CTEQ SS 2002 Stephen MRENNA Fermilab 1 Introduction to Event Introduction to Event Generators Generators Stephen Mrenna CD/Simulations Group Fermilab Email: mrenna@fnal. gov
Feb 06, 2016
CTEQ SS 2002 Stephen MRENNA Fermilab 1
Introduction to Event Introduction to Event GeneratorsGenerators
Stephen MrennaCD/Simulations Group
FermilabEmail: [email protected]
CTEQ SS 2002 Stephen MRENNA Fermilab 2
MotivationMotivation Experiments rely on Monte Carlo
programs which calculate physical observables Correct for finite detector acceptance Find efficiency of isolation cuts Jet Energy (out of cone) corrections Connect particles to partons Determine promising signatures of “new”
physics Optimize cuts for discovery/limit Planning of future facilities . . .
CTEQ SS 2002 Stephen MRENNA Fermilab 3
Field Theory TrinityField Theory Trinity Many different calculational schemes
from same basic principles Tree level (lowest order)
Many partons All spin correlations Full color structure
NNLO Smaller theoretical errors More inclusive kinematics
“All” orders in towers of logarithms Leading Logarithm, NLL, … Analytic resummation (soft gluons integrated
out) Parton showers (soft gluons at leading log)
How to make sense of it all?
How to use the best parts of each?
CTEQ SS 2002 Stephen MRENNA Fermilab 4
Many computer programs CompHEP / Madgraph / Whizard / … MCFM / DYRad / JetRad / … Pythia / Herwig / Isajet / Ariadne / …
Often treated as Black Boxes Purpose of the Lectures: Open the Box
Separate the regions of validity Determine overlap Merge (use the best of each) Special role of Event Generators
CTEQ SS 2002 Stephen MRENNA Fermilab 5
An Important Topic!An Important Topic! Uncertainties in how events should be
generated are significant or most important errors for: Top mass determination Precision W-mass extraction
Together, a window to new physics NNLO jet predictions with kT-algorithm …
Our ignorance limits what we can learn about Nature
CTEQ SS 2002 Stephen MRENNA Fermilab 6
Event Generators: IntroductionEvent Generators: Introduction Most theorists make predictions about
Partons Valid to a specific order in perturbation theory The asymptotic states are not the physical ones
Quarks & gluons confined within hadrons Some predictions have peculiar properties
Slicing of phase space with cutoffs Negative weights cancelling positive ones
Experimentalists measure Objects in detector No distinction between Perturbative and Non-
Perturbative physics In- and Out-states are quasi-stable particles
Multiplicities can be large Observe (positive) integer number of events
CTEQ SS 2002 Stephen MRENNA Fermilab 7
Event Generators Connect “Theory” to Event Generators Connect “Theory” to “Experiment”“Experiment”
Describe the complicated Experimental Observable in terms of a chain of simpler, sequential processes Some components are perturbative
hard scattering, parton showering, some decays, … Others are non-perturbative and require modelling
hadronization, underlying event, kT smearing, … models are not just arbitrary parametrizations, but have
semi-classical, physical pictures Sometimes as important as the perturbative pieces
The Chain contains complicated integrals over probability distributions Positive Definite Rely heavily on Monte Carlo techniques to choose a
history Final Output is E,p,x,t of stable and quasi-stable
particles Ready to Interface with Detector Simulations
CTEQ SS 2002 Stephen MRENNA Fermilab 8
Partial Event Partial Event DiagramDiagram
Hard ScatterFSRFSR
Resonance Decay
Remnant
“Underlying Event”
ISRISR
Hadronization
Particle Decay
Interconnection Bose-Einstein
σ̂)Q(x,f 2i/p
)Qz,(P 2qq
)Qz,(D 2h/i
)Qz,(P 2qq
CTEQ SS 2002 Stephen MRENNA Fermilab 9
Hard ScatteringHard Scattering Characterizes the rest of the event
Sets a high energy scale Q Fixes a short time scale where partons are free
objects Allows use of perturbation theory External partons can be treated as on the mass-shell
Valid to 1/Q Properties at scales below Q are swept into PDFs
