a track parameter constraint
since the dependence of the track parameters with respect tothe alignment parameters is considered notnull Therefore thedπda has to be evaluated
dπda= minus(ET
t Vminus1Et + ZTt Sminus1Zt)minus1(ET
t Vminus1
partr(π0a)parta
drt(π0 a)da
+ ZTt Sminus1
0dRt(π0)
da) (B5)
Including B5 in B2 one obtains
sum
t
(
partrt(π0 a)parta
minus Et(ETt Vminus1Et + ZT
t Sminus1Zt)minus1ETt Vminus1partrt(π0 a)
parta
)T
Vminus1rt(π0 a)
+sum
t
(
minusZt(ETt Vminus1Et + ZT
t Sminus1Zt)minus1ETt Vminus1partrt(π0 a)
parta
)T
Sminus1Rt (π0 a) = 0
(B6)
In order to simplify the equation one can definedXprime = (ETt Vminus1Et + ZT
t Sminus1Zt)minus1ETt Vminus1 Therefore
sum
t
(
partrt(π0 a)parta
)T
[ I minus EtXprime]TVminus1rt (π0 a) minus
sum
t
(
partrt(π0 a)parta
)T
(ZtXprime)TSminus1Rt(π0) = 0 (B7)
Now calculating the residuals for an initial set of alignment parameters (a0) using again a Taylorexpansion (r = r0 +
partrpartaδa) the expression looks as follows
Mprime︷ ︸︸ ︷
sum
t
(
partrt(π0 a)parta
)T
[ I minus EtXprime]TVminus1
(
partrt(π0 a)parta
)
δa +
νprime
︷ ︸︸ ︷
sum
t
(
partrt(π0 a)parta
)T
[ I minus EtXprime]TVminus1rt(π0 a)
minussum
t
(
partrt(π0 a)parta
)T
(ZtXprime)TSminus1Rt (π0)
︸ ︷︷ ︸
w
= 0
(B8)
The impact of the track parameter constraint in the final alignment corrections is clearly seen The bigmatrix Mprime includes a new termXprime which is built as a function of the covariance matrix V and thepartialderivatives of both residual vectors (rt andRt) with respect to the track parameters The big vectorν
prime
is modified by the same term Finally a new vectorw appears exclusively due to the introduction of theconstraint term
In a more compact notation the final solution can be written as
Mprimeδa+ νprime + w = 0 minusrarr δa = minusMprime(νprime + w) (B9)
A
CCSC detector geometry
The Computing System Commissioning (CSC) provided the optimal framework to test the ATLASphysics calibration and alignment algorithms with a realistic (distorted) detector geometry Concretelyfor the ID this geometry included misalignments of different sub-systems as expected from the partsassembly accuracy (as-builtgeometry) different amounts of ID material and different distorted magneticfield configurations [95]
The ID CSC geometry was generated at different levels (L1 L2 and L3) in order to mimic the realdetector misalignments observed during the construction of the detector components Generally thesedisplacements were computed in the global reference frameexcept for the L3 where the local referenceframe was used (Section 31) In addition to these misalignments the CSC geometry also contains somesystematic deformations a curl distortion was included byrotating the SCT barrel layers and a kind oftelescope effect was introduced due to the SCT layers translations in the beam direction These detectordistortions affect the track parameters of the reconstructed particles leading to systematic biases
Level 1
Table C1 shows the size of the misalignments applied for thePixel and SCT sub-detectors at L1
Level 2
The misalignments applied at L2 are displayed in Table C2 For the Pixel discs the misalignmentswere generated as follows from a flat distribution of width of [-150+150]microm for the X and Y displace-ments and [-200+200] microm in the Z direction and the rotations around the axis (α β andγ) from a flatdistribution of width [-1+1] mrad
Level 3
The L3 misalignments have been applied for each Pixel and SCTmodule The misalignments havebeen generated using flat distributions with their widths defined by the numbers quoted in Table C3
167
168 C CSC detector geometry
System TX (mm) TY (mm) TZ (mm) α (mrad) β (mrad) γ (mrad)Pixel Detector +060 +105 +115 -010 +025 +065
SCT ECC -190 +200 -310 -010 +005 +040SCT Barrel +070 +120 +130 +010 +005 +080SCT ECA +210 -080 +180 -025 0 -050
Table C1 L1 as built positions for the Pixel and SCT detectors
System LayerDisc TX (mm) TY (mm) TZ (mm) α (mrad) β (mrad) γ (mrad)Pixel Barrel L0 +0020 +0010 0 0 0 +06
L1 -0030 +0030 0 0 0 +05L2 -0020 +0030 0 0 0 +04
SCT Barrel L0 0 0 0 0 0 -10L1 +0050 +0040 0 0 0 +09L2 +0070 +0080 0 0 0 +08L3 +0100 +0090 0 0 0 +07
SCT ECA D0 +0050 +0040 0 0 0 -01D1 +0010 -0080 0 0 0 0D3 -0050 +0020 0 0 0 01D4 -0080 +0060 0 0 0 02D5 +0040 +0040 0 0 0 03D6 -0050 +0030 0 0 0 04D7 -0030 -0020 0 0 0 05D8 +0060 +0030 0 0 0 06D9 +0080 -0050 0 0 0 07
SCT ECC D0 +0050 -0050 0 0 0 +08D1 0 +0080 0 0 0 0D3 +0020 +0010 0 0 0 +01D4 +0040 -0080 0 0 0 -08D5 0 +0030 0 0 0 +03D6 +0010 +0030 0 0 0 -04D7 0 -0060 0 0 0 +04D8 +0030 +0030 0 0 0 +06D9 +0040 +0050 0 0 0 -07
Table C2 L2 as built positions for the layers and discs of the Pixel and SCT detectors
Module Type TX (mm) TY (mm) TZ (mm) α (mrad) β (mrad) γ (mrad)Pixel Barrel 0030 0030 0050 0001 0001 0001
Pixel End-cap 0030 0030 0050 0001 0001 0001SCT Barrel 0150 0150 0150 0001 0001 0001
SCT end-cap 0100 0100 0150 0001 0001 0001
Table C3 L3 as built positions for the modules of the Pixel and SCT detectors
A
DMultimuon sample
One of the goals of the multimuon sample was to commission thecalibration and alignment algorithmsThis sample consists insim 105 simulated events with the following properties
bull Each event contains ten particles which properties are given below
bull Half of the sample is composed by positive charged particlesand the other half by negative chargedparticles
bull All tracks are generated to come from the same vertex which has been simulated using a Gaussianfunction centred at zero and a width of
radic2times15microm in the transverse plane and
radic2times56 mm in the
longitudinal plane
bull The transverse momentum of the tracks ranges from 2 GeV to 50 GeV
bull Theφ presents a uniform distributions in the range of [0minus 2π]
bull Theη has a uniform distributions in the range of [minus27+27]
Some of the characteristic distributions for the multimuonsample reconstructed with a perfect knowl-edge of the detector geometry (CSC geometry Appendix C) areshown in this appendix
Number of silicon hits
Figure D1 shows the number of reconstructed hits per track for the Pixel (left) and SCT (right) detec-tors The hits per track mean values aresim3 andsim8 for the Pixel and SCT detectors respectively Thesenumbers agree with the expected ones since each track produced at the beam spot usually crosses threePixel layers and four SCT layers
Hit maps
The muon tracks have been generated to be uniformly distributed in the detector without any preferreddirection Figure D2 shows the hit maps for the four SCT layers Each module is identified by its ringand sector position The Z axis indicates the number of reconstructed hits per module (the exact numberis written on each module)
169
170 D Multimuon sample
PIX hits0 2 4 6 8 10 12 14 16
Tra
cks
0
100
200
300
400
500
600
310times
Multimuonsmean = 330
Number of PIX hits
SCT hits0 2 4 6 8 10 12 14 16
Tra
cks
0
100
200
300
400
500310times
Multimuonsmean = 832
Number of SCT hits
Figure D1 Number of reconstructed Pixel (left) and SCT (right) hits
Figure D2 Hit maps for the SCT layers The numbers of the layers are ordered for inside to outside ofthe SCT detector
171
Track parameters
The track parameter distributions can be used to check the correct track reconstruction Any deviationfrom their expected shapes could point out the presence of detector misalignments Figure D3 displaysthe impact transverse parameter (d0) (left) and the longitudinal impact parameter (z0) (right) Both dis-tributions present a Gaussian shape with a resolution of 229 microm and 793 mm ford0 andz0 respectively
(mm)0d-015 -01 -005 0 005 01 015
0
2
4
6
8
10
12
310times 0Reconstructed d
(mm)0z-400 -200 0 200 400
0
20
40
60
80
100
120
140
310times 0Reconstructed z
Figure D3 Left reconstructedd0 distribution Right reconstructedz0 distribution
Figure D4 shows the polar angle (θ0) (left) and the pseudorapidity (η1) (right) Due to the detectoracceptance theθ0 covers a region between [016 298] rad and according to this theη range goes from[minus25+25]
(rad)0θ00 05 10 15 20 25 300
10
20
30
40
50
310times 0θReconstructed
η-3 -2 -1 0 1 2 3
Tra
cks
0
2
4
6
8
10
12310times
ηRec track
Figure D4 Left reconstructedθ0 distribution Right reconstructedη distribution
Finally Figure D5 shows the reconstructed azimutal angle(φ0) (left) and the transverse momentumdistribution multiplied by the charge of each particle (q middot pT) (right) Theφ0 presents a flat behaviour
1The pseudorapidity is defined asη = minusln tan(θ02)
172 D Multimuon sample
between [0 2π] Theq middot pT distribution exhibits the same quantity of positive and negative muon tracksas expected
(rad)0
φ-3 -2 -1 0 1 2 3
0
2
4
6
8
10
12
14
16
310times0
φReconstructed
(GeV)T
ptimesq-60 -40 -20 0 20 40 60
Tra
cks
0
2
4
6
8
10
310times T ptimesReconstructed q
Figure D5 Left reconstructedφ0 distribution Right reconstructedq middot pT distribution
Vertex
The primary vertex profiles for the transverse and longitudinal planes can be seen in Figure D6 Theirposition and resolution agree with the simulated values
