CMS Generator WorkshopCERN

3 November 2004

Monte Carlos for LHCTorbjorn Sjostrand

CERN and Lund University

Generator and Physics OverviewMatrix Elements vs. Parton ShowersUnderlying Event and Hadronization

Outlook

Event Generator Position

“real life”

Machine ⇒ eventsproduce

events

“virtual reality”

Event Generator

observe & store events

Detector, Data Acquisition Detector Simulation

what is

knowable?Event Reconstruction

compare real and

simulated dataPhysics Analysis

conclusions, articles, talks, . . .

“quick

and dirty”

where and why?

• detector requirements

• analysis strategies

• acceptance corrections

physics is complex

Event Physics Overview

Structure of the basic generation process:

1) Hard subprocess:|M|2, Breit-Wigners,

parton densities.

q

q Z0 Z0

h0

2) Resonance decays:includes correlations.

Z0

µ+

µ−

h0

W−

W+

ντ

τ−

s

c

3) Final-state parton showers.

q → qg

g → gg

g → qq

q → qγ

4) Initial-state parton showers.

g

q

Z0

5) Multiple parton–partoninteractions.

6) Beam remnants,with colour connections.

p

p

b

b

ud

ud

u

u

�

�

�

�

�

5) + 6) = Underlying Event

7) Hadronization

c

g

g

b

D−s

Λ0

n

η

π+

K∗−

φ

K+

π−

B0

8) Ordinary decays:hadronic, τ , charm, . . .

ρ+

π0

π+

γ

γ

9) QCD interconnection effects:

e−

e+

W−

W+

q3

q4

q2

q1

�

�

π+

π+

�

� BE

a) colour rearrangement(⇒ rapidity gaps?);b) Bose-Einstein.

10) The forgotten orunexpected: a chain

is never stronger thanits weakest link!

Many aspects still poorly understood,but most good enough to work with

Generator Landscape

Hard Processes

Resonance Decays

Parton Showers

Underlying Event

Hadronization

Ordinary Decays

General-Purpose

HERWIG

PYTHIA

ISAJET

SHERPA

Specialized

a lot

HDECAY, . . .

Ariadne/LDC, NLLjet

DPMJET

none (?)

TAUOLA, EvtGen

specialized often best at given task, but need General-Purpose core

The Smaller Picture: Subprocess Survey

Kind Process PYT HER ISA

QCD & related Soft QCD ? ? ?Hard QCD ? ? ?Heavy flavour ? ? ?

Electroweak SM Single γ∗/Z0/W± ? ? ?

(γ/γ∗/Z0/W±/f/g)2 ? ? ?Light SM Higgs ? ? ?Heavy SM Higgs ? ? ?

SUSY BSM h0/H0/A0/H± ? ? ?SUSY ? ? ?R/ SUSY ? ? —

Other BSM Technicolor ? — (?)New gauge bosons ? — —Compositeness ? — —Leptoquarks ? — —H±± (from LR-sym.) ? — —Extra dimensions (?) (?) (?)

. . . but processes usually only in lowest nontrivial order

The Bigger Picture

Process Selection

Resonance Decays

Parton Showers

Multiple Interactions

Beam Remnants

Hadronization

Ordinary Decays

Detector Simulation

ME Generator

ME Expression

SUSY/. . .spectrum

calculation

Phase Space

Generation

PDF Library

τ Decays

B Decays

=⇒ need standardized interfaces

The Les Houches Accord

Specialized Generator

=⇒ Hard Process

Les Houches Interface

HERWIG or PYTHIA

(Resonance Decays)

