Monte Carlo tools Monte Carlo tools for the LHC for the LHC Michelangelo Mangano Michelangelo Mangano TH Division, CERN TH Division, CERN Nov 6, 2002 Nov 6, 2002
Jan 12, 2016
Monte Carlo Monte Carlo tools tools
for the LHCfor the LHCMichelangelo ManganoMichelangelo Mangano
TH Division, CERNTH Division, CERN
Nov 6, 2002Nov 6, 2002
Final states at the LHCFinal states at the LHCProcessProcess Evts/secEvts/sec
((LL=10=103333))
Evts/yrEvts/yr
Jet, EJet, ETT>100GeV>100GeV 101033 10101010
Jet, EJet, ETT>1TeV>1TeV 1.5x101.5x10-2-2 1.5x101.5x1055
WWl l 2020 2x102x1088
bbbb 5x105x1055 5x105x101212
tttt 11 101077
WW WW l l l l 6x106x10-3-3 6x106x1044
Goal of MC development for the LHC is to provide a description as accurate as possible of these events (and more),
as well as of the features of new physics processes:rates, distributions, fine details of the final states (overall
multiplicities, heavy-quark content)
Use and abuse of MC Use and abuse of MC simulationsimulation
o Use:Use:o benchmarks for the design of detectors, trigger benchmarks for the design of detectors, trigger
and analysis strategies and analysis strategies o tests and measurements of SMtests and measurements of SMo study of properties of new particles (masses, study of properties of new particles (masses,
cross-sections, couplings)cross-sections, couplings)o Abuse: claims of discoveries!Abuse: claims of discoveries!
o top and SUSY discovery in UA1top and SUSY discovery in UA1o RRbb at LEP at LEPo quark compositeness at CDFquark compositeness at CDF
o Only the benchmarking against real data Only the benchmarking against real data can turn MC simulation into powerful study can turn MC simulation into powerful study toolstools
Example: HExample: Hbb in qq bb in qq HqqHqq
mmHH procsprocs
120 GeV120 GeV 140 GeV140 GeV
SignalSignal 2.8 x 103
1.1 x 103
bbjjbbjj 8.0 x 105
5.7 x 105
jjjjb b jj jjbb 7.9 x 103
9.0 x 103
• bbjj bg is ≈102 times the signal, but can be extracted from data (smooth behaviour under the signal peak)• bg from multiple collisions (jjjjb b jj jjbb) ≈ signal, but peak under the signal! Much more sensitive to MC simulation uncertainties!
MLM, Moretti, Piccinini, Pittau, Polosa
Factorization TheoremFactorization Theorem
ddX
f j (x1,Qi ) fk (x2 ,Qi )d ˆ jk(Qi ,Q f )
d ˆ X F( ˆ X X;Qi ,Q f )
ˆ X
j,k
ˆ f(x,Qi)
ˆ X
XF
F( ˆ X X;Qi ,Q f )
transition from partonic final state to the hadronic observable (hadronization, fragm. function, jet definition, etc) Sum over all histories with X in them
f j (x,Q)
sum over all initial state histories leading, at the scale Q, to:
p j x
P proton
The possible histories of initial and final The possible histories of initial and final state, and their relative probabilities, are state, and their relative probabilities, are in principle independent of the hard in principle independent of the hard process (they only depend on the flavours process (they only depend on the flavours of partons involved and on the scales of partons involved and on the scales QQ))
Once an algorithm is developed to describe Once an algorithm is developed to describe IS and FS evolution, it can be applied to IS and FS evolution, it can be applied to partonic IS and FS arising from the partonic IS and FS arising from the calculation of an arbitrary hard processcalculation of an arbitrary hard process
Depending on the extent to which different Depending on the extent to which different possible FS and IS histories affect the possible FS and IS histories affect the value of the observable value of the observable XX, different , different realizations of the factorization theorem realizations of the factorization theorem can be usedcan be used
`Cross-section evaluators’`Cross-section evaluators’ Only some component of the final state is singled out for the Only some component of the final state is singled out for the
measurement, all the rest being ignored (i.e. integrated over). measurement, all the rest being ignored (i.e. integrated over). E.g. ppE.g. ppee++ee-- + X + X
No ‘events’ are ‘generated’, only cross-sections are evaluated:No ‘events’ are ‘generated’, only cross-sections are evaluated:
