Introduction to Event Generators
Stephen Mrenna
CD/Simulations Group
Fermilab
Email: mrenna@fnal.gov
CTEQ SS 2002
Stephen MRENNA  Fermilab
1
Motivation
 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
...
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Stephen MRENNA  Fermilab
2
Field 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
How to make sense of
it all?
How to use the best
parts of each?
 “All” orders in towers of logarithms
 Leading Logarithm, NLL, …
 Analytic resummation (soft gluons integrated out)
 Parton showers (soft gluons at leading log)
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Stephen MRENNA  Fermilab
3
 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
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Stephen MRENNA  Fermilab
4
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
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Stephen MRENNA  Fermilab
5
Event 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 NonPerturbative physics
 In- and Out-states are quasi-stable particles
 Multiplicities can be large
 Observe (positive) integer number of events
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Stephen MRENNA  Fermilab
6
Event Generators Connect “Theory” to
“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, k T smearing, …
 models are not just arbitrary parametrizations, but have semiclassical, 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
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Stephen MRENNA  Fermilab
7
Interconnection
Bose-Einstein
Partial Event
Diagram
Particle
Decay
Remnant
Hadronization
Dh/i (z, Q 2 )
“Underlying
Event”
ISR
Hard Scatter
FSR
Resonance
Decay
Pqq(z, Q 2 )
fi/p (x, Q )
2
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Pqq(z, Q 2 )
ˆ
σ
Stephen MRENNA  Fermilab
8
Hard 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
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Stephen MRENNA  Fermilab
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Examples of color flows
gg  gg
gg  tt  bW  b W -
Can influence:
1.
Pattern of additional soft gluon radiation
2.
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Fragmentation/Hadronization
Stephen MRENNA  Fermilab
10
Tree Level Calculation of Hard Scatter
 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 / …
Number of graphs
grows quickly
with number
of partons
 Calculate (Matrix Element)2
 Evaluate Amplitudes, Add them, and Square (MadGraph)
 Symbolically Square, Evaluate (CompHEP)
 Do something trickier (Alpha)
Efficiency
decreases with
 (Monte Carlo) Integrate over Phase Space
number of
 VEGAS …
internal lines
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Stephen MRENNA  Fermilab
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CompHEP Diagrams for udW+bb
g2s
g
2
ew
g
2
ew
g2ew
g
2
ew
g
2
ew
g2ew
g
2
s
Vub
g2ew
Vtd
Vcd
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Vcb
g2ew
Stephen MRENNA  Fermilab
Naïve application of
rules leads to many
diagrams!
12
Higher Order = Higher Topology
How sensitive is Mbb
to additional gluon
radiation?
Both diagrams have 6 colored lines
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Stephen MRENNA  Fermilab
Amplitudes diverge in
soft/collinear limit
13
Tree Level Overview

 Leading order matrix
element calculations
describe explicit, manyparticle 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
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
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
 gg10 g (5,348,843,500 diagrams)
Stephen MRENNA  Fermilab
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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
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Stephen MRENNA  Fermilab
15
NLO: Looking Beyond the Trees
Example: hb+X
gs
gs2
gs3
2
2
σ ~ g  gs  g  g
 

2
s
3bdy
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3
s
2
s
2
 gs  2Re(g sg3s )  
2
2-bdy
Stephen MRENNA  Fermilab
16
NLO: 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
W  bb
at Tevatron
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Stephen MRENNA  Fermilab
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Wbb and Zbb
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Stephen MRENNA  Fermilab
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W+jj also to NLO
 W+jj can still be used to normalize W+bb
 Overall scale dependence of W/Z+jj reduced
 Program MCFM (Campbell, R.K. Ellis)
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Stephen MRENNA  Fermilab
19
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
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Stephen MRENNA  Fermilab
20
Resummation: Beyond Fixed Order
 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
LO :
 
NLO :
CTEQ SS 2002
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

ˆ
dσ
 δ Q T σ0
dQ 2T
ˆ
αS  Q 2
dσ

ln
dQ 2T Q 2T  Q 2T
 Cross sections at large QT
2

2 Q
 c1  c2αSln  2

 QT


  ...


 N lnM(Q2/QT2)
 Sums up infinite series of
soft gluon emissions
 kT dependent PDF’s
Stephen MRENNA  Fermilab
21
Sudakov Effect
 Solid: resummed
 Superior at lower QT
 Dot/Dash-dot: W+1j/W+2j
Multiple soft and collinear gluon
emissions included, but
integrated out
 Superior at high QT
 Ln(Q/Q)=0
CTEQ SS 2002
Stephen MRENNA  Fermilab
22
Higher 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
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Stephen MRENNA  Fermilab
23
Review of “Hard Scattering”
 Tree Level Predictions
 Cons
 Also requires large PT’s
and angular separations
 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
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 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
Stephen MRENNA  Fermilab
 Color must be screened
24
Monte Carlo Event Generator
 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 is essential for this to work
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Stephen MRENNA  Fermilab
25
“Monte Carlo” “Event 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 W MAX (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
26
Parton 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
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Stephen MRENNA  Fermilab
27
Parton Showering: More Motivation
Semi-classical description
 Accelerated charges radiate