Figure D6 Generated primary vertex distribution for the multimuon sample
A
ECosmic rays samples
The cosmic rays natural source of real data were extensively used during the detector commissioningin order to improve the alignment calibration and track reconstruction algorithms
The cosmic ray sample is basically composed of muons that cross the entire detector According totheir nature the simulation of the cosmic muons passing though ATLAS is done by running a generatorwhich provides muons at ground level and posteriorly they are propagated within the rock [91]
Some of the characteristic distributions for the cosmic raysample are shown in this appendix Thesample used to produce these distributions consists insim100 k simulated events filtered for the inner-most ID volume with the magnetic fields switched on The perfect CSC geometry has been used in thereconstruction
Number of hits
Figure E1 shows the number of reconstructed hits per track for the Pixel (left) and SCT (right) detec-tors A track-hit requirement in the number of SCT hits has been imposed in order to improve the cosmictrack reconstruction (NSCT gt 10) This requirement selects tracks that pass at least through three layersof the SCT Therefore the number of Pixel hits per track can be zero Actually the most probable valueof the reconstructed hits per track for the Pixel detector is0 as only few tracks cross the Pixel detectorvolume For the SCT the most probable value is 16 which corresponds to the tracks crossing the fourSCT layers
Hit maps
The cosmic ray tracks are not equally along the detector but there are privileged regions Figure E2shows the hitmaps for the four SCT layers where the non-uniformity illumination can be seen The upperand bottom parts of the detector corresponding toφ=90 andφ=270 respectively are more populatedsince the cosmic particles come from the surface In addition one can also notice that the number of hitsis also lower at largeη regions due to the difficult reconstruction of the cosmic rays in the end-caps Eachmodule is identified by its ring and sector position The Z axis measures the number of reconstructed hitsper module (the exact number is written on each module)
173
174 E Cosmic rays samples
PIX hits0 2 4 6 8 10 12 14
Tra
cks
0
5
10
15
20
25
30
35
310times
Cosmic Rays
mean = 120
Number of PIX hits
SCT hits0 5 10 15 20 25
Tra
cks
0
2
4
6
8
10
12
310times
Cosmic Rays
mean = 1509
Number of SCT hits
Figure E1 Number of reconstructed Pixel (left) and SCT (right) hits
Figure E2 Hit maps for the SCT layers The numbers of the layers are ordered for inside to outside ofthe detector
175
Track parameters
Figure E3 displays the impact transverse parameter (d0) (left) and the longitudinal impact parameter(z0) (right) Both parameters present flat distributions due tothe flux distribution of the cosmic rays troughthe detector The shape of thed0 can be understood since the generated sample was filtered to cross theinnermost ID volume The range of thez0 distribution is mainly limited by the length of the SCT barreldetector (sim850 mm)
(mm)0d-600 -400 -200 0 200 400 6000
200
400
600
800
1000
1200
1400
1600
1800
20000Reconstructed d
(mm)0z-1500 -1000 -500 0 500 1000 1500
200
400
600
800
1000
0Reconstructed z
Figure E3 Left reconstructedd0 distribution Right reconstructedz0 distribution
Figure E4 shows the polar angle (θ0) (left) and the pseudorapidity (η) (right) The two peaks presentin both distributions correspond to the position of the cavern shafts and reflect the fact that particles couldenter into the ATLAS cavern through the access of shafts moreeasily than through the rock
(rad)0θ00 05 10 15 20 25 300
1000
2000
3000
4000
50000θReconstructed
η-3 -2 -1 0 1 2 3
Tra
cks
0
500
1000
1500
2000
2500
3000
3500
4000
ηRec track
Figure E4 Left reconstructedθ distribution Right reconstructedη distribution
Figure E5 displays the reconstructed azimutal angle (φ0) distribution (left) and the transverse momen-tum distribution multiplied by the charge of each particle (q middot pT) (right) Theφ0 presents only one peakat -π2 since the cosmic rays comes from the surface Theq middot pT distribution exhibits amicro+microminus asymmetry
176 E Cosmic rays samples
as expected since this ratio has been measured by other experiments [4] Nevertheless this asymmetry ishigher in the low momentum bins due to the toroid deflectingmicrominus coming from the shafts away from theID
(rad)0
φ-3 -2 -1 0 1 2 3
0
1000
2000
3000
4000
5000
6000
70000
φReconstructed
(GeV)T
ptimesq-60 -40 -20 0 20 40 60
Tra
cks
0
200
400
600
800
1000
1200
T ptimesReconstructed q
Figure E5 Left reconstructedφ0 distribution Right reconstructedq middot pT distribution
A
FTop data and MC samples
This appendix summarizes the data and the MC samples used to perform the top-quark mass measure-ment presented in Chapter 5
Data samples
The top-quark mass analysis has been done with the LHC data collected during 2011 at center of massenergy of 7 TeV The used data amount to an integrate luminosity of 47 fbminus1 The official data files havebeen grouped according to the different data taking periods
Electron data
usermolesDataContainerdata11_7TeVperiodBDphysics_EgammamergeNTUP_TOPELp937v1usermolesDataContainerdata11_7TeVperiodEHphysics_EgammamergeNTUP_TOPELp937v1usermolesDataContainerdata11_7TeVperiodIphysics_EgammamergeNTUP_TOPELp937v1usermolesDataContainerdata11_7TeVperiodJphysics_EgammamergeNTUP_TOPELp937v1usermolesDataContainerdata11_7TeVperiodKphysics_EgammamergeNTUP_TOPELp937v1usermolesDataContainerdata11_7TeVperiodLMphysics_EgammamergeNTUP_TOPELp937v1
Muon data
usermolesDataContainerdata11_7TeVperiodBDphysics_MuonsmergeNTUP_TOPMUp937v1usermolesDataContainerdata11_7TeVperiodEHphysics_MuonsmergeNTUP_TOPMUp937v1usermolesDataContainerdata11_7TeVperiodIphysics_MuonsmergeNTUP_TOPMUp937v1usermolesDataContainerdata11_7TeVperiodJphysics_MuonsmergeNTUP_TOPMUp937v1usermolesDataContainerdata11_7TeVperiodKphysics_MuonsmergeNTUP_TOPMUp937v1usermolesDataContainerdata11_7TeVperiodLMphysics_MuonsmergeNTUP_TOPMUp937v1
tt signal MC samples
The baselinett sample has been produced with full mc11c simulation atmtop=1725 GeV with a statis-tics of 10 M of events It has been generated with P with CT10 pdf The parton shower andunderlying event has been modelled using P with the Perugia 2011C tune The dataset name corre-sponds to
mc11_7TeV117050TTbar_PowHeg_Pythia_P2011CmergeNTUP_TOPe1377_s1372_s1370_r3108_r3109_p937
177
178 F Top data and MC samples
Additional tt samples have been produced with different top-quark masses ranging from 165 GeV until180 GeV All those samples have been also generated with PH+P with Perugia P2011C tuneThe statistics is about 5 M of events per sample These ones can be identified as
mc11_7TeV117836TTbar_MT1650_PowHeg_Pythia_P2011CmergeNTUP_TOPe1736_s1372_s1370_r3108_r3109_p937mc11_7TeV117838TTbar_MT1675_PowHeg_Pythia_P2011CmergeNTUP_TOPe1736_s1372_s1370_r3108_r3109_p937mc11_7TeV117840TTbar_MT1700_PowHeg_Pythia_P2011CmergeNTUP_TOPe1736_s1372_s1370_r3108_r3109_p937mc11_7TeV117842TTbar_MT1750_PowHeg_Pythia_P2011CmergeNTUP_TOPe1736_s1372_s1370_r3108_r3109_p937mc11_7TeV117844TTbar_MT1775_PowHeg_Pythia_P2011CmergeNTUP_TOPe1736_s1372_s1370_r3108_r3109_p937mc11_7TeV117846TTbar_MT1800_PowHeg_Pythia_P2011CmergeNTUP_TOPe1736_s1372_s1370_r3108_r3109_p937
Background MC samples
Different SM physics backgrounds have been simulated to estimate their contribution in the finalmtopmeasurement
Single top
The single top samples have been generated using PH+P with Perugia P2011C tune for s-channel and Wt production while the t-channel has used A with P P2011C tune They areidentified as
mc11_7TeV110101AcerMCPythia_P2011CCTEQ6L1_singletop_tchan_leptmergeNTUP_TOPe1682_a131_s1353_a145_r2993_p937mc11_7TeV110119st_schan_Powheg_Pythia_P2011CmergeNTUP_TOPe1778_s1372_s1370_r3108_r3109_p937mc11_7TeV110140st_Wtchan_incl_DR_PowHeg_Pythia_P2011CmergeNTUP_TOPe1778_s1372_s1370_r3108_r3109_p937
The single top mass variation samples have been produced using AFII mc11c and themtop rangingfrom 165 GeV until 180 GeV The corresponding identifiers arethe following
ntuple_mc11_7TeV110123st_schan_PowHeg_Pythia_P2011C_mt_165mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV110125st_schan_PowHeg_Pythia_P2011C_mt_167p5mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV110127st_schan_PowHeg_Pythia_P2011C_mt_170mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV110129st_schan_PowHeg_Pythia_P2011C_mt_175mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV110131st_schan_PowHeg_Pythia_P2011C_mt_177p5mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV110133st_schan_PowHeg_Pythia_P2011C_mt_180mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937mc11_7TeV110113AcerMCPythia_P2011CCTEQ6L1_singletop_tchan_lept_mt165GeVmergeNTUP_TOPe1682_a131_s1353_a145_r2993_p937mc11_7TeV110114AcerMCPythia_P2011CCTEQ6L1_singletop_tchan_lept_mt167p5GeVmergeNTUP_TOPe1682_a131_s1353_a145_r2993_p937mc11_7TeV110115AcerMCPythia_P2011CCTEQ6L1_singletop_tchan_lept_mt170GeVmergeNTUP_TOPe1682_a131_s1353_a145_r2993_p937mc11_7TeV110116AcerMCPythia_P2011CCTEQ6L1_singletop_tchan_lept_mt175GeVmergeNTUP_TOPe1682_a131_s1353_a145_r2993_p937mc11_7TeV110117AcerMCPythia_P2011CCTEQ6L1_singletop_tchan_lept_mt177p5GeVmergeNTUP_TOPe1682_a131_s1353_a145_r2993_p937mc11_7TeV110118AcerMCPythia_P2011CCTEQ6L1_singletop_tchan_lept_mt180GeVmergeNTUP_TOPe1682_a131_s1353_a145_r2993_p937mc11_7TeV110124st_Wtchan_incl_DR_Powheg_Pythia_P2011C_mt_165mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937mc11_7TeV110126st_Wtchan_incl_DR_Powheg_Pythia_P2011C_mt_167p5mergeNTUP_TOPe1778_a131_s1353_