Experimental selection criteria (e.g. jet definition or Experimental selection criteria (e.g. jet definition or acceptance) are applied on parton-level quantities. Provided acceptance) are applied on parton-level quantities. Provided these are infrared/collinear finite, it therefore doesn’t matter these are infrared/collinear finite, it therefore doesn’t matter what what F(X)F(X) is, as we assume ( is, as we assume (fact. theorem)fact. theorem) that: that:
Thanks to the inclusiveness of the result, it is Thanks to the inclusiveness of the result, it is `straightforward’ to include higher-order corrections, as well `straightforward’ to include higher-order corrections, as well as to resum classes of dominant and subdominant logsas to resum classes of dominant and subdominant logs
pp Z 0 , ddM(ee ) dy(ee )
,
F( ˆ X ,X ) 1X
ˆ X
State of the artState of the art
NLO available for:NLO available for: jet and heavy quarks productionjet and heavy quarks production prompt photon productionprompt photon production gauge boson pairsgauge boson pairs most new physics processes (e.g. SUSY)most new physics processes (e.g. SUSY)
NNLO available for:NNLO available for: W/Z/DY productionW/Z/DY production Higgs production Higgs production
(qq W )
(gg H )
Parton-level (Parton-level (akaaka matrix-elementmatrix-element) ) MC’sMC’s
Parton level configurations (i.e. sets of Parton level configurations (i.e. sets of quarks and gluons) are generated, with quarks and gluons) are generated, with probability proportional to the respective probability proportional to the respective perturbative M.E. perturbative M.E.
Transition function between a final-state Transition function between a final-state parton and the observed object (jet, parton and the observed object (jet, missing energy, lepton, etc) is unitymissing energy, lepton, etc) is unity
No need to expand No need to expand f(x)f(x) or or F(X)F(X) in terms of in terms of histories, since they all lead to the same histories, since they all lead to the same observableobservable
Experimentally, equivalent to assumingExperimentally, equivalent to assuming `smart’ jet clustering (`smart’ jet clustering (parton parton jet jet) ) linear detector responselinear detector response
Codes available for:Codes available for:
W/Z/gamma + N jets (NW/Z/gamma + N jets (N6)6) W/Z/gamma + Q Qbar + N jets (NW/Z/gamma + Q Qbar + N jets (N4)4) Q Qbar + N jets (NQ Qbar + N jets (N4)4) Q Qbar Q’ Q’bar + N jets (NQ Qbar Q’ Q’bar + N jets (N2)2) Q Qbar H + N jets (NQ Qbar H + N jets (N3)3) nW + mZ + kH + N jets (n+m+k+N nW + mZ + kH + N jets (n+m+k+N
8, N8, N2)2) N jets (NN jets (N5)5)
Shower Monte CarloShower Monte Carlo After the generation of a given parton-level After the generation of a given parton-level
configuration (typically LO, 2configuration (typically LO, 21 or 21 or 22) , 2) , each possible IS and FS parton-level each possible IS and FS parton-level history (`history (`showershower’) is generated, with ’) is generated, with probability defined by the shower probability defined by the shower algorithm algorithm (unitary evolution).(unitary evolution).
`̀AlgorithmAlgorithm’: numerical, Markov-like ’: numerical, Markov-like evolution, implementing within a given evolution, implementing within a given appoximation scheme the QCD dynamics:appoximation scheme the QCD dynamics: branching probabilitiesbranching probabilities infrared cutoff schemeinfrared cutoff scheme hadronization model hadronization model
Herwig, Pythia, IsajetHerwig, Pythia, Isajet
Complementarity of the 3 approachesComplementarity of the 3 approachesShower MC’sShower MC’sX-sect evaluatorsX-sect evaluatorsME MC’sME MC’s
Full information Full information available at the available at the hadron levelhadron level
Limited access Limited access to final state to final state structurestructure
Hard partons Hard partons jets. jets. Describes geometry, Describes geometry, correlations, etccorrelations, etc
Final state Final state descriptiondescription
Approximate, Approximate, incomplete phase incomplete phase space at large anglespace at large angle
Straighforward Straighforward to implement, to implement, when availablewhen available
Included, up to Included, up to high orders high orders (multijets)(multijets)
Higher order Higher order effects: hard effects: hard emissionsemissions
Unitary Unitary implementation implementation (i.e. correct shapes, (i.e. correct shapes, but not total rates)but not total rates)
Possible, when Possible, when availableavailable
????