Parton ShowersUnderlying Event

HadronizationOrdinary Decays

Some Specialized Generators:• AcerMC: ttbb, . . .• ALPGEN: W/Z+ ≤ 6j,

nW + mZ + kH+ ≤ 3j, . . .• AMEGIC++: generic LO• CompHEP: generic LO• GRACE+Bases/Spring:

generic LO+ some NLO loops• GR@PPA: bbbb• MadCUP: W/Z+ ≤ 3j, ttbb

• MadGraph+HELAS: generic LO• MCFM: NLO W/Z+ ≤ 2j,

WZ, WH, H+ ≤ 1j

• O’Mega+WHIZARD: generic LO• VECBOS: W/Z+ ≤ 4j

Apologies for all unlisted programs

Matrix Elements vs. Parton Showers

ME : Matrix Elements+ systematic expansion in αs (‘exact ’)+ powerful for multiparton Born level+ flexible phase space cuts− loop calculations very tough− negative cross section in collinear regions

⇒ unpredictive jet/event structure− no easy match to hadronization p2

⊥,θ2,m2

dσdp2

⊥

, dσdθ2, dσ

dm2

real

virtual

PS : Parton Showers− approximate, to LL (or NLL)− main topology not predetermined

⇒ inefficient for exclusive states+ process-generic ⇒ simple multiparton+ Sudakov form factors/resummation

⇒ sensible jet/event structure+ easy to match to hadronization p2

⊥,θ2,m2

dσdp2

⊥

, dσdθ2, dσ

dm2

real×Sudakov

Parton Shower Approach

3 common algorithms:HERWIG: θ-ordered emissions (ISR & FSR)PYTHIA: M2, Q2-ordered emissions (ISR & FSR)ARIADNE: p⊥-ordered emissions (FSR primarily)

Steady evolution:HERWIG: new angular evolution variable⇒ improved phase space coverage,

better massive quark treatmentPYTHIA: p⊥-ordered emissions (ISR & FSR)⇒ improved coherence,

interleaved multiple interactions,(to prove:) simplified vetoed parton showers

LDCMD, CASCADE: CCFM generators for ISR at small x

Matrix Elements and Parton Showers

Marriage desirable! But how?

Problems: • gaps in coverage?• doublecounting of radiation?• Sudakov?• NLO consistency?

Much work ongoing =⇒ no established orthodoxy

Three main areas, in ascending order of complication:

1) Match to lowest-order nontrivial process — merging

2) Combine leading-order multiparton process —vetoed parton showers (cf. talk by M. Mangano)

3) Match to next-to-leading order process —MC@NLO (covered in talk by S. Frixione)

Merging

= cover full phase space with smooth transition ME/PS

Want to reproduce WME =1

σ(LO)

dσ(LO + g)

d(phasespace)

by shower generation + correction procedure

wanted︷ ︸︸ ︷

WME =

generated︷ ︸︸ ︷

WPS

correction︷ ︸︸ ︷

WME

WPS

• Exponentiate ME correction by shower Sudakov form factor:

WPSactual(Q

2) = WME(Q2) exp

(

−∫ Q2

max

Q2WME(Q′2) dQ′2

)

• Normally several shower histories ⇒ ∼equivalent approaches

• Use dσ = K σ0 dWPS

where K = 1 + O(αs) is set separately (ambiguity of O(α2s ))

PYTHIA performs merging with generic FSR a → bcg ME,in SM: γ∗/Z0/W± → qq, t → bW+, H0 → qq,and MSSM: t → bH+, Z0 → qq, q → q′W+, H0 → qq, q → q′H+,χ → qq, χ → qq, q → qχ, t → tχ, g → qq, q → qg, t → tg

g emission for different Rbl3 (yc): mass effects

colour, spin and parity: in Higgs decay:

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

0 0.02 0.04 0.06 0.08 0.1

R3bl

yc

VectorAxial vector

ScalarPseudoscalar

angle (degrees)

PYTHIA ISR: only qq → γ∗/Z0/W± and gg → H0 (for mt → ∞)(but K factor not implemented here)

HERWIG: fewer for FSR, comparable for ISR

Vetoed Parton ShowersS. Catani, F. Krauss, R. Kuhn, B.R. Webber, JHEP 0111 (2001) 063; L. Lonnblad, JHEP0205 (2002) 046;