and fragmentation functions This is the Factorization Theorem
Sets flow of Quantum numbers (particularly Color) Note: Parton shower and hadronization models work
in 1/NC approximation Gluon replaced by color-anticolor lines All color flows can be drawn on a piece of paper
CTEQ SS 2002 Stephen MRENNA Fermilab 10
Examples of color flowsExamples of color flows
gggg - WbbWttgg
Can influence:Can influence:
1.1. Pattern of additional soft gluon radiationPattern of additional soft gluon radiation
2.2. Fragmentation/HadronizationFragmentation/Hadronization
CTEQ SS 2002 Stephen MRENNA Fermilab 11
Tree Level Calculation of Hard Tree Level Calculation of Hard ScatterScatter Read Feynman rules from iLint
Use Wave Functions from Relativistic QM Propagators (Green functions) for internal lines
Specify initial and final states Track spins/colors/etc. if desired
Draw all valid graphs connecting them Tedious, but straight-forward
Algorithm can be coded in a computer program MadGraph / CompHEP / …
Calculate (Matrix Element)2
Evaluate Amplitudes, Add them, and Square (MadGraph) Symbolically Square, Evaluate (CompHEP) Do something trickier (Alpha)
(Monte Carlo) Integrate over Phase Space VEGAS …
Number of graphsgrows quicklywith number
of partons
Efficiency decreases with
number of internal lines
CTEQ SS 2002 Stephen MRENNA Fermilab 12
CompHEP Diagrams for CompHEP Diagrams for ududWW++bbbb
Vcb
Vub
Vcd
2sg
2sg
2ewg
2ewg2
ewg 2ewg
2ewg
2ewg
Vtd
2ewg
2ewg
Naïve application of rules leads to many
diagrams!
CTEQ SS 2002 Stephen MRENNA Fermilab 13
Higher Order = Higher TopologyHigher Order = Higher TopologyHow sensitive is Mbb to
additional gluon radiation?
Both diagrams have 6 colored lines Amplitudes diverge in soft/collinear limit
CTEQ SS 2002 Stephen MRENNA Fermilab 14
Tree Level OverviewTree Level Overview Leading order matrix
element calculations describe explicit, many- particle topologies Well-separated
partons Full spin correlations Color flow
Many computer programs Different approaches
to the same problem Analytic vs Numeric Matrix Element vs
Phase Space
CompHep SM + MSSM + editable models Symbolic evaluation of squared matrix
element 2 4-6 processes with all QCD and
EW contributions color flow information outputs cross sections/plots/etc.
Grace similar to CompHep
Madgraph SM + MSSM helicity amplitudes “unlimited” external particles (12?) color flow information not much user interface (yet)
Alpha + O’Mega does not use Feynman diagrams gg10 g (5,348,843,500 diagrams)
CTEQ SS 2002 Stephen MRENNA Fermilab 15
Why Go Beyond Tree Level ?Why Go Beyond Tree Level ? Tree level (lowest order) prediction X has a large
dependence on the scale in couplings “the” hard scale is ambiguous Ideally dX/d=0, but not possible if X ~ g()N
More likely if X= a g()N + b g()N+1
No clear way to merge different topologies Some W/Z+N parton events will be reconstructed as
W/Z + N-1 jet events Some W/Z+N-1 parton events will be W+N-1 jet
events No way to avoid soft and/or collinear singularities
In fact, multiple gluon emission occurs in these kinematic configurations
No direct connection to hadronization
CTEQ SS 2002 Stephen MRENNA Fermilab 16
NLO: Looking Beyond the TreesNLO: Looking Beyond the TreesExample: hb+XExample: hb+X
ggss
ggss33
ggss22
)g2Re(gg g gg g~ 3sss
2s
bdy-2
23ss
bdy
2s
22
3
2σ
CTEQ SS 2002 Stephen MRENNA Fermilab 17
NLO: Some ImprovementNLO: Some Improvement Scale dependence greatly reduced Shape of some distributions similar up to
scale (K) factor But kinematics are inclusive Separation of different topologies depends on
cutoff Multiple, soft-collinear gluon emissions are not
included
Tevatron at bbW
CTEQ SS 2002 Stephen MRENNA Fermilab 18
Wbb and ZbbWbb and Zbb
CTEQ SS 2002 Stephen MRENNA Fermilab 19
W+jj also to NLOW+jj also to NLO W+jj can still be used to normalize W+bb Overall scale dependence of W/Z+jj
reduced Program MCFMMCFM (Campbell, R.K. Ellis)
CTEQ SS 2002 Stephen MRENNA Fermilab 20