179
a145_r2993_p937mc11_7TeV110128st_Wtchan_incl_DR_Powheg_Pythia_P2011C_mt_170mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937mc11_7TeV110130st_Wtchan_incl_DR_Powheg_Pythia_P2011C_mt_175mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937mc11_7TeV110132st_Wtchan_incl_DR_Powheg_Pythia_P2011C_mt_177p5mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937mc11_7TeV110134st_Wtchan_incl_DR_Powheg_Pythia_P2011C_mt_180mergeNTUP_TOPe1778_a131_s1353_a145_r2993_p937
Diboson
The diboson processes (ZZWWZW) are produced at LO with lowest multiplicity final state usingH standalone
mc11_7TeV105985WW_HerwigmergeNTUP_TOPe825_s1310_s1300_r3043_r2993_p937mc11_7TeV105986ZZ_HerwigmergeNTUP_TOPe825_s1310_s1300_r3043_r2993_p937mc11_7TeV105987WZ_HerwigmergeNTUP_TOPe825_s1310_s1300_r3043_r2993_p937
Z+jets
The Z boson production in association with jets is simulatedusing A generator interfaced withHJIMMY
mc11_7TeV107650AlpgenJimmyZeeNp0_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107651AlpgenJimmyZeeNp1_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107652AlpgenJimmyZeeNp2_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107653AlpgenJimmyZeeNp3_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107654AlpgenJimmyZeeNp4_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107655AlpgenJimmyZeeNp5_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107660AlpgenJimmyZmumuNp0_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107661AlpgenJimmyZmumuNp1_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107662AlpgenJimmyZmumuNp2_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107663AlpgenJimmyZmumuNp3_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107664AlpgenJimmyZmumuNp4_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107664AlpgenJimmyZmumuNp4_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107665AlpgenJimmyZmumuNp5_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107670AlpgenJimmyZtautauNp0_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107671AlpgenJimmyZtautauNp1_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107672AlpgenJimmyZtautauNp2_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107673AlpgenJimmyZtautauNp3_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107674AlpgenJimmyZtautauNp4_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107675AlpgenJimmyZtautauNp5_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV109300AlpgenJimmyZeebbNp0_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109301AlpgenJimmyZeebbNp1_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109302AlpgenJimmyZeebbNp2_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109303AlpgenJimmyZeebbNp3_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109305AlpgenJimmyZmumubbNp0_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109306AlpgenJimmyZmumubbNp1_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109307AlpgenJimmyZmumubbNp2_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109308AlpgenJimmyZmumubbNp3_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109310AlpgenJimmyZtautaubbNp0_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109311AlpgenJimmyZtautaubbNp1_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109312AlpgenJimmyZtautaubbNp2_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV109313AlpgenJimmyZtautaubbNp3_nofiltermergeNTUP_TOPe835_s1310_s1300_r3043_r2993_p937mc11_7TeV116250AlpgenJimmyZeeNp0_Mll10to40_pt20mergeNTUP_TOPe959_s1310_s1300_r3043_r2993_p937mc11_7TeV116251AlpgenJimmyZeeNp1_Mll10to40_pt20mergeNTUP_TOPe959_s1310_s1300_r3043_r2993_p937mc11_7TeV116252AlpgenJimmyZeeNp2_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937mc11_7TeV116253AlpgenJimmyZeeNp3_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937mc11_7TeV116254AlpgenJimmyZeeNp4_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937mc11_7TeV116255AlpgenJimmyZeeNp5_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937mc11_7TeV116260AlpgenJimmyZmumuNp0_Mll10to40_pt20mergeNTUP_TOPe959_s1310_s1300_r3043_r2993_p937mc11_7TeV116261AlpgenJimmyZmumuNp1_Mll10to40_pt20mergeNTUP_TOPe959_s1310_s1300_r3043_r2993_p937mc11_7TeV116262AlpgenJimmyZmumuNp2_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937mc11_7TeV116263AlpgenJimmyZmumuNp3_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937mc11_7TeV116264AlpgenJimmyZmumuNp4_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937mc11_7TeV116265AlpgenJimmyZmumuNp5_Mll10to40_pt20mergeNTUP_TOPe944_s1310_s1300_r3043_r2993_p937
180 F Top data and MC samples
W+jets
The W boson production in association with jets is simulatedusing A generator interfaced withHJIMMY
mc11_7TeV107280AlpgenJimmyWbbFullNp0_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV107281AlpgenJimmyWbbFullNp1_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV107282AlpgenJimmyWbbFullNp2_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV107283AlpgenJimmyWbbFullNp3_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117284AlpgenWccFullNp0_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117285AlpgenWccFullNp1_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117286AlpgenWccFullNp2_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117287AlpgenWccFullNp3_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117293AlpgenWcNp0_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117294AlpgenWcNp1_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117295AlpgenWcNp2_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117296AlpgenWcNp3_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV117297AlpgenWcNp4_pt20mergeNTUP_TOPe887_s1310_s1300_r3043_r2993_p937mc11_7TeV107680AlpgenJimmyWenuNp0_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107681AlpgenJimmyWenuNp1_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107682AlpgenJimmyWenuNp2_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107683AlpgenJimmyWenuNp3_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107684AlpgenJimmyWenuNp4_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107685AlpgenJimmyWenuNp5_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107690AlpgenJimmyWmunuNp0_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107691AlpgenJimmyWmunuNp1_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107692AlpgenJimmyWmunuNp2_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107693AlpgenJimmyWmunuNp3_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107694AlpgenJimmyWmunuNp4_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107695AlpgenJimmyWmunuNp5_pt20mergeNTUP_TOPe825_s1299_s1300_r3043_r2993_p937mc11_7TeV107700AlpgenJimmyWtaunuNp0_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107701AlpgenJimmyWtaunuNp1_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107702AlpgenJimmyWtaunuNp2_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107703AlpgenJimmyWtaunuNp3_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107704AlpgenJimmyWtaunuNp4_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937mc11_7TeV107705AlpgenJimmyWtaunuNp5_pt20mergeNTUP_TOPe835_s1299_s1300_r3043_r2993_p937
QCD multijets
The QCD multijet background has been estimated running the matrix method over real data The filesused are those summarized earlier in the section ofData Samples
Systematic MC samples
Usually the systematic uncertainties are evaluated varying plusmn 1 standard deviation the parameters thataffect the measurement Many of them can be evaluated applying the variation directly over the baselinett sample Nevertheless there are systematic variations that can not be introduced at ntuple level andspecific MC samples have to be generated These ones are explained here
Signal MC generator
PH and MCNLO generator programs have been used to evaluate thesystematic uncertainty Bothsamples have been generated with AFII mc11b atmtop=1725 GeV In order to evaluate the generatorcontribution alone both samples have performed the hadronization using H
mc11_7TeV105860TTbar_PowHeg_JimmymergeNTUP_TOPe1198_a131_s1353_a139_r2900_p937mc11_7TeV105200T1_McAtNlo_JimmymergeNTUP_TOPe835_a131_s1353_a139_r2900_p937
Hadronization
181
This systematic is evaluated using samples with the same generator (PH) and different hadronisationmodels It compares AFII mc11b P with P2011C tune and H