ResummatioResummation of large n of large logslogs
Included as vertex Included as vertex corrections corrections (Sudakov FF’s)(Sudakov FF’s)
Straighforward Straighforward to implement, to implement, when availablewhen available
Hard to implement, Hard to implement, require introduction require introduction of negative of negative probabilities probabilities
Higher order Higher order effects: loop effects: loop correctionscorrections
w=-∞ dw=-∞ w=-∞ dw=-∞
2’ guide to shower MC’s2’ guide to shower MC’s Evaluate parton-level probability, from Feynman rules + phase space. E.g.:
q
q
q’
q’
As a result of acceleration, q’ will emit radiation The probability that radiation will (or will not) be emitted is evaluated as a function of the acceleration of the colour charges: Q2 = (q’- q)2 = - t
q q’
SudakoSudakovv
1)1) Generate Generate 11
2)2) If If 1 1 < P(Q , Q< P(Q , Q00)) no radiation, no radiation, q’ goes directly on-shell at q’ goes directly on-shell at scale Qscale Q00≈GeV≈GeV
3)3) ElseElsea)a) calculate calculate QQ11 / P(Q / P(Q11,Q,Q00)= )= 11
b)b) emission at scale Qemission at scale Q11
4)4) Go back to 1) and reiterate, Go back to 1) and reiterate, until shower stops in 2). At until shower stops in 2). At each step the probability of each step the probability of emission gets smaller and emission gets smaller and smallersmaller
Q0 QQ1
1
P(Q,Q0 ) exp dq
qs q
Q0
Q
P
11
Q2
22
Q1= relative momentum
prob. of no radiation between Q and Q0
Problems (1):Problems (1): Quantum coherence Quantum coherence
+
2 2
+2
x e
R
x
e
R
x
e
x
R
3if
R
x , coherent
e min( x1 , x2 ) ifR
x , incoherent
Solution Solution (a.k.a. angular (a.k.a. angular
ordering)ordering)
2
2
1
2
(1
(2
2
= +
lack of hard, large-angle emission poor description of multijet events
no emission outside C1 C2:C1
C2
loss of accuracy for intrajet radiation
incoherent emission inside C1 C2:
Drawbacks:
HadronizationHadronizationAt the end of the perturbative evolution, the final state consists of quarks and gluons, forming, as a result of angular-ordering, low-mass clusters of colour-singlet pairs:
p
p
N
N
ExamplExample: e:
Wbb+jeWbb+jets ts
Proc Nj=2
Nj=3
Nj=4 Nj=5
Nj=6
q qbarW bb g..g 2.6 0.6 0.14 0.04
0.01
q g W bb q g..g 3.0 2.1 1.1 0.47
q qbarW bb qq g..g
0.29 0.24
0.13
q gW bb qqq g..g 0.03
0.03
Tot (pb) 2.6 3.6 2.5 1.4 0.64
Issues to be addressed for the Issues to be addressed for the evaluation of multiparton matrix evaluation of multiparton matrix
elementselements
nnjj 22 33 44 55 66 77 88
diag’sdiag’s
44 2255
222200
24824855
3430343000
5x105x1055
101077
For example, for ggnj gluons:
Complexity of multiparton amplitudesComplexity of multiparton amplitudes
Evaluation of probabilities for configurations with given colour flows
Colour-flow decompositionColour-flow decompositionThe angular ordering prescription can be extended to cases with higher parton multiplicity. To enforce it, we need to be able to associate probabilities to colour-flow configurations. String theory taught us how to do it:
A(g1,g2 ,,gn ) tr a1a2 an P(1,2,,n 1)
m( p1, p2 ,, pn )
A(g1,,gn )colors
2Nn 2(N2 1) m( p1, p2 ,, pn )
Zn/Z2
2O(1/N2 )
m(p1,p2,…,pn) =
The ALPHA algorithm for the The ALPHA algorithm for the computation of multi-parton processes computation of multi-parton processes
(Caravaglios, M.Moretti)(Caravaglios, M.Moretti)1. A multiparton amplitude can be obtained from:
Z J J(x) (x)
J
nZ J J1J2 Jn
where and (x) is a classical field, solution of:
J p a j p p j j1
n
x bm p Pm m
, Pm cml pl
l1
n
, cml 0,1
2. In the case of tree-level scattering, J(x) is a trivial source:
and the solutions for (x) must be of the simple form:
3. E.g. for a 3 theory, we have:
Z ai lm blbm l,m
Dlmk blbmbk l,m,k
li blail,i
where
lm 1 Pl2 if Pl Pm 0 and Dlmk if Pl Pm Pk 0
4. Minimization w.r.t. bl gives:
lm bm Dlmk bmbk li ai
5. Since
nZ J J1J2 Jn
nZ J
a1a2 an ai 0
only the truncation of Z[J] multilinear in ai
is required finite iterative solution of the above quadratic system!!