F. Krauss, JHEP 0208 (2002) 015; S. Mrenna, P. Richardson, JHEP0405 (2004) 040;

M.L. Mangano, in preparation

Generic method to combine ME’s of several different ordersto NLL accuracy; will be a ‘standard tool’ in the future

Basic idea:• consider (differential) cross sections σ0, σ1, σ2, σ3, . . .,

corresponding to a lowest-order process (e.g. W or H production),with more jets added to describe more complicated topologies,in each case to the respective leading order

• σi, i ≥ 1, are divergent in soft/collinear limits• absent virtual corrections would have ensured “detailed balance”,

i.e. an emission that adds to σi+1 subtracts from σi

• such virtual corrections correspond (approximately)to the Sudakov form factors of parton showers

• so use shower routines to provide missing virtual corrections⇒ rejection of events (especially) in soft/collinear regions

Veto scheme:1) Pick hard process, mixing according to σ0 : σ1 : σ2 : . . .,

above some ME cutoff, with large fixed αs0

2) Reconstruct imagined shower history (in different ways)3) Weight Wα =

∏

branchings(αs(k2⊥i)/αs0) ⇒ accept/reject

CKKW-L:4) Sudakov factor for non-emission

on all lines above ME cutoffWSud =

∏

“propagators′′

Sudakov(k2⊥beg, k2

⊥end)

4a) CKKW : use NLL Sudakovs4b) L: use trial showers5) WSud ⇒ accept/reject6) do shower,

vetoing emissions above cutoff

MLM:4) do parton showers5) (cone-)cluster

showered event6) match partons and jets7) if all partons are matched,

and njet = nparton,keep the event,else discard it

Multiple Interactions

Consequence of composite nature of hadrons!

Evidence:

• direct observation: AFS, UA1, CDF

• implied by width of multiplicitydistribution + jet universality: UA5

• forward–backward correlations: UA5

• pedestal effect: UA1, H1, CDF

One new free parameter: p⊥min

1

2σjet =

∫ s/4

p2⊥min

dσ

dp2⊥

dp2⊥ ⇐=

∫ s/4

0

dσ

dp2⊥

p4⊥

(p2⊥0 + p2

⊥)2dp2

⊥

g g

d

resolved

g g

d

screened

λ ∼ 1/p⊥

Measure ofcolour screening length d

in hadron:p⊥min 〈d〉 ≈ 1(= h)

Event Structure and Beam Remnants

(TS & P.Z. Skands, JHEP 03 (2004) 053)

pg

u

s

s

u

d

tohardint.

beamremn.

Need to assign:

• correlated flavours• correlated xi = pzi/pztot

• correlated primordial k⊥i

• correlated colours

for initiators and remnants

+ showers

Example: parton densities after first interaction:

• valence: scale by #remaining/#original

• sea: bookkeep ‘companion’ by

s(x′;x) ∝g(x + x′)

x + x′Pg→ss

(x

x + x′

)

Interleaved Multiple Interactions

(TS & P.Z. Skands, hep-ph/0408302)

interactionnumber

p⊥

hard int.

1

mult. int.

2

mult. int.

3

mult int.

4

p⊥max

p⊥min

p⊥1

p⊥2

p⊥3

p⊥4

p⊥23

ISR

ISR

ISR

ISR

p′⊥1

Data comparisons:usually ∼ Tune Abut need good tuning

0.3

0.4

0.5

0.6

50 100 150nch

<p ⊥

>

Tevatron Run II: <p⊥>(nch)

Tune ARapSharp ISRLow FSRHigh FSR

〈p⊥〉(nch) problem:colour correlations?

Hadronization: Lund String Model

In QCD, for large charge separation, field lines seem to be compressedto tubelike region(s) ⇒ string(s)

String tension: F (r) ≈ const = κ ⇐⇒ V (r) ≈ κr

Confirmed e.g. by quenched lattice QCDUnquenched =⇒ nonperturbative string breakings

q (r)

g (rb)

q (b)

snapshots of string position

strings stretched

from q (or qq) endpoint

via a number of gluons

to q (or qq) endpoint

Gluon = kink on string,

carrying energy

and momentum.