mc11_7TeV117050TTbar_PowHeg_Pythia_P2011CmergeNTUP_TOPe1377_a131_s1353_a139_r2900_p937mc11_7TeV105860TTbar_PowHeg_JimmymergeNTUP_TOPe1198_a131_s1353_a139_r2900_p937
Underlying Event
Comparison of the AFII mc11c samples generated with PH+P with different settings for theparameters affecting the multiple parton interaction (MPI)
ntuple_mc11_7TeV117428TTbar_PowHeg_Pythia_P2011mergeNTUP_TOPe1683_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV117429TTbar_PowHeg_Pythia_P2011mpiHimergeNTUP_TOPe1683_a131_s1353_a145_r2993_p937
Color Reconnection
Comparison of AFII mc11c samples generated with PH+P P2011C with different tunes af-fecting color reconnection
ntuple_mc11_7TeV117428TTbar_PowHeg_Pythia_P2011mergeNTUP_TOPe1683_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV117430TTbar_PowHeg_Pythia_P2011noCRmergeNTUP_TOPe1683_a131_s1353_a145_r2993_p937
Initial and Final QCD state radiation
Both samples were generated with AMC but differ in the amount of initial and final state radiation(more or less radiation)
ntuple_mc11_7TeV117862AcerMCttbar_Perugia2011C_MorePSmergeNTUP_TOPe1449_a131_s1353_a145_r2993_p937ntuple_mc11_7TeV117863AcerMCttbar_Perugia2011C_LessPSmergeNTUP_TOPe1449_a131_s1353_a145_r2993_p937
Proton PDF
The defaulttt signal has been generated with CT10 PDF In addition the NNPDF23 and the MSTW2008have been considered to evaluate the systematic uncertainty A problem in the ntuple generation producedempty PDF variables In order to fix it the PDF variables werestored separately in the the following ntu-ple
userdtapowhegp4105860ttbar_7TeVTXTmc11_v1PDFv8
182 F Top data and MC samples
A
GTop reconstruction packages
The collision data and MC samples used to perform the top-quark mass analysis have been recon-structed following the recommendation provided by the Top Reconstruction Group The prescriptions forthe analysis performed with the ATLAS 2011 collision data are described inhttpstwikicernchtwikibinviewauthAtlasProtectedTopReconstructionGroupRecommendations_for_
2011_rel_17
The software packages used for reconstructing the different objects involved in the analysis are the fol-lowings
MuonsatlasoffPhysicsAnalysisTopPhysTopPhysUtilsTopMuonSFUtilstagsTopMuonSFUtils-00-00-15atlasoffPhysicsAnalysisMuonIDMuonIDAnalysisMuonEfficiencyCorrectionstagsMuonEfficiencyCorrections-01-01-00atlasoffPhysicsAnalysisMuonIDMuonIDAnalysisMuonMomentumCorrectionstagsMuonMomentumCorrections-00-05-03
ElectronsatlasoffPhysicsAnalysisTopPhysTopPhysUtilsTopElectronSFUtilstagsTopElectronSFUtils-00-00-18atlasoffReconstructionegammaegammaAnalysisegammaAnalysisUtilstagsegammaAnalysisUtils-00-02-81atlasoffReconstructionegammaegammaEventtagsegammaEvent-03-06-19
JetsatlasperfCombPerfFlavorTagJetTagAlgorithmsMV1TaggertagsMV1Tagger-00-00-01atlasoffReconstructionJetApplyJetCalibrationtagsApplyJetCalibration-00-01-03atlasperfCombPerfJetETMissJetCalibrationToolsApplyJetResolutionSmearingtagsApplyJetResolutionSmearing-00-00-03atlasoffPhysicsAnalysisTopPhysTopPhysUtilsTopJetUtilstagsTopJetUtils-00-00-07atlasoffReconstructionJetJetUncertaintiestagsJetUncertainties-00-05-07ReconstructionJetJetResolutiontagsJetResolution-01-00-00atlasoffPhysicsAnalysisJetTaggingJetTagPerformanceCalibrationCalibrationDataInterfacetagsCalibrationDataInter-face-00-01-02atlasoffPhysicsAnalysisTopPhysTopPhysUtilsJetEffiProvidertagsJetEffiProvider-00-00-04atlasoffPhysicsAnalysisTopPhysMultiJesInputFilestagsMultiJesInputFiles-00-00-01
Missing ET
atlasoffReconstructionMissingETUtilitytagsMissingETUtility-01-00-09
183
184 G Top reconstruction packages
Event WeightingatlasoffPhysicsAnalysisTopPhysFakesMacrostagsFakesMacros-00-00-32atlasoffPhysicsAnalysisAnalysisCommonPileupReweightingtagsPileupReweighting-00-00-17atlasoffPhysicsAnalysisTopPhysTopPhysUtilsWjetsCorrectionstagsWjetsCorrections-00-00-08
Event QualityatlasoffDataQualityGoodRunsListstagsGoodRunsLists-00-00-98
The correct implementation of these packages has been validated against the rdquoevent challengerdquo pagesin which the analysers confront their results and compare them with the reference ones The numbers ob-tained by the analysers should agree with the reference oneswithin certain tolerances These tolerancesvary depending on the sample from less than 1 fortt signal until 20 for QCD background
The systematic uncertainties have been evaluated following the Top Group Systematic prescriptionsreported inhttpstwikicernchtwikibinviewauthAtlasProtectedTopSystematicUncertainties2011
A
HSelection of the hadronic W bo-son
In order to select the jet pair associated to the hadronically decaying W boson some requirements wereimposed (Section 551) The values for these cuts were selected taking into account the efficiency andthe purity of the sample at each stage These quantities weredefined as follow
efficiency= events passing the cut
events satisfying thett rarr ℓ + jets preselection
purity = jet pairs with correct matching of the truth hadronicWrarr qq decay
events passing the cut
As commented in Section 551 exactly twob-tagged jets were required in the analysis providing aninitial efficiency ofsim43 and a purity ofsim31 After that each of the applied cuts was studied within arange of possible values The selection of a specific value was motivated by obtaining a larger rejectionof the combinatorial background while retaining enough statistics to not compromise the analysis Nev-ertheless in some cuts as the transverse momentum of the jets also other effects related with the JESuncertainty were considered for choosing the value The cuts were applied consecutively
Figures H1 H2 H3 and H4 display the distributions of the observables related with the cuts afterapplying the previous ones and before evaluating them These figures show the contributions of the goodcombinations (black) and combinatorial background (red)
Tables H1 H2 H3 H4 and H5 summarize the efficiency and the purity for each cut Notice that theefficiency is calculated always with respect to the events that satisfy the standard top pre-selection Theselected values are marked in gray
The figures found at the end of this analysis were 14 and 54 for efficiency and purity respectivelyMost of the statistics was rejected with the requirement of exactly twob-tagged jets and the mass windowof the jet pair candidate
185
186 H Selection of the hadronic W boson
Table H1 Cut in thepT of the leading light jet
Channel e+jets micro+jetspT (GeV) Efficiency () Purity () Efficiency () Purity ()
25 432 312 431 31330 428 313 427 31435 418 316 416 31740 401 318 400 319
Table H2 Cut in thepT of the second light jet
Channel e+jets micro+jetspT (GeV) Efficiency () Purity () Efficiency () Purity ()
25 401 318 400 31930 352 310 352 31335 302 296 302 29940 253 280 253 282
Table H3 Cut in the∆Rof the jet pair candidate
Channel e+jets micro+jets∆R Efficiency () Purity () Efficiency () Purity ()31 336 325 336 32730 328 331 328 33429 315 341 315 34428 300 350 300 354
Table H4 Cut in the invariant mass of the jet pair candidate
Channel e+jets micro+jetsmj j (GeV) Efficiency () Purity () Efficiency () Purity ()
25 210 487 212 48820 192 511 193 51415 166 536 167 53810 128 558 129 557
187
Table H5 Cut in theχ2
Channel e+jets micro+jetsχ2 Efficiency () Purity () Efficiency () Purity ()40 160 540 161 54130 153 541 154 54320 141 543 141 54510 112 546 113 547
[GeV]leadTP
0 20 40 60 80 100 120 140 160 180 2000
2000
4000
6000
8000
10000
12000 PowHeg+Pythiae+jetsrarrtt
Correct
Comb Back
Correct
Comb Back
[GeV]leadTP
0 20 40 60 80 100 120 140 160 180 2000
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000
PowHeg+Pythia+jetsmicrorarrtt
Correct
Comb Back
Correct
Comb Back
Figure H1pT of the leading jet of the pair for thee+ jets(left) and themicro + jets (right) channel
[GeV]secTP
0 20 40 60 80 100 120 140 160 180 2000
5000
10000
15000
20000
25000
30000
35000
PowHeg+Pythiae+jetsrarrtt
Correct
Comb Back
Correct
Comb Back
[GeV]secTP
0 20 40 60 80 100 120 140 160 180 2000
10000
20000
30000
40000
50000
60000
PowHeg+Pythia+jetsmicrorarrtt
Correct
Comb Back
Correct
Comb Back
Figure H2 pT of the second jet fro thee+ jets(left) andmicro + jets(right) channel
188 H Selection of the hadronic W boson
R∆0 1 2 3 4 5 6 7
0
1000
2000
3000
4000
5000
6000 PowHeg+Pythiae+jetsrarrtt
Correct
Comb Back
Correct
Comb Back
R∆0 1 2 3 4 5 6 7
0
2000
4000
6000
8000
10000 PowHeg+Pythia+jetsmicrorarrtt
Correct
Comb Back
Correct
Comb Back
Figure H3∆R between the light jets for thee+ jets(left) andmicro + jets (right) channel
[GeV]jjm50 60 70 80 90 100 110
500
1000
1500
2000
2500
3000 PowHeg+Pythiae+jetsrarrtt
Correct
Comb Back
Correct
Comb Back
[GeV]jjm50 60 70 80 90 100 110
500
1000
1500
2000
2500
3000
3500
4000
4500
5000PowHeg+Pythia
+jetsmicrorarrtt
Correct
Comb Back
Correct
Comb Back
Figure H4 Invariant mass of the jet pair candidate for thee+ jets(left) andmicro + jets(right) channel
A
IIn-situ calibration with thehadronic W