The need for even higher order…The need for even higher order… As long as
observables are inclusive enough, this is extremely important and useful
Beware of correlations between kinematics of different objects These can be
sensitive to multiple, soft gluon emission
CTEQ SS 2002 Stephen MRENNA Fermilab 21
Consider W production At LO in pQCD, the
rapidity Y and transverse momentum QT of the W are fixed by incoming partons
At NLO, single gluon emission occurs with QT>0
Cross sections at large QT or QT averaged are described well by fixed order in S
However, some observables are sensitive to region QT « Q For W/Z production, this
is most of the data! Solution: Reorganize
perturbative expansion N lnM(Q2/QT
2) Sums up infinite series
of soft gluon emissions kT dependent PDF’s
Resummation: Beyond Fixed Resummation: Beyond Fixed OrderOrder
...Q Qlnαc cQ
QlnQα
dQσ̂d
:NLO
σ QδdQσ̂d
:LO
2T
22
S212T
2
2T
S2T
0T2T
CTEQ SS 2002 Stephen MRENNA Fermilab 22
Sudakov EffectSudakov Effect Solid: resummed
Superior at lower QT
Dot/Dash-dot: W+1j/W+2j Superior at high QT
Ln(Q/Q)=0
Multiple soft and collinear gluon emissions included, but
integrated out
CTEQ SS 2002 Stephen MRENNA Fermilab 23
Higher Order vs All OrderHigher Order vs All Order In the lower QT region, significantly
different predictions from NLO Decay products retain information about W
production Important for MW measurement in Run II
NLO prediction depends on cutoff
CTEQ SS 2002 Stephen MRENNA Fermilab 24
Review of “Hard Scattering”Review of “Hard Scattering” Tree Level Predictions
Pros Full spin and color
correlations “Easy” to calculate Good for large PT’s and
angular separations Cons
Rate not reliable Not clear how to
merge different topologies
(N)NLO Predictions Pros
Reduced scale dependence
Merging of topologies
Cons Also requires large PT’s
and angular separations
Resummation Pros
(N)NLO accuracy with all orders accuracy in kinematics
Cons No information on soft
gluons All of these approaches
ignore details of physics below hard scale Not yet connected to
hadronization Color must be screened
CTEQ SS 2002 Stephen MRENNA Fermilab 25
Calculate the probability of a hard scattering at scale Q treating in and out partons as on-shell
Rest of the event can be described by positive probability distributions Prior to and after hard scatter, evolution of partons
is sensitive to quantum fluctuations below scale Q Cancellation of Virtual (-) and Real (+) effects occurs at
scales too small to resolve For color evolution, scale is typically QCD
In-partons evolved from some parents with P=1 Out-partons evolve into daughters with P=1 Final state partons hadronize with P=1 Beam particle remnant also hadronizes with P=1
The Factorization Theorem Factorization Theorem is essential for this to work
Monte Carlo Event GeneratorMonte Carlo Event Generator
CTEQ SS 2002 Stephen MRENNA Fermilab 26
““Monte Carlo” “Event Monte Carlo” “Event Generator”Generator” Improving the Physics complicates the Numerics
Difficult Integrand in Many dimensions Well-suited to Monte Carlo methods
Integrands are positive definite Normalize to be probability distributions
Hit-or-Miss Test integrand to find maximum weight WMAX (or just guess) Calculate weight W at some random point If W > r WMAX, then keep it, otherwise pick new W Sample enough points to keep error small
Can generate events like they will appear in an experiment N = [Xb] L[Xb-1]
NNLO QCD programs are not event generators Not positive definite (Cancellations between N and N+1) Superior method for calculating suitable observables
Tree level programs are not event generators Only limited topologies Can follow spins/color exactly
CTEQ SS 2002 Stephen MRENNA Fermilab 27
Parton ShowerParton Shower Hard Scattering sets scale Q Structure f(x,Q2) or fragmentation D(x,Q2) functions,
couplings S(Q2), etc. are evaluated at Q Asymptotic states have a scale Q0~1 GeV
Incoming/Outgoing partons are highly virtual How do incoming partons acquire mass2 ~ -Q2 ?