β

n
  
 en
 (n  β)
dP
e2    2
E


n  (n  β)
c
R
dΩ 4πc
 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)
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Stephen MRENNA  Fermilab
28
Example: gluon emission in * events
Q2
t
u
s
ee  q q g
 α dt 
t  α du 
u 
dσ(q q g)  σ0  s
dzPqq (z)  2   s
dzPqq (z)  2  
Q  2π u
Q 


2π t
z1 when gluon is
Soft, collinear or both
t 0 when gluon is
Soft, collinear or both
s
4 1 z2
z  2 ,Pqq (z) 
Q
3 1 z
s  2pq  p q , t  2pq  pg,u  2p q  pg
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

Stephen MRENNA  Fermilab
Factorization of Mass
Singularities
Probability of one additional
soft emission proportional to
rate without emission
 dN+1 = N S/2 dt/t dz P(z)
29
Tower of emissions described by Sudakov Form Factor
 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
z (t)
1 b,c


dz
z  (t)
α S (t)
Pa bc (z)δt
2π
Sum over all numbers of irresolvable emissions :
z  (t )
 t

α S (t)
'
S(t)  exp  dt b,c  dz
Pa bc (z)   Δ(t0 , t)
2π
 t0

z  (t ' )
z ~ 1 zC , z ~ zC
'
 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
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Stephen MRENNA  Fermilab
30
Virtuality-Ordered PS
Highly virtual
Nearly on-shell
t1  t2  t3
ti  ln(Q i2 )
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Stephen MRENNA  Fermilab
31
Initial State Radiation
 Similar picture, but solving DGLAP for PDFs
BRANCHINGS











NO BRANCHING
"

 

t 1
α
(z,
t
)ˆ
dz
Δ
(t'
)
"
abc
fa (x,t' )  fa (x,t) Δ(t' )   '  dt"
P
(z)
f
(x/z,
t
)
a bc
b
"
t x
z Δ(t )
2π
Increasing parton
virtuality
Parent has more momentum
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Stephen MRENNA  Fermilab
32
Backwards Showering
Sjostrand
- ln(S) 
tMAX

t
z
dt'  dz
z-
α abc (z, t' ) ˆ
x' fa (x', t' )
Pa bc (z)
; x'  x/z
2π
x fb (x,t' )
ˆa bc (z)
α (z, t) P
Δ(t) fa (x,t' )
; Prob(z) abc
fa (x', t' )
fb (x,t) Δ(t' )
2π
z
Marchesini/Webber
 -Q02>-Q12>…>-Qn2
 showering added after
hard scatter with unit
probability
 Something
happens, even if
not resolvable
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Q
2
C
Stephen MRENNA  Fermilab
 Q12
 Q32
 Q22
PRIMORDIAL KT
 QC2
33
Parton Shower is a Resummation
 Analytic Resummation
 Parton Showering
 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 nonperturbative physics
 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
scales
Similar physics, but different approach with
different regimes of applicability
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Stephen MRENNA  Fermilab
34
Comparison of Predictions
Analytic
Resum
Example of
Treating
Kinematics
differently in
shower
Example of Matrix
Element Corrections to
Parton Showering
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Stephen MRENNA  Fermilab
35
Color 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
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Stephen MRENNA  Fermilab
36
Angular-Ordered PS
 Showers should be Angular-Ordered
  = pI • pJ / EI EJ = (1 - cosIJ) ~ IJ2/2
 1 > 2 > 3 …
 Running coupling depends on kT2  z(1-z)Q2

Dead Cone for Emissions




Q2 = E2  < Q2max
Q2max = z2 E2
 < 1 [not 2]
 < /2
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 No emission in backwards
hemisphere
Stephen MRENNA  Fermilab
37
Color Coherence in Practice
 Emission is restricted inside cones defined by
the color flow
Partonic picture
Large N picture
Enhanced
emission
Beam line
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Stephen MRENNA  Fermilab
38
Essential to Describe Data
 3 Jet Distributions in Hadronic Collisions
Full
Coherence
No
Coherence
Soft
emissions
know about
beam line
(large Y)
Partial
Coherence
Pseudorapidity of Gluon Jet
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Stephen MRENNA  Fermilab
39
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
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Stephen MRENNA  Fermilab
40
Parton 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 models to connect with data
 Shower evolves virtualities of partons to a low enough values
where this connection is possible
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Stephen MRENNA  Fermilab
41
Comparison
 Strings (Pythia)
See Bill Gary’s
lectures
 Clusters (Herwig)
 PRODUCTION of
HADRONS is nonperturbative, collective
phenomena
 Careful Modelling of
non-perturbative
dynamics
 Improving data has meant
successively refining
perturbative phase of
evolution
 PERTURBATION THEORY
can be applied down to
low scales if the
coherence is treated
correctly
 There must be nonperturbative physics, but
it should be very simple
 Improving data has meant
successively making nonpert phase more stringlike
STRING model includes some nonperturbative aspect of color coherence
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Stephen MRENNA  Fermilab
42
The Programs
 ISAJET
 Independent fragmentation & incoherent parton
showers
 JETSET (now PYTHIA)
 THE implementation of the Lund string model
 Excellent fit to e+ e- data
 HERWIG
 THE implementation of the cluster model
 OK fit to data, but problems in several areas
 String effect a consequence of full angular-ordering
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Stephen MRENNA  Fermilab
43
W + Jet(s) at the Tevatron
 Good testing ground for
parton showers, LO,NLO
 Large Scale dependence at LO
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 Good agreement with NLO
Stephen MRENNA  Fermilab
44
W + N jet Rates