The in-situ calibration corrections (α1 α2) have been calculated for all events passing the cuts in Sec-tion 551 and their final distributions are shown in Figure 58 Here these distributions are plotted againin Figure I1 but presented separately for correct combinations (green) and combinatorial background(red)
1α09 095 1 105 11
Ent
ries
00
1
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
PowHeg+Pythia P2011C
e+jetsrarrtt
CorrectComb BackgroundCorrectComb Background
2α09 095 1 105 11
Ent
ries
00
1
0
1000
2000
3000
4000
5000
6000PowHeg+Pythia P2011C
e+jetsrarrtt
CorrectComb BackgroundCorrectComb Background
1α09 095 1 105 11
Ent
ries
00
1
0
2000
4000
6000
8000
10000
12000
14000
PowHeg+Pythia P2011C
+jetsmicrorarrtt
CorrectComb BackgroundCorrectComb Background
2α09 095 1 105 11
Ent
ries
00
1
0
2000
4000
6000
8000
10000PowHeg+Pythia P2011C
+jetsmicrorarrtt
CorrectComb BackgroundCorrectComb Background
Figure I1tt rarr ℓ+ jetsMC correction factorsα1 (left) andα2 (right) obtained from the in-situ calibrationfit of the hadronically decayingW for the e+jets channel (upper row) andmicro+jets channel (bottom row)
The fitted mass of the hadronicW candidate is also displayed separately for the correct and combi-natorial background events in Figure I2 Themj j distributions are shown under two conditions with(right) and without (left) in-situ calibration factors applied The impact of the calibration is clearly seen
189
190 I In-situ calibration with the hadronic W
as the correspondingmj j distributions becomes narrower The combinatorial background exhibits broaderdistributions than the correct combinations
[GeV] jjrecom
50 60 70 80 90 100 110
Ent
ries
2 G
eV
0
002
004
006
008
01
012
014
PowHeg+Pythia P2011C
e+jetsrarrtt
Correct
Comb Background
Correct
Comb Background
[GeV] jjfittedm
50 60 70 80 90 100 110
Ent
ries
2 G
eV
0
002
004
006
008
01
012
014
016
PowHeg+Pythia P2011C
e+jetsrarrtt
Correct
Comb Background
Correct
Comb Background
[GeV] jjrecom
50 60 70 80 90 100 110
Ent
ries
2 G
eV
0
002
004
006
008
01
012 PowHeg+Pythia P2011C
+jetsmicrorarrtt
Correct
Comb Background
Correct
Comb Background
[GeV] jjfittedm
50 60 70 80 90 100 110
Ent
ries
2 G
eV
0
002
004
006
008
01
012
014
016
PowHeg+Pythia P2011C
+jetsmicrorarrtt
Correct
Comb Background
Correct
Comb Background
Figure I2 MC study of the invariant mass of the jets associated to the hadronically decayingW in thett rarr e+ jets channel (upper row) andtt rarr micro + jets channel (bottom row) Left with the reconstructedjets before the in-situ calibration Right with the jets after the in-situ calibration
A
J
Hadronic W boson mass for deter-mining the jet energy scale factor
Figure 510 presents the computedmj j in data andtt rarr ℓ + jets MC It shows a bias in the MCcompared with data The observed mismatch is attributed to adifferent jet energy calibration betweenboth This unbalance must be corrected for the proper use of the template method Otherwise a bias inthemtop could be introduced Themj j is a good reference as it should be independent of themtop andcan be used to extract a robust jet energy scale factor
Hence a linearity test of themj j was performed using different MC samples with varying themtopgenerated value For each sample themj j mean value (micro) was extracted by fitting the distribution withthe following model
bull a Gaussian shape for the correct jet-pairs
bull a Novosibirsk distribution to shape the combinatorial background contribution
bull the fraction of signal and background is taken from the MC
The independence and robustness of themj j was studied under two conditions
bull from those distributions constructed with the reconstructed jets (Figure J1)
bull from those distributions constructed with the jets once their energy have been corrected (Figure511 in Section 551)
The results are presented in Figure J1 They prove that thisobservable is robust and independent ofthe top-quark mass Therefore one can average all the mass points to extract amW mass in MC with allthe available statistics When thatmW mass is confronted withMPDG
W a small deviation is found The ratio
αMCJES = mf itted
W MPDGW is presented in Table 53 in section 551
This methodology needs to extract theαdataJES from the fitted mass value (mf itted
W ) in real data (Figure 510)It must be said that the fitting of the real data distributions(which also contains correct and combinatorialbackground combinations plus the physics background) is improved by relating some parameters follow-ing the same ratios as in the MC fit (that is the means and the sigmas of the correct and combinatorialbackground as they are independent ofmtop) Figure J2 shows the relation between these parametersThe fraction of signal and combinatorial background was taken to be the average of the 1minus ǫ 1 versusdifferent mass points fit These values correspond tosim55 for e+jets andmicro+jets channels
1ǫ is the fraction of correct combinations
191
192 J Hadronic W boson mass for determining the jet energy scalefactor
[GeV]generatedtopm
155 160 165 170 175 180 185
[GeV
]re
coW
m
80
805
81
815
82
825
83
ndof = 07772χ
Avg = (81611 +- 0041)
PowHeg+Pythia P2011C
e+jetsrarrtt
[GeV]generatedtopm
155 160 165 170 175 180 185
[GeV
]re
coW
m
80
805
81
815
82
825
83
ndof = 02382χ
Avg = (81800 +- 0029)
PowHeg+Pythia P2011C
+jetsmicrorarrtt
Figure J1 Invariant mass of the reconstructed hadronically decaying W jet pair candidate versusmgeneratedtop
for e+ jets(left) andmicro + jets(right) channels
[GeV]generatedtopm
155 160 165 170 175 180 185
fitte
dsi
gnal
microfit
ted
bkg
micro
094
096
098
1
102
104
106
ndof = 15042χAvg = (0990 +- 0001)
PowHeg+Pythia P2011C
e+jetsrarrtt
[GeV]generatedtopm
155 160 165 170 175 180 185
fitte
dsi
gnal
σfit
ted
bkg
σ
08
09
1
11
12
13
14
15
16
17
18
ndof = 03692χAvg = (1191 +- 0008)
PowHeg+Pythia P2011C
e+jetsrarrtt
[GeV]generatedtopm
155 160 165 170 175 180 185
fitte
dsi
gnal
microfit
ted
bkg
micro
094
096
098
1
102
104
106
ndof = 27052χAvg = (0990 +- 0001)
PowHeg+Pythia P2011C
+jetsmicrorarrtt
[GeV]generatedtopm
155 160 165 170 175 180 185
fitte
dsi
gnal
σfit
ted
bkg
σ
08
09
1
11
12
13
14
15
16
17
18
ndof = 44992χAvg = (1200 +- 0004)
PowHeg+Pythia P2011C
+jetsmicrorarrtt
Figure J2 Left ratio between the mean of the combinatorial background and the mean of the correctcombinations (micro f itted
bkg microf ittedsignal) Right ratio between the sigma of the combinatorial background and the
sigma of the correct combinations (σf ittedbkg σ
f ittedsignal) The results are shown for thee+jets (upper row) and
micro+jets (bottom row) channels
A
KDetermination of neutrinorsquos pz
The reconstruction of the leptonicaly decayingW is difficult because theν escapes undetected TheWrarr ℓν decay leads toEmiss
T in the event which here is attributed in full to the neutrinopT On the otherhand the longitudinal component of theν momentum (pz) has to be inferred from the energy-momentumconservation The method used here is the same as in [138]
Wrarr ℓν minusrarr pW = pℓ + pν
(
pW)2=
(
pℓ + pν)2minusrarr M2
W = m2ℓ + 2(Eℓ pℓ) middot (Eν pν) +m2
ν (K1)
In what follows the tiny neutrino mass is neglected (mν asymp 0) Also the assumption is made thatpνT = Emiss
T thus the neutrino flies along theEmissT direction Basic relations are then
pνx = EmissT cosφEmiss
Tand pνy = Emiss
T sinφEmissT
Eν =
radic
EmissT + (pνz)2
Therefore the Equation K1 can be written as follows
M2W = m2
ℓ + 2Eℓ
radic
EmissT + (pνz)2 minus 2
(
pℓxpνx + pℓypℓy + pℓzpνz)
where all the terms are known exceptpνz which is going to be computed solving the equation Forconvenience one can write it down as a quadratic equation where (mℓ
T)2 = E2ℓminus (pℓz)
2 is the leptontransverse mass
A(pνz)2 + Bpνz +C = 0 minusrarr
A = (mℓT)2
B = pℓz(
m2ℓminus M2
W minus 2(pℓxpνx + pℓypνy))
C = E2ℓ (E
missT )2 minus 1
4
(
M2W minusm2
ℓ + 2(pℓxpνx + pℓypνy))2
Thuspνz has two possible solutions
pνz = minuspℓz
(
m2ℓ minus M2
W minus 2(pℓxpνx + pℓypνy))
2(mℓT)2
plusmnEℓ
radic[(
M2W minusm2
ℓ+ 2(pℓxpνx + pℓypνy)
)2minus 4(Emiss
T )2(mℓT)2
]
2(mℓT)2
(K2)
Of the two pνz solutions only one did materialized in the event The eventanalysis tries to distinguishwhich one is physical and which only mathematical
Figure K1 shows the graphical representation of the twopνz solutions for different events The redfunction describes the quadratic difference of the computedMW with Equation K1 andMPDG
W as a func-tion of thepνz The two minima marked with black lines correspond to thepνz solutions (remember that
193
194 K Determination of neutrinorsquospz
the pνzused was chosen according to the criteria given in Section 554) The blue line indicates the truthvalue and the green line corresponds to the computed one after the Globalχ2 fit Therefore the figureon the left displays an event with a correctpνz determination while figure on the right shows a wrongpνzassociation
[GeV]νz
p-200 -150 -100 -50 0 50 100 150 2000
100
200
300
400
500
600
700
800
900
1000
PowHeg+Pythia P2011C
Event Number 370057
[GeV]νz