Force ratiogluon/ quark = 2,

cf. QCD NC/CF = 9/4

• Few parameters to describe energy–momentum structure!• Many parameters to describe flavour composition!

Lund hadronization news: fragmentation of junction topology,in R-parity violating SUSY decays χ0

1 → uds,or when 2 valence quarks kicked out of proton beam(TS & P.Z. Skands, NPB659 (2003) 243)

lab frame

z

x

u (r)

d (g)

s (b)

J

junctionrest frame

u (r)

d (g)

s (b)

J

120◦

120◦

120◦

flavour space

q3

q4

q5q3 q2 q2 qq1 qq1 u

q4

d

q5

s

More complicated

(but ≈solved) with

gluon emission and

massive quarks

Also new: fragmentation of stable gluino

Hadronization: HERWIG Cluster Model

Introduce forcedg → qq branchings:

●

subprocess

underlyingevent

p

jet jet

p

hard

●

+

0Z

ee −

� �� �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �

� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �� � � � � � � � � �

� � � � �� � � � �

� �� �� �

� �� � � � � � �� � � � �� � � � �

� � � � �� � � � �� � � � �

� �� �� �� � ��� ���

��� ��� ��� � �� � �� � �� � �� � �� � �

� � � � �� � � � �� � � � �� � � � �

� � � � �� � � � �� � � � �� � � � �

� � � � �� � � � �� � � � �� � � � �

� � � � �� � � � �� � � � �� � � � � �

! !" "# ## #$ $$ $

%�% &�&

'�' (�(

)*

+�+ ,�,

●

Large-mass clusters require special attention• Many parameters to describe energy–momentum structure!

• Few parameters to describe flavour composition!

Standards and Interfaces

? ? ? PDG particle codes

? ? ? HEPEVT hadron-level Event Record

? ? ? Les Houches Accord User Process Interface

? ? ? LHAPDF: Les Houches Accord Parton Density Functions(supersedes PDFLIB)

? ? ? SLHA: SUSY mass/coupling spectrum calculator interface

?? HepMC hadron-level Event Record in C++

?? JetWeb/HZtools: automated data comparisons

? StdHep, StdHepC++: converts non-standard particle codes

? HepPDT particle data tables in C++

? For C++ era: (improved) Les Houches Interface for HO or NLO ME’s,standardized cuts, standard cone clustering algorithm, . . .

On To C++

PYTHIA7 project =⇒ ThePEGToolkit for High Energy Physics Event Generation:

general-purpose framework, kinematics, ME machinery, decays, . . .(L. Lonnblad; S. Gieseke, A. Ribon, P. Richardson)

ARIADNE/LDC: to do ISR/FSR showers, multiple interactions(L. Lonnblad; N. Lavesson)

PYTHIA7 leftover: old showers + incomplete string fragmentation⇒ restart from scratch 2 months ago (TS)

HERWIG++: new final-state shower + improved cluster modeland decays ⇒ e+e− complete, pp underway

(B.R. Webber; S. Gieseke, A. Ribon, P. Richardson, M. Seymour, P. Stephens)

SHERPA: does pp, but partly wrappers to PYTHIA Fortran; has CKKW(F. Krauss; T. Gleisberg, S. Hoeche, A. Schaelicke, S. Schumann, J. Winter)

• Conversion effort: everything takes longer and costs more(as for LHC machine, detectors and software)

• The physics hurdle is as steep as the C++ learning curve

Outlook

Generators in state of continuous development:• better & more user-friendly general-purpose

matrix element calculators+integrators• new libraries of physics processes, also to NLO

• more precise parton showers• better matching matrix elements ⇔ showers

• improved models for underlying events / minimum bias• upgrades of hadronization and decays

• moving to C++⇒ always better, but never enough

But what are the alternatives, when event structures are complicatedand analytical methods inadequate?