INITIAL STATE RADIATION (ISR) How do outgoing partons approach the mass shell ?
FINAL STATE RADIATION (FSR) Typically, resolving smaller scales generates many
partons with lower virtuality Virtualities on the order of QCD are expected for partons
bound in hadrons “traditional” calculations based on a small number of
Feynman diagrams are incomplete Parton Showering Monte Carlos are an approximation to
high-order, perturbative QCD
CTEQ SS 2002 Stephen MRENNA Fermilab 28
Parton Showering: More Parton Showering: More MotivationMotivation Semi-classical description
Accelerated charges radiate
22)n(n c4
eddP R
)n(nceE β
πΩβ
Color is a charge, and thus quarks also radiate Gluon itself has charge (=q-q* pair to 1/Nc)
Field Theory Block and Nordsieck (QED)
Must include virtual and real (emission) corrections to obtain IR finite cross section Electron is ALWAYS accompanied by
cloud of quanta (photons)
nβ
CTEQ SS 2002 Stephen MRENNA Fermilab 29
2qqs
2qqs
0 Qu(z)Pdzu
du2Q
t(z)Pdztdt
2g)q(qd
gqqee
πα
πασσ
Example: gluon emission in Example: gluon emission in ** events events
Q2 st
u
gqgqqq
2
qq2
p2pu,p2pt,p2psz1z1
34(z)P,Q
sz
t t 0 when gluon is 0 when gluon is Soft, collinear or bothSoft, collinear or both
zz1 when gluon is1 when gluon isSoft, collinear or bothSoft, collinear or both
Factorization of Mass Singularities
Probability of one additional soft emission proportional to rate without emission dN+1 = N S/2 dt/t dz P(z)
CTEQ SS 2002 Stephen MRENNA Fermilab 30
Tower of emissions described by Sudakov Form Tower of emissions described by Sudakov Form FactorFactor
Series of subsequent showers “exponentiate” Shower of resolvable emissions q*(p) q(zp) + g([1-z]p)
Emission RESOLVED if zC < z < 1 - zC Sudakov built from Probability of no resolvable emission
for small t
Prob(tmax,t) = S(tmax)/S(t) = random r Pick random r and solve for new t Resolvable emission at the end of “nothing”: dS/dt Continue picking new t’s down to tmin ~ QCD Stop shower & begin hadronization
CC
0
t
tcb, bca
)(tz
)(tz
S'
cb, bca
(t)z
(t)z
S
z~z,z1~z
t),(t(z)P2(t)dzdtexpS(t)
:emissions leirresolvab of numbers all over Sum
t(z)P2(t)dz1
0
'
'
Δπ
α
δπ
α
CTEQ SS 2002 Stephen MRENNA Fermilab 31
Virtuality-Ordered PSVirtuality-Ordered PS
Highly virtual
Nearly on-shell
)ln(Q tt t t2ii
321
CTEQ SS 2002 Stephen MRENNA Fermilab 32
Initial State RadiationInitial State Radiation Similar picture, but solving DGLAP for
PDFs
BRANCHINGS
"bbca
"abc
"t
t
1
x"
BRANCHING NO
aa )t(x/z,f (z)P̂2)t(z,
)(t)(t'
zdzdt )(t' t)(x,f )t'(x,f '
πα
ΔΔΔ
Increasing parton
virtuality
Parent has more momentum
CTEQ SS 2002 Stephen MRENNA Fermilab 33
Backwards ShoweringBackwards Showering
-Q02>-Q1
2>…>-Qn2
showering added after hard scatter with unit probability Something
happens, even if not resolvable
)t',(x'f z(z)P̂
2 t)(z, Prob(z) ;)(t'
)t'(x,ft)(x,f
(t)
x/zx' ;)t'(x,f x)t',(x'f x' (z)P̂2
)t'(z, dzdt' ln(S)-
abcaabca
b
t
t
z
z b
abca