VECBOS for N hard partons
HERWIG for additional gluon
radiation and hadronization
CTEQ SS 2002


VECBOS for N-1 hard partons
HERWIG for 1 “hard” parton plus …
Stephen MRENNA  Fermilab
45
W + N jet Shapes
 Start with W + N jets from
VECBOS + HERWIG
CTEQ SS 2002
 Start with W + (N-1) jets
from VECBOS + HERWIG
Stephen MRENNA  Fermilab
46
When good Monte Carlos go bad
CDF Run0 Data
VECBOS
starting point
More jets generated
by HERWIG parton
shower
Results are cut dependent
PS only has collinear
part of matrix element
PS has ordering in
angles
CTEQ SS 2002
#events >1 jet
pT>10 GeV/c
>2 jets
>3 jets
>4 jet
Data
213
42
10
VECBOS + HERPRT (Q=<pT>)
W + 1jet 920
178
21
W + 2jet ----213
43
W + 3jet --------42
1
6
10
920
VECBOS+HERPRT(Q=mW)
W + 1jet 920
W + 2jet ---W + 3jet ----
176
213
-----
24
46
42
2
6
7
Normalize 1st bin to data
Stephen MRENNA  Fermilab
47
Correcting 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
48
Parton Showering and Heavy Quarks
 Heavy Quarks look like light quarks at large
angles but are sterile at small angles
Eikonal expressionfor soft gluon emission :
2
 p1
dσ(q q g)
p2  d3p3

 

dσ(q q )
 p1  p3 p2  p3  E3
2
dσ(x3, θ13,r  mQ/E Q )  θ13



  2
2
dσ(x3, θ13,0)
 θ13  r 
2
 Naïve -ordered shower has a cutoff
 > 0 = mQ/EQ = r
 Creates ‘dead cone’
 Virtuality-ordered shower also needs a special
treatment
CTEQ SS 2002
Stephen MRENNA  Fermilab
49
Pythia 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
Not
Significant
Parton Level Mtop
CTEQ SS 2002
Stephen MRENNA  Fermilab
Hadron Level Mtop
50
CTEQ SS 2002
Stephen MRENNA  Fermilab
51
Not
Significant
CTEQ SS 2002
Stephen MRENNA  Fermilab
52
Top 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
53
Correcting 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
54
 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
55
Parton 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
56
PS, Factorization, and Resummation
 b/QT-space resummation yields (N)NLO rate
and “all orders” kinematics
dσ
(h1h2  W  X) 
2
2
dQ dQ T dy
d ~
W(Q T , Q, x1, x2 )  Y
dQ 2T
~
W  (C  f)(C  f)exp(-T) H(Q)
T(Q T , Q) 

Q
2
Q 2T
(C  f)[x] 
Q
dm 

A
ln

m 
m
2
1


  B


dz
x z C(x/z)f(z)


 1

exp T(Q 0 , Q)  f(x, Q T ) 

dσ
d 

 2

At LO,

σ


0
dQ 2T
dQ 2T 
 1

exp T(Q 0 , Q T ) f(x, Q) 


 2



 MW PS algorithm


 Sudakov determines PTW
Soft gluon emissions are
integrated out
 Sudakov contains soft pieces
not in DGLAP
Total rate can be calculated to
any given order in S
 Y = Fixed order-Asymptotic = Overlap!
 Contains negative weights – just aesthetics?
CTEQ SS 2002
Stephen MRENNA  Fermilab
57
Summary of NLO Showering
 Correct the PS for emissions that are not soft/collinear
enhanced
 Reweight by (ME2PS)/(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
58
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
59
Related Ideas
 QCD Matrix Elements + Parton Showers
 Catani/Kraus/Kuhn/Webber & Lönnblad
 Attempts to piece together many tree level processes
using PS
 Generate all ZN 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
60
Conclusions
 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
61
Interconnection
Bose-Einstein
Topics Not
Discussed
Particle
Decay
Remnant
Hadronization
Dh/i (z, Q 2 )
“Underlying
Event”
ISR
Hard Scatter
FSR
Resonance
Decay
Pqq(z, Q 2 )
fi/p (x, Q )
2
CTEQ SS 2002
Pqq(z, Q 2 )
ˆ
σ
Stephen MRENNA  Fermilab
62
Topics 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
63
Overall 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)
CTEQ SS 2002
Stephen MRENNA  Fermilab
64