Alpha, Alpha, continuecontinue
No need to explicitly evaluate Feynman graphsNo need to explicitly evaluate Feynman graphs Technique extended to QCD: allows calculations of both dual Technique extended to QCD: allows calculations of both dual
and full amplitudesand full amplitudes Numerical complexity Numerical complexity O(aO(ann)) with with a~2-3a~2-3, , instead of instead of n!n! Achieved calculation of processes with up to 10 final-state Achieved calculation of processes with up to 10 final-state
gluons -- over 5x10gluons -- over 5x1099 Feynman diagrams Feynman diagrams (Maltoni et al)(Maltoni et al)
Complete evaluation of multijet processes requires inclusion of Complete evaluation of multijet processes requires inclusion of quarks quarks extra complexity, due to all possible flavour extra complexity, due to all possible flavour combinations.combinations.
nn # distinct # distinct ampsamps 55 3,8533,853
22 3535 66 31,08731,087
33 123123 77 200,45200,4555
44 777777 88 1,676,81,676,88585
Enumeration of independent amplitudes vs number of jets. Asymptotic estimates related to partition function of 0-dim field theories. (Kleiss&Draggiotis)
Problems (2):Problems (2): Q Q22 choice for choice for evolutionevolution
The choice is almost unambiguous for final states with 1 or 2 partons:
Ex:Ex: q
qZ, W Q2 = s
Ex:Ex: q
q
g
g
Q2 pT2 – t
the factorization theorem is easily implemented, due to the existence of a single scale
The choice is more difficult in more complex cases
q
q
g2
gn
g1 If pT1 << pT2 << … << pTn , or (pi+pj)2 varying significantly for different (i,j) Ambiguous implementation of the factorization theorem Potential problem of double counting:
g3
q
q
g1 (from shower evolution)
g4 (from matrix element)
g2
versusversus
g3
q
q
g4 (from shower evolution)
g1 (from matrix element)
g2
with with ppT1T1 << p << pT4 T4 << p<< pT2T2,, ppT3T3
Leading vs subleading double countingLeading vs subleading double countingExample: corrections to 3-parton final statesExample: corrections to 3-parton final states
p1
p2
p3
p4which gives a contribution to 3-jet of order
s logp2 p3 2
ET jet2
s logpT
max
pTmin
log1
R
Double counting is sub-leading provided R and are not too large
pTmax
pTmin
p1
p2
p3
p4
is of s relative to the LO process
p1
p2
p3unless:
Example -- W+3 jet Example -- W+3 jet events events
Bottom line:Bottom line:
Implementation of quantum coherence in Implementation of quantum coherence in shower MC’s is possible, in the limit of shower MC’s is possible, in the limit of large-Nlarge-Ncc and for soft and collinear emission. and for soft and collinear emission.
Large-angle, hard emission cannot be Large-angle, hard emission cannot be described accuratelydescribed accurately
Possible cure requires starting the shower Possible cure requires starting the shower with “seed” multi-parton configurations, with “seed” multi-parton configurations, evaluated using exact (possibly tree-level evaluated using exact (possibly tree-level only) matrix elements.only) matrix elements.