abcMAX
-
πα
ΔΔ
πα
Sjostrand
Marchesini/Webber
PRIMORDIAL KT
21Q 2
2Q2CQ2
CQ23Q
CTEQ SS 2002 Stephen MRENNA Fermilab 34
Parton Shower is a Parton Shower is a ResummationResummation Analytic Resummation
soft gluon emissions exponeniate into Sudakov form factor
kT conserved Total rate at (N)NLO
modified PDF's corrections for hard
emission soft gluons are
integrated out Predicts observables for
a theoretical W Needs modelling of non-
perturbative physics
Parton Showering DGLAP evolution generates
a shower of partons LL with some N-LL
Exact gluon kinematics LO event rates underestimates single,
hard emissions Explicit history of PS
More closely related to object identified with a W
natural transition to hadronization models Follow color flow down to
small scalesSimilar physics, but different approach with
different regimes of applicability
CTEQ SS 2002 Stephen MRENNA Fermilab 35
Comparison of PredictionsComparison of Predictions
Example of Matrix Element Corrections to
Parton Showering
Example of Treating
Kinematics differently in
shower
Analytic Resum
CTEQ SS 2002 Stephen MRENNA Fermilab 36
Color CoherenceColor Coherence In previous discussion of PS, interference effects
were ignored, but they can be relevant
Add a soft gluon to a shower of N almost collinear gluons incoherent emission:
couple to all gluons |M(N+1)|2 ~ N S NC
coherent emission: soft means long wavelength resolves only overall
color charge (that of initial gluon)
|M(N+1)|2 ~ 1 S NC
CTEQ SS 2002 Stephen MRENNA Fermilab 37
Angular-Ordered PSAngular-Ordered PS Showers should be Angular-Ordered
= pI • pJ / EI EJ = (1 - cosIJ) ~ IJ2/2
1 > 2 > 3 … Running coupling depends on kT
2 z(1-z)Q2
Dead Cone for Emissions Q2 = E2 < Q2
max Q2
max = z2 E2
< 1 [not 2] < /2
No emission in backwards hemisphere
CTEQ SS 2002 Stephen MRENNA Fermilab 38
Color Coherence in PracticeColor Coherence in Practice Emission is restricted inside cones
defined by the color flow
Partonic picture Large N picture
Enhanced
emissionBeam line
CTEQ SS 2002 Stephen MRENNA Fermilab 39
Essential to Describe DataEssential to Describe Data 3 Jet Distributions in Hadronic Collisions
Full Coherence
No Coherence
Partial Coherence
Pseudorapidity of Gluon Jet
Soft Soft emissions emissions
know about know about beam line beam line (large Y)(large Y)
CTEQ SS 2002 Stephen MRENNA Fermilab 40
The Programs (Pyt/Isa/Wig/Aria)The Programs (Pyt/Isa/Wig/Aria) ISAJET
Q2 ordering with no coherence large range of hard processes
PYTHIA Q2 ordering with veto of non-ordered emissions large range of hard processes
HERWIG complete color coherence & NLO evolution for
large x smaller range of hard processes
ARIADNE complete color dipole model (best fit to HERA data) interfaced to PYTHIA/LEPTO for hard processes
CTEQ SS 2002 Stephen MRENNA Fermilab 41
Parton Shower SummaryParton Shower Summary Accelerated color charges radiate gluons
Gluons are also charged Showers of partons develop