p-400 -300 -200 -100 0 100 200 300 4000
100
200
300
400
500
600
700
800
900
1000
PowHeg+Pythia P2011C
Event Number 361450
Figure K1 Quadratic difference between the computedMW andMPDGW ((MW(pνz)minusMPDG
W )2) as a functionof the pνz Left Event with goodpνz selection since the final solution (green line) agrees with the truthvalue (blue line) Right Event with wrongpνz selection
These solutions rely on the assumption that the neutrino is the only contributor toEmissT which is not
always the case Moreover under certain circumstances (detector resolution particle misidentificationetc) the radicand of Equation K2 is found to be negative and in principle no solution is available In orderto find a possible solution one must rescale theEmiss
T in such a way that the radicand becomes null and atleast onepνz is found Therefore one has to recomputeEmiss
T value with the prescription of keeping thesame directionφEmiss
Tprime = φEmiss
T Of courseEmiss
Tprime is the solution of the following quadratic equation
[(
M2W minusm2
ℓ + 2(pℓxEmissTprime cosφEmiss
T+ pℓyE
missTprime sinφEmiss
T))2 minus 4(Emiss
Tprime)2(mℓ
T)2]
= 0
which again has two solutions
EmissTprime =
(
m2ℓminusm2
W
) [
minus(
pℓx cosφEmissT+ pℓy sinφEmiss
T
)
plusmn (mℓT)2
]
2[
(mℓT)2 minus
(
pℓx cosφEmissT+ pℓy sinφEmiss
T
)] (K3)
but only the positive solution is retained
K1 EmissT when no pνz solution is found
As mentioned above about 35 of the events have a negative value for the radicand of Equation K2That would mean that thepνz would become complex
On one hand the charged lepton is usually very well reconstructed On the other hand the neutrinofour-momentum is inferred from the reconstructed1 Emiss
T In this way problems in thepνz calculationpoint to a defectiveEmiss
T determination
1Of course there is no such a thing like the reconstructedEmissT This is an abuse of language to simplify the notation The
computation of theEmissT is explained in Section 33
K1 EmissT when nopνz solution is found 195
Apart form the mathematical argument given above in order to check that theEmissT needs effectively a
rescaling is by comparing the reconstructedEmissT with the true neutrino properties (which are accessible
in the MC) Figure K2 presents that comparison As one can see there are good reasons to rescale theEmiss
T because the reconstructed one overestimates thepνT On the other hand theEmissT rescaling seems to
work quite accurately as shown in Figure 513
trueνT
pmissTE
0 05 1 15 2 25 3
Ent
ries
01
0
0
500
1000
1500
2000
2500
3000
3500
PowHeg+Pythia P2011C
e+jetsrarrtt
RescaledTrueTE RecoTrueTE RescaledTrueTE RecoTrueTE
[GeV] trueνT
p0 20 40 60 80 100 120 140 160 180 200
[GeV
] m
iss
T E
0
20
40
60
80
100
120
140
160
180
200
0
20
40
60
80
100
120
140
160
180
200
PowHeg+Pythia P2011C
e+jetsrarrtt
Figure K2 Evaluation of the rawEmissT for those events with initially complex solution forpνz Left
comparison of the raw reconstructedEmissT pν true
T (red histogram) with the rescaled one (white histogram)Right scatter plot of the raw reconstructedEmiss
T vs pν true
T Both plots show how the raw reconstructedEmiss
T is over estimated (EmissT pν true
T above 1 in the left plot and above the diagonal in the right plot)
The performance of theEmissT in ATLAS is reported in [131] where the biggest contributorsto the
distortion of theW transverse mass inWrarr ℓν decays are reported
196 K Determination of neutrinorsquospz
A
L
Globalχ2 formalism for the top-quark mass measurement
In the Globalχ2 formalism the residuals vectorr depend on the local and global variables of the fitr = r(tw) wheret is the set of global parameters of the fit (which will be related with the top quarkproperties) andw is the set of local parameters of the fit (in its turn is relatedwith the leptonically decayingW) Therefore one can build theχ2 which has to be minimized with respect to thet parameters
χ2 = rT(tw)Vminus1r(tw) minusrarr dχ2
dt= 0 (L1)
whereV is the covariance matrix of the residuals The minimizationcondition gives
dχ2
dt=
(
drdt
)T
Vminus1r
T
+
[
rTVminus1
(
drdt
)]
= 2
(
drdt
)T
Vminus1r
T
= 0 minusrarr(
drdt
)T
Vminus1r = 0 (L2)
The minimization condition allows to compute the corrections (δt) to the initial top fit parameters (t0)The minimum of theχ2 occurs for the following set of global and local parameterst = t0 + δt andw = w0 + δw The residuals at the minimum will change according to
t = t0 + δtw = w0 + δw
minusrarr r = r0 +
(
partrpartw
)
δw +(
partrpartt
)
δt
Inserting the above expresion into Eq L2 and keeping up to the first order derivatives one obtains(
drdt
)T
Vminus1
[
r0 +
(
partrpartw
)
δw +(
partrpartt
)
δt]
= 0
(
drdt
)T
Vminus1r0 +
(
drdt
)T
Vminus1
(
partrpartw
)
δw +
(
drdt
)T
Vminus1
(
partrpartt
)
δt = 0 (L3)
Local parameters fit
Theδw correction is first determined in the fit of the local parameters (or inner fit) One has to expressagain the minimization condition of theχ2 Only this time it is computed just with respect to thewparameters set
partχ2
partw= 0 minusrarr
(
partrpartw
)T
Vminus1r = 0 minusrarr(
partrpartw
)T
Vminus1r0 +
(
partrpartw
)T
Vminus1
(
partrpartw
)
δw = 0
197
198 L Globalχ2 formalism for the top-quark mass measurement
δw = minus
(
partrpartw
)T
Vminus1
(
partrpartw
)
minus1 (
partrpartw
)T
Vminus1r0 (L4)
which already provides a solution for the local parameter set (w)
Global parameters fit
Reached this point is worth to mention that solving the innerfit (δw) involves the calculation of the[(
partrpartw
)TVminus1
(partrpartw
)]
matrix This way the possible correlation among the residuals that depend onw is
computed and fed into the global fit
The solving of the system requires to compute the derivativeterms ofr = r(tw) with respect totandw and alsodwdt One of the keys of the Globalχ2 technique is that the later derivative is not nullthe parameters of the inner fit (w) depend on the parameters of the outer fit (t) Otherwise ifw wereindependent oft then one would have to face a normalχ2 fit with two independent parameters
dr =partrpartt
dt +partrpartw
dw minusrarr drdt=partrpartt+partrpartw
dwdt
(L5)
Thedwdt term can be computed from Eq L4 and gives
dwdt= minus
(
partrpartw
)T
Vminus1
(
partrpartw
)
minus1 (
partrpartt
)T
Vminus1
(
partrpartt
)
(L6)
Inserting Eq L4 into Eq L3 and performing the matrix algebra one reaches
(
drdt
)T
Vminus1r0 +
(
drdt
)T
Vminus1
(
partrpartt
)
δt = 0
δt = minus
(
drdt
)T
Vminus1
(
partrpartt
)
minus1 (
drdt
)T
Vminus1r0 (L7)
which allows to compute the correctionsδt to the set of global parameters (related with the top quarkproperties)
A
MProbability density functions
In this appendix summarizes the probability density functions (pdf) which are used for the fit of themass distribution
M1 Lower tail exponential distribution
The exponential distribution is well known (for example [139]) and commonly used for lifetime deter-mination as well as for radioactive decays studies The usual shape is to have a maximum at 0 followedby an exponential decay towards positive values In our implementation the distribution has a maximumhowever not at 0 but at a cut-off value and the exponential tail occurs towards smaller values The cut-offhas been implemented usingθ(m0 minus x) as the Heaviside step function The pdf properties as expectedvalue and variance can be expressed as
Variable and parameters
symbol type propertyx positive real number variablem0 positive real number cut-off valueλ positive real number steepness of the tail
Probability density function
f (x m0 λ) =
[
1
λ (1minus eminusm0λ)e(xminusm0)λ
]
θ(m0 minus x) (M1)
Expected value
E(x) =m0 minus λ
1minus eminusm0λ(M2)
Variance
V(x) =eminusm0λ
(
1minus eminusm0λ)2
[
λ2(
em0λ minus 2)
+ 2m0λ minusm20
]
(M3)
Cumulative distribution
F(x m0 λ) =int x
0f (xprime m0 λ) dxprime = 1minus 1minus e(xminusm0)λ
1minus eminusm0λθ(m0 minus x) (M4)
199
200 M Probability density functions
An example of lower tail exponential distribution is shown in Figure M1 (green line)
M2 Lower tail exponential with resolution model
The experimental resolution may affect the shape of the observables distributions Letrsquos consider aGaussian resolution model Let beG(x m σ) the probability to observe a mass value ofx when the truemass value ism and the experimental resolution isσ The convolution of the lower tail exponential pdf(Apendix M1) with a Gaussian resolution function leads to the following pdf
f (x m0 λ σ) = f otimesG =int infin
0f (m m0 λ) middotG(x m σ) dm (M5)
Variable and parameters
symbol type propertyx positive real number variablem0 positive real number cut-offmassλ positive real number steepness of the exponential tailσ positive real number mass resolution
Probability density function
f (x m0 λ σ) =e(xminusm0)λ
1minus eminusm0λ
eσ22λ2
2λ
[
Erf
(
minus(xminusm0)λ minus σ2
radic2λσ
)
+ Erf
(
xλ + σ2
radic2λσ
)]
(M6)
Expected value
E(x) = m0 minus λ +m0eminusm0λ
1minus eminusm0λ(M7)
Variance
V(x) =
(
λ2 + σ2) (
1+ eminus2m0λ)
minus eminusm0λ(
m20 + 2(λ2 + σ2)
)
(