Potential problems, however, due to double Potential problems, however, due to double counting for extra jet emission counting for extra jet emission
Progress towards Progress towards solutions solutions
(I) matrix element (I) matrix element correctionscorrections
Ex: Z03 jets
x1=2E1/MZ
x2=2E2/MZ
≤ x x2≤2
x10
x1 =
1 gq
2
I2
I1
x2
1
1x2=1 gq1
I1: ph.space
covered by angular-ordered emission
I2: ph.space NOT
covered by angular-ordered emission
Algorithm: (M.Seymour)
• generate events in I2 with (finite!) probability:
M (Z qq g)
I2 2
(I1) (I2 )
and distributions given by
M (Z qq g) 2
• Use (qqg) matrix element to correct MC weights in I1
Drawback:• requires analytic representation of the phase-space domain generated by the angular-ordering prescription
Progress towards solutions (II) vetoed Progress towards solutions (II) vetoed showersshowers
((Catani, Krauss, Kuhn, WebberCatani, Krauss, Kuhn, Webber))
yij 2 min Ei
2 ,E j2 1 cosij s
ycut Qcut
2
s
1
2
3
4y34 > ycut
From the sample of 4-hard-parton events
: Sudakov correction
(splitting rejected if y45<ycut )
1
2
453
From the sample of 3-hard-parton events
• Generate samples of different jet multiplicities according to exact tree-level ME’s, with Njet defined using a kperp algorithm
• Reweight the matrix elements by vertex Sudakov form factors, assuming jet clustering sequence defines the colour flow• Remove double counting by vetoing shower histories (i.e. yij sequences already generated by the matrix elements)• Fully successfull for e+e- collisions, being extended to hadronic collisions
MM((ontecarloontecarlo) ) oo((ff) ) EE((verythingverything))
Shower MC’sShower MC’s
Matrix Element Matrix Element MC’sMC’s
Cross-Section Cross-Section Evaluators Evaluators
• Parton Level generators at NLO• KLN negative-wgt events• Formalism for extension to NNLO
• Implementation of NNLO• Implementaiton of resummation corrections to X-sections
• Formalism for extraction of colour flows• Common standards for event coding
• Implementation of double-counting removal in hadronic collisions
available
in progress
• Better treatment of radiation off heavy quarks• Full treatment of spin correlations in production and decay• Better description of underlying event• Better decay tables• …………..
• Formalism for inclusion of NLO• Applications to WW and QQ
• Implementaiton of resummation corrections to X-sections• NLO accuracy in shower evolution• Inclusion of power corrections
Urgent items, nobody working on them to my Urgent items, nobody working on them to my knowledge:knowledge:
Parton-level NNLO MC for W and Z:Parton-level NNLO MC for W and Z: matrix elements available, simplest and most matrix elements available, simplest and most
useful system where to test NNLO formalismuseful system where to test NNLO formalism should allow should allow OO(1%) accuracy in determination (1%) accuracy in determination
of cross-section of cross-section best possible luminometer best possible luminometer at the LHC: at the LHC:
(W)(W)MRSTMRST
20002000MRSTMRST
20012001
NLONLO
FnalFnal 2.392.39 2.412.41
LHCLHC 20.520.5 20.620.6
NNLONNLO
FnalFnal 2.512.51 2.502.50
LHCLHC 19.919.9 20.020.0
NLL description of `jet shapes’, and NLL description of `jet shapes’, and inclusion of power corrections (see LEP)inclusion of power corrections (see LEP)
formalism established and tested with great formalism established and tested with great success at LEP, where it provides an essential tool success at LEP, where it provides an essential tool for the high-accuracy determination of for the high-accuracy determination of ss essential to extend the formalism to hadronic essential to extend the formalism to hadronic collisions, to exploit the lever arm in collisions, to exploit the lever arm in Q Q in the in the measurement of measurement of ss
Power Power correctionscorrections• Classes of non-perturbative effects
linked to the dominant power-like (1/Q) corrections can be parametrised in terms of a single quantity, formally given by:
0 0 1
0
dq0
0
s q
• In the case of 1st moments of shape variables, for example:F=FPT + Fnon-PT
Fnon-PT=cF P, withandP=P0 [0()-0( S)] /S
F 1-T
M2
H
BT BW
cF 2 2 1 1/2
• The impact of these effects at LEP is very large, and their understanding is essential for any quantitative QCD study
Their effect is expected to be very large even at the Tevatron, and in general for LHC events with jets in the few-hundred GeV energy range.
Final remarksFinal remarks A lot of progress has taken place in the recent A lot of progress has taken place in the recent
years, but years, but 30 yrs after QCD, still a lot of work to be done to 30 yrs after QCD, still a lot of work to be done to
achieve a satisfactory description of all high-Qachieve a satisfactory description of all high-Q22 processes accessible at LHCprocesses accessible at LHC
most of the key conceptual difficulties have been most of the key conceptual difficulties have been recently, or are being, solved, and their recently, or are being, solved, and their implementation into concrete MC schemes should implementation into concrete MC schemes should be achievable in the next 5 yearsbe achievable in the next 5 years
forthcoming data from Tevatron will help improving forthcoming data from Tevatron will help improving our tools, but the final test will need real LHC dataour tools, but the final test will need real LHC data
there is plenty of room for creative and rewarding there is plenty of room for creative and rewarding work for young phenomenologists!work for young phenomenologists!
Workshop on MCs for the LHC, July 7 - Aug 2 Workshop on MCs for the LHC, July 7 - Aug 2 2003, at CERN2003, at CERN