IMPORTANT effect for experiments Showering is a Markov process and is added to
the hard scattering with P=1 Derived from factorization theorems of full gauge
theory Performed to LL and some sub-LL accuracy with
exact kinematics Color coherence leads to angular ordering
Modern PS models are very sophisticated implementations of perturbative QCD Still need hadronization modelshadronization models to connect with data Shower evolves virtualities of partons to a low
enough values where this connection is possible
CTEQ SS 2002 Stephen MRENNA Fermilab 42
ComparisonComparison Strings (Pythia)
PRODUCTION of HADRONS is non-perturbative, collective phenomena
Careful Modelling of non-perturbative dynamics
Improving data has meant successively refining perturbative phase of evolution
Clusters (Herwig) PERTURBATION
THEORY can be applied down to low scales if the coherence is treated correctly
There must be non-perturbative physics, but it should be very simple
Improving data has meant successively making non-pert phase more stringlikeSTRING model includes some non-STRING model includes some non-
perturbative aspect of color coherenceperturbative aspect of color coherence
See Bill Gary’s lectures
CTEQ SS 2002 Stephen MRENNA Fermilab 43
The ProgramsThe Programs ISAJET
Independent fragmentation & incoherent parton showers
JETSET (now PYTHIA) THETHE implementation of the Lund string model Excellent fit to e+ e- data
HERWIG THETHE implementation of the cluster model OK fit to data, but problems in several areas
String effect a consequence of full angular-ordering
CTEQ SS 2002 Stephen MRENNA Fermilab 44
W + Jet(s) at the TevatronW + Jet(s) at the Tevatron Good testing ground for
parton showers, LO,NLO Large Scale dependence
at LO
Good agreement with NLO
CTEQ SS 2002 Stephen MRENNA Fermilab 45
W + N jet RatesW + N jet Rates VECBOS for N hard partons HERWIG for additional gluon
radiation and hadronization
VECBOS for N-1 hard partons HERWIG for 1 “hard” parton
plus …
CTEQ SS 2002 Stephen MRENNA Fermilab 46
W + N jet ShapesW + N jet Shapes Start with W + N jets
from VECBOS + HERWIG
Start with W + (N-1) jets from VECBOS + HERWIG
CTEQ SS 2002 Stephen MRENNA Fermilab 47
When good Monte Carlos go badWhen good Monte Carlos go bad
#events >1 jet >2 jets >3 jets >4 jetpT>10 GeV/c
Data 920 213 42 10
VECBOS + HERPRT (Q=<pT>)W + 1jet 920 178 21 1W + 2jet ----- 213 43 6W + 3jet ----- ----- 42 10
VECBOS+HERPRT(Q=mW)
W + 1jet 920 176 24 2W + 2jet ---- 213 46 6W + 3jet ---- ----- 42 7
CDF Run0 DataCDF Run0 Data
VECBOS starting point
More jets generated by HERWIG parton
shower
Normalize 1st bin to data
Results are cut dependent
PS only has collinear part of matrix element
PS has ordering in angles
CTEQ SS 2002 Stephen MRENNA Fermilab 48
Correcting the Parton ShowerCorrecting the Parton Shower PS is an accurate description for soft/collinear
kinematics Most of the data for a given process!