1minus eminusm0λ)2
(M8)
Cumulative distribution
F(x m0 λ σ) =int x
0f (xprime m0 λ σ) dxprime =
e(xminusm0)λeσ22λ2
[
Erf
(
xλ + σ2
radic2λσ
)
minus Erf
(
(xminusm0)λ + σ2
radic2λσ
)]
minus eminusm0λErf
(
xradic
2σ
)
+ Erf
(
xminusm0radic2σ
)
2(
1minus eminusm0λ)
(M9)
One of the features of this distribution is that (contrary toa Gaussian distribution)m0 is not the mostprobable value Figure M1 compares a Gaussian distribution with f (x m0 λ σ) given by Equation M6
M3 Novosibirsk probability distribution 201
m130 140 150 160 170 180 190 200
Pro
babi
lity
dens
ity fu
nctio
n
0
002
004
006
008
01 = 1750m = 8λ = 4σ
0m=m
)σλ0
f(mm
)λ0
Exp(mm
)σ0
G(mm
Figure M1 Comparison of the pdfrsquos for a Gaussian (red dashed line) a lower tail exponential (greendashed line) and a lower tail exponential with resolution model (black line) All pdfrsquos make use ofthe samem0 σ andλ values (175 8 and 4 respectively) The Gaussian peaks atm0 but the lower tailexponential with resolution model peaks at a lower value clearly shifted fromm0
In that figure both distributions have the samem0 andσ values While the most probable value for theGaussian is them0 the lower tail exponential with resolution model peaks atmlt m0 The f (x m0 λ σ)has also a non symmetric shape While its upper tail is quite close to a Gaussian tail its lower tail departsmore from the Gaussian
M3 Novosibirsk probability distribution
The Novosibirsk pdf may be regarded as a sort of distortedGaussian distribution It is parametrizedas follows
Variable and parameters
symbol type propertyx real number variablex0 real number most probable value (or peak position)σ positive real number width of the peakΛ positive real number parameter describing the tail
202 M Probability density functions
x100 150 200 250 300
Pro
babi
lity
dens
ity fu
nctio
n
0
0005
001
0015
002
0025
003
0035
004)Λσ
0f(xm
= 1600x = 20σ = 040Λ
Figure M2 An example of the Novosibirsk pdf
Probability density function
f (x x0 σ λ) = eminus
12
(ln qy
Λ
)2
+ Λ2
ln qy = 1+ Λ( xminus x0
σ
)
sinh(Λradic
ln 4)
Λradic
ln 4
(M10)
An example of the Novosibirsk pdf is shown in figure M2
A
NStudy of the physics background
The irreducible physics background has been defined as all the SM processes (excludingtt) that pro-duce a final topology similar to thett rarr ℓ + jets and satisfy the selection criteria applied through theanalysis sections After the Globalχ2 fit the physics background has been reduced toasymp 5 (Table 55)The main contribution comes from the production of single top events (amounting around the 50 of thetotal) The shape of themtop distribution due to the irreducible physics background is computed from thesum of all processes This distribution includes of course the single top events which could introduce amass dependent in its shape
In order to asses the effect of the single top events in themtop background distribution the single topMC samples generated at differentmtop masses were used The obtainedmtop physics background distri-bution (including single top) has been studied at each generated mass point from 165 GeV to 180 GeVThe shape of this distribution was modelled by a Novosibirskfunction (Appendix M)
The values of the Novosibirsk parameters (microphysbkg σphy bkg andΛphy bkg) have been extracted FiguresN1 N2 and N3 display the dependence of each parameter with respect to the input single top mass pointAll distributions are compatible with a flat distribution Therefore one can assume that the parametersdescribing the physics background do not depend on the inputtop-quark mass So the influence of singletop events in the worst of the cases will be very mild
[GeV]generatedtopm
155 160 165 170 175 180 185
[GeV
]ph
ybac
kmicro
150
155
160
165
170
175
180
ndof = 0812χ
=1725) = 16238 +- 110top
p0(m
e+jetsmicrorarrtt
Physics Background
Figure N1 Fittedmicrophy bkg as a function of the true single top-quark mass
203
204 N Study of the physics background
[GeV]generatedtopm
155 160 165 170 175 180 185
[GeV
]ph
ybac
kσ
20
22
24
26
28
30
32
34
36
38
40
ndof = 0092χ
=1725) = 2835 +- 067top
p0(m
e+jetsmicrorarrtt
Physics Background
Figure N2 Fittedσphy bkg parameters as a function of the true single top-quark mass
[GeV]generatedtopm
155 160 165 170 175 180 185
[GeV
]ph
ybac
kΛ
0
01
02
03
04
05
06
07
08
09
1
ndof = 1492χ
=1725) = 043 +- 002top
p0(me+jetsmicrorarrtt
Physics Background
Figure N3 FittedΛphy bkg parameters as a function of the true single top-quark mass
A
OMini-template linearity test
The linearity of the mini-template method with respect to the generated top-quark mass has been eval-uated in the same way that for the template method At each mass point 500 pseudoexperiments havebeen performed each randomly filled using the content of thetop-quark mass histogram for the nominalMC sample with the same number of entries The physic background has neither been included in thistest since it exhibited a flat dependence with the generated mass (Appendix N)
Figure O1 (left) shows the difference between the fitted top-quark mass versus the generated top-quarkmass (true value) As one can see there is a quite large dispersion Although it must be noted that theeach sample has a different statistics Actually the point atmtop=1725 GeV had 10 M of events whilethe other had 5 M of events Moreover this sample also exhibits a better prediction than the rest thusevidences that the mini-template method is quite statistics dependent This was somewhat expected asthe accurate determination of the parameters of the distribution will improve with the statistics of thesample
The pull distributions are produced and fitted with a Gaussian The width of the pull distribution as afunction of the top-quark mass generated is shown in Figure O1 (right) The average value is close tounity (1042plusmn0015) which indicates a quite good estimation of the statistical uncertainty
[GeV]generatedtopm
155 160 165 170 175 180 185
[GeV
]in to
p-m
out
top
m
-2
-15
-1
-05
0
05
1
15
2
0048plusmnAvg = 0186
PowHeg+Pythia P2011C
e+jetsmicrorarrtt
Mini-Template Method
[GeV]generatedtopm
155 160 165 170 175 180 185
pul
l wid
thto
pm
0
02
04
06
08
1
12
14
16
18
2
0015plusmnAvg = 1042
PowHeg+Pythia P2011C
e+jetsmicrorarrtt
Mini-Template Method
Figure O1 Left difference between the fitted top mass with the mini-template andthe generated massas a function of the generated top-quark mass Right Width of the pull distributions as a function of thegenerated top-quark mass
205
206 O Mini-template linearity test
A
PValidation of the b-jet energyscale using tracks
Theb-quark originated jets play an important role in many ATLAS physics analyses Therefore theknowledge of theb-jet energy scale (b-JES) is of great importance for the final results Among others thetop-quark mass measurement performed in thett rarr ℓ + jetschannel which contains twob-tagged jetsin the final state is strongly affected by theb-JES uncertainty leading one of the dominant systematicuncertainties In this way a huge effort has been done by the collaboration in order to understand reduceand validate theb-JES uncertainty
Theb-JES quantifies how well the energy of the reconstructed jet reflects the energy of theb-partoncoming from the hard interaction MC and data studies have been performed to evaluate the relativedifference in the single hadron response of inclusive jets andb-jets Theb-JES uncertainty has been com-puted adding quadratically the both following contributions the uncertainty in the calorimeter responsefor b-jets with respect to the response of the inclusive jets [140] and the uncertainty on the MC modellingthat includes among others the production and fragmentation of b-quarks [69] This uncertainty hasbeen tested using a track based method which compares thepT of the jet measured by the calorimeter andby the Inner detector
Data and Monte-Carlo samples
This analysis was performed withpminuspcollisions recorded by the ATLAS detector during 2010 atradic
s=7 TeV Only data periods with stable beam and perfect detector operation were considered amounting toan integrated luminosity ofL = 34 pbminus1 TheMinBias L1Calo andJetEtMiss data streams wereused together in order to increase the statistics and cover awide pT spectrum
The MC sample used to perform the analysis was the QCD di-jet sample produced with P gener-ator program with MC10 tune The QCD di-jet samples cover an extensivepT range fromsim10 GeV tosim2000 GeV
Notice that in order to validate theb-JES uncertainty to measure themtop the first attempt was to usethett sample Nevertheless the low statistics of the sample madethis option unfeasible
207
208 P Validation of theb-jet energy scale using tracks
Object reconstruction and selection
An event selection was applied in order to keep well reconstructed events The requirements appliedwere the following
bull Event selection at least one good vertex was required Moreover those events with more than500 tracks or 50 jets were rejected to avoid events poorly reconstructed