Underestimates wide angle emissions Also, no 1/NC suppressed color flows Tails of kinematic distributions are often most
interesting PS with a single emission can be reweighted to
behave like fixed-order result Correct all or hardest-so-far emissions this way
Populate kinematic regions not included in PS Delicate matching between different regions
Actual correction is generator dependent No attempt to generate NLO rate
Sjostrand/Miu/Seymour/Gorcella …
CTEQ SS 2002 Stephen MRENNA Fermilab 49
Parton Showering and Heavy Parton Showering and Heavy QuarksQuarks Heavy Quarks look like light quarks at
large angles but are sterile at small angles
Naïve -ordered shower has a cutoff > 0 = mQ/EQ = r Creates ‘dead cone’
Virtuality-ordered shower also needs a special treatment
2
2213
213
133
QQ133
3
332
32
2
31
1
r,0),(xd)/Emr,,(xd
Epd
ppp
ppp
)q(qdg)q(qd
:emission gluon soft for expression Eikonal
θθ
θσθσ
σσ
CTEQ SS 2002 Stephen MRENNA Fermilab 50
Pythia Corrections to Top DecayPythia Corrections to Top Decay Relatively easy for Q2
ordered showering Rewrite Parton
Shower weight in terms of Matrix Element kinematics
Modify PS probability by WME / WPS
Angle btw. Quark and Gluon
Parton Level MtopHadron Level Mtop
Not Significant
CTEQ SS 2002 Stephen MRENNA Fermilab 51
CTEQ SS 2002 Stephen MRENNA Fermilab 52
Not Significant
CTEQ SS 2002 Stephen MRENNA Fermilab 53
Top with Hard EmissionsTop with Hard Emissions For top events with one very hard or two
hard jets, the PS description will not be valid Can estimate the relative importance of this
using COMPHEP Rely on ME predictions plus parton
showering Not the perfect solution Will not merge smoothly onto other predictions
NO ME Corrections
to PS in Pythia or
Herwig for Production
CTEQ SS 2002 Stephen MRENNA Fermilab 54
Correcting the NLO CalculationCorrecting the NLO Calculation Total rate is more stable to hard scale
variation Single wide-angle emission from onset
“models” soft-collinear region by single gluon with an inclusive subtraction of singularities
Desire: (N+1)xPS + (N)xPS – Overlap Overlap ~ (N)xPS (all orders) truncated to fixed
order Implementations
Phase space slicing with chosen to remove (N) Only one configuration to shower Positive definite weights Sensitivity to large logarithms of must arise in some
distributions Expansion to fixed order will not agree with NLO result
Baer/Reno/Dobbs/Potter/ …
CTEQ SS 2002 Stephen MRENNA Fermilab 55
Subtraction No dependence on a cutoff NLO calculation fixes initial kinematics for PS and
relative weights of (modified) N and N+1 body contributions
Suitably modified subtraction expands to NLO result
Negative weights are generated Can be treated practically using positive
definite integrands but keeping track of sign Relies on unmodified PS algorithm
Consistent? Power law dependence on some showering
parameters Should be small Frixione/Webber
CTEQ SS 2002 Stephen MRENNA Fermilab 56
Parton Shower and FactorizationParton Shower and Factorization Standard Result
Some freedom in defining PDF/Fragmentation function
Differences not observable for inclusive calculations Parton Shower needs a special treatment [Collins]
Exact kinematics throughout shower NLO predicts gauge boson at rapidity Y PS starts from Y0 and generates Y from emission/boost Mismatch involving evaluation of PDFs at different x Affects Overlap computed in previous approaches
PDFs for PS depend on process and showering algorithm Demonstrated large effect for small parton x
Same conclusion from considering the analytic resummation methods ala Collins/Soper/Sterman [Mrenna]
CTEQ SS 2002 Stephen MRENNA Fermilab 57
PS, Factorization, and PS, Factorization, and ResummationResummation b/QT-space resummation yields (N)NLO
rate and “all orders” kinematics
Y = Fixed order-Asymptotic = Overlap! Contains negative weights – just aesthetics?
1
x
2Q
QT
21T2T
2 12T
2
C(x/z)f(z)zdzf)[x](C
BmQlnA m
dm Q),T(Q
H(Q) f)exp(-T)f)(C(C W~Y)x,xQ,,(QW~dQ
d
X)W h(hdydQdQd
2
2T
σ
Q)f(x,)Q,T(Q2
1exp
)Qf(x,Q),T(Q21exp
dQd
dQd LO, At
T0
T0
2T
02T
σσ
MW PS algorithm Sudakov determines PT
W
Soft gluon emissions are integrated out Sudakov contains soft
pieces not in DGLAP Total rate can be calculated
to any given order in S
CTEQ SS 2002 Stephen MRENNA Fermilab 58
Summary of NLO ShoweringSummary of NLO Showering Correct the PS for emissions that are not
soft/collinear enhanced Reweight by (ME2
PS)/(ME2Exact) [PYTHIA]
Fill out Dead Cone and correct shower [HERWIG] Still have to normalize to NLO rate
Add PS to (N)-(N+1) body configurations of full NLO calculation with suitable subtractions Phase Space Slicing with chosen to eliminate (N)
body configurations Approximation to kinematics sensitive to log()
Subtraction method with modifications to (N) and (N+1) body “Kernels” NLO predictions recovered upon expansion to O(2) Negative weight events are generated
Inconsistency in using “inclusive” definitions of PDFs/Fragmentation functions with exact kinematics
CTEQ SS 2002 Stephen MRENNA Fermilab 59
Summary (cont)Summary (cont) Process dependent PS
Factorization must be re-evaluated when exact kinematics are treated
Integration over KT and virtualities implicit to usual PDFs/Fragmentation functions
Feature also seen in analytic resummation (Collins/Soper/Sterman)
Analytic Resummation has essential ingredients Process dependent PDFs recover NLO rate and
weight Sudakov Y-piece subtraction corrects for soft-gluon
approximation inside Sudakov Introduces negative weights
CTEQ SS 2002 Stephen MRENNA Fermilab 60
Related IdeasRelated Ideas QCD Matrix Elements + Parton Showers
Catani/Kraus/Kuhn/Webber & Lönnblad Attempts to piece together many tree level
processes using PS Generate all ZN parton (tree level) processes
simultaneously For a given N, select a given topology Match topology to a PS history Reject if event would have been generated by
M<N with a parton shower attached Not clear how to match to higher-order rate
Fully numerical NLO in Coulomb gauge Soper and Kramer
Claims a more natural connection to PS
CTEQ SS 2002 Stephen MRENNA Fermilab 61
ConclusionsConclusions Great activity amongst relatively few
practitioners to develop NLO parton showering Several good ideas which need to be synthesized
Hadron collider phenomenology has greatest priority now Naively, effects will be larger with initial state
radiation Precision physics is sensitive to our
understanding of the parton shower Already a large “systematic” uncertainty to Run II
measurements (MW and mt) Perhaps a larger “systematic” at LEP than we think
b-quark asymmetries “4-jet” events …
CTEQ SS 2002 Stephen MRENNA Fermilab 62
Topics Not Topics Not DiscussedDiscussed
Hard ScatterFSRFSR
Resonance Decay
Remnant
“Underlying Event”
ISRISR
Hadronization
Particle Decay
Interconnection Bose-Einstein
σ̂)Q(x,f 2i/p
)Qz,(P 2qq
)Qz,(D 2h/i
)Qz,(P 2qq
CTEQ SS 2002 Stephen MRENNA Fermilab 63
Topics Not CoveredTopics Not Covered Some aspects of the event are beyond the scope of this
introductory set of lectures [and my expertise], yet can be important when comparing to data and can impact new physics searches Treatment of the beam remnant may be relevant for
forward jet tagging studies Higgs production through WW fusion
Underlying event affects isolation and jet-energy corrections Observing Higgs in photons or jets
Interconnection and Bose-Einstein effects are relevant to precision EW measurements
Tau leptons and b-hadrons must be decayed correctly to understand polarization effects & tagging efficiency Is phase space enough?
The objects that experimentalists observe are not the same as the output of an event generator!
CTEQ SS 2002 Stephen MRENNA Fermilab 64
Overall SummaryOverall Summary Event Generators accumulate our knowledge and
intuition about the Standard Model into one package Apply perturbation theory whenever possible
hard scattering, parton showering, decays Rely on models or parametrizations when present
calculational methods fail hadronization, underlying event, beam remnants
Out of the box, they give reliable estimates of the full, complicated structure of an event Sophisticated users will find more flexibility & applications
And will avoid easy mistakes Understanding the output will lead to a broad
understanding of the Standard Model (and physics beyond)