bull Track selection tracks were reconstructed as explained in Chapter 3 Each track associated to ajet had to have apT gt1 GeV A hit requirement was also imposedNPIX gt 1 andNSCT gt 6 Inaddition cuts in the transverse and longitudinal impact parameters respect to the primary vertex(PV) were applieddPV
0 6 15 mm andzPV0 middot sinθ 6 15 mm These cuts ensured a good tracking
quality and minimized the contributions from photon conversions and from tracks not arising fromthe PV
bull Jet selectionjets were reconstructed with the Anti-Kt algorithm with a cone size of R= 04 Thesejets were calibrated at EM+JES scale (Section 33) A jet quality criteria was applied to identifyand reject jets reconstructed from energy deposits in the calorimeters originating from hardwareproblems Moreover jets with apT larger than 20 GeV and| η |lt25 were required These jets hadto be isolated and contain at least one track passing the track selection
bull b-jet selection theb-jets were selected with the SV0 tagger [142] This tagger iteratively recon-structs a secondary vertex in jets and calculates the decay length with respect to the PV The decaylength significance calculated by the algorithm is assignedto each jet as tagging weight Only thosejets with a weightgt585 were identify asb-jets Theb-tagging SF were applied to MC in order tomatch the real datab-tagging efficiency and mis-tag rates
Calorimeter b-JES validation using tracks
In order to validate theb-JES and its uncertainty an extension of the method used to validate the JESuncertainty was proposed [141] The method compares thepT of the jet measured by the calorimeter andby the ID tracker This comparison is done trough thertrk variable which is defined as follows
rtrk =| sum ptrack
T |p jet
T
(P1)
where thep jetT is the transverse momentum of the reconstructed jet measured by the calorimeter and the
sum
ptrackT is the total transverse momentum of the tracks pointing to the jet The track-to-jet association
is done using a geometrical selection all tracks with apT gt1 GeV located within a cone of radius R=04 around the jet axis are linked to the jet (∆R(jet track)lt04) The mean transverse momentum ofthese tracks provides an independent test of the calorimeter energy scale over the entire measuredpT
range within the tracking acceptance Thertrk distribution decreases at lowpT bins due to thepT cutof the associated tracks In order to correct for thispT dependence instead ofrtrk the double ratio ofcharged-to-total momentum observed in data and MC is used
Rr trk =[〈rtrk〉]data
[〈rtrk〉]MC(P2)
209
〈rtrk〉 corresponds to the mean value of thertrk distribution extracted from data and MC ThisR variablecan be built for inclusive jets (Rr trkinclusive) andb-tagged jets (Rr trkbminus jet) Finally the relative response ofb-jets to inclusive jetsRprime is used to validate theb-JES uncertainty TheRprime variable is defined as
Rprime =Rr trkbminus jet
Rr trkinclusive(P3)
Systematic uncertainties
The most important systematic sources affecting thertrk R andRprime variables are the following
bull MC Generator this takes into account the choice of an specific generator program The analysiswas performed with P (as default) and H++ (as systematic variation) The variation ofdata to MC ratios was taken as the systematic uncertainty
bull b-tagging efficiency and mis-tag rate in order to evaluate theb-tagging systematic uncertaintythe SF values were changed byplusmn1σ The analysis was repeated and the ratio re-evaluated Theresulting shift was associated to the systematic uncertainty
bull Material description the knowledge on the tracking efficiency modelling in MC was evaluatedin detail in [143] The systematic uncertainty on the tracking efficiency of isolated tracks increasedfrom 2 (| ηtrack |lt 13) to 4 (19lt| ηtrack |lt 21) for tracks withpT gt500 MeV
bull Tracking in jet core high track densities in the jet core influences the tracking efficiency due toshared hits between tracks fake tracks and lost tracks In order to evaluate this effect a systematicuncertainty of 50 on the loss of efficiency was assigned The change of the ratio distribution dueto this systematic was evaluated using MC truth charged particles and the relative shift was takenas the systematic uncertainty
bull Jet energy resolutionthis systematic quantifies the impact of the jet energy resolution uncertaintyon the measurement A randomised energy amount that corresponds to a resolution smearing of10 was added to each jet The difference in the ratio was calculated and taken as the systematicuncertainty
Results
The analysis was performed using different bins inpT and rapidity The accessible kinematicpT rangewas from 20 GeV to 600 GeV and the binning was chosen in order tokeep enough statistics The rapidityrage was split up in three bins| y |lt 12 126| y |lt 21 and 216| y |lt 25
Figure P1(a) P1(c) and P1(e) show theRr trkbminus jets ratio of data to MC An agreement within 2 in thebin |y| lt12 within 4 in the bin 126| y |lt 21 and within 6 in the bin 216| y |lt 25 was obtainedThe systematic uncertainties displayed in Figures P1(b) P1(d) and P1(f) were found of the order of 34 and 8 for the same rapidity ranges respectively The larger contributions came from the materialdescription and MC generator
The Rprime distributions can be seen in Figures P2(a) P2(c) and P2(e) The results show an agreementwithin 2 in the bin|y| lt12 within 25 in the bin 126| y |lt 21 and 6 for the bin 216| y |lt 25
210 P Validation of theb-jet energy scale using tracks
In order to compute the systematic uncertainty ofRprime several assumptions were done For example at firstorder the uncertainties associated with the tracking efficiency and material description were taken as fullycorrelated and cancelled In addition the jetpT resolution for inclusive andb-jets was considered to be ofthe same order for hightpT and of the order of 2 per mille for lowpT therefore this systematic was alsoneglected Thus the significant systematic uncertaintieson Rprime arose from the MC generator choice andb-tagging calibration These ones were evaluated and added in quadrature to compute the final systematicuncertainty being of the order of 3 for the first two rapiditybins and 6 for the most external rapiditybin (Figures P2(b) P2(d) and P2(f))
Summing up a newRprime variable was defined to estimate the relativeb-jet energy scale uncertaintyfor anti-Kt jets with a∆R = 04 and calibrated with the EM+JES scheme This method validated thecalorimeterb-JES uncertainty using tracks and improved the knowledge ofthe jet energy scale of theb-jets These results were reported in an ATLAS publication [69] Posteriorly the validation of theb-JESuncertainty withtt events were also performed providing a more accurateb-JES validation for themtopanalyses [144]
211
[GeV]jet
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Data 2010
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ATLAS|y|lt25leb-jets 21
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Figure P1Rr trkbminus jet variable (left) and its fractional systematic uncertainty(right) as a function ofp jetT
for | y |lt12 (upper) 126| y |lt21 (middle) and 216| y |lt 25 (bottom) The dashed lines indicate theestimated uncertainty from the data and MC agreement Only statistical uncertainties are shown on thedata points
212 P Validation of theb-jet energy scale using tracks
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Figure P2 The ratioRprime (left) and the fractional systematic uncertainty (right) as a function ofp jetT for
| y |lt12 (upper) 126| y |lt21 (middle) and 216| y |lt 25 (bottom) The dashed lines indicate theestimated uncertainty from the data and MC agreement Only statistical uncertainties are shown on thedata points
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- Certificate
- Contents
- Particle Physics overview
-
- The Standard Model
- Top-quark physics in the SM and beyond
-
- Top-quark mass
- Top-quark mass in the EW precision measurements
- Top-quark mass in the stability of the electroweak vacuum
-
- The ATLAS Detector at the LHC
-
- The LHC
- The ATLAS Detector
-
- Inner Detector
- Calorimetry system
- Muon Spectrometer
- Trigger
- Grid Computing
-
- ATLAS Reconstruction
-
- Coordinate systems
- Track reconstruction
- Object reconstruction
-
- Alignment of the ATLAS Inner Detector with the Global2
-
- The Inner Detector alignment requirements
- Track-Based Alignment
- The Global2 algorithm
-
- The Global2 fit with a track parameter constraint
- The Global2 fit with an alignment parameter constraint
- Global2 solving
- Center of Gravity (CoG)
-
- The ID alignment geometry
- Weak modes
- Alignment datasets
- Validation of the Global2 algorithm
-
- Analysis of the eigenvalues and eigenmodes
- Computing System Commissioning (CSC)
- Constraint alignment test of the SCT end-cap discs
- Full Dress Rehearsal (FDR)
-
- Results of the Global2 alignment algorithm with real data
-