Monte Carlo Event Generators for the LHC - uni-mainz.de

Monte Carlo Event Generators for the LHCor How to relate Theory with Experiment?

Steffen Schumann

ITP, University of Heidelberg

EMG Annual Retreat 2010

Bingen am Rhein

27. - 29.09. 2010

Introduction & Monte Carlo Techniques

Hard Processes at (Next-to-)Leading Order

Parton Showers & Matching with Fixed Order

Multiple Interactions, Hadronization & Hadron Decays

Steffen Schumann Monte Carlo Event Generators for the LHC

http://www.thphys.uni-heidelberg.de

http://www.montecarlonet.org

http://www.sherpa-mc.de

http://www.thphys.uni-heidelberg.de


Outline Lecture 2


The QCD parton-shower pictureMerging parton showers with multi-leg tree-level amplitudesMatching to One-Loop computations

Multiple Interactions, Hadronization & Hadron Decays

Remnant-Remnant interactionsThe cluster hadronization model






Recap: The Hard Process

The Hard Process

σpp→Xn =∑a,b

∫dxadxb fa(xa, µ

2F )fb(xb, µ

2F ) |Mab→Xn |2 dΦn

+ |Mab→Xn |2 fundamental physics, interferences, off-shell effects, full colour

+ accounts for high-pT , well separated partons

− few-parton final states only, poor for log-enhanced phase-space regions

'

&

$

%|Mqq→e+e−g|2

γ∗/Z0

0 25 50 75 100 125 150 175 200pT [GeV]

10-4

10-3

10-2

10-1

100

101

dσ/d

p T [p

b/G

eV]

CDF 2000e

+e

-g (scaled)

pT(e+e

-) @ Tevatron Run1

0 5 10 15 20pT [GeV]

5

10

15

20

25

30

dσ/d

p T [p

b/G

eV]

∣∣∣∣Mqq→e+e−g

∣∣∣∣2 ∼ ∣∣∣∣Mqq→e+e−∣∣∣∣2 αS (µ2

R )

p2T

σpp→e+e−g

∼ σpp→e+e−αS (µ2

R ) logpmaxT

pminT

|M|2 factorise in IR limes (universal) large logs need to be resummed to all orders



Recap: The Hard Process

The Hard Process

σpp→Xn =∑a,b

∫dxadxb fa(xa, µ

2F )fb(xb, µ

2F ) |Mab→Xn |2 dΦn

+ |Mab→Xn |2 fundamental physics, interferences, off-shell effects, full colour

+ accounts for high-pT , well separated partons

− few-parton final states only, poor for log-enhanced phase-space regions

'

&

$

%|Mqq→e+e−g|2

γ∗/Z0

0 25 50 75 100 125 150 175 200pT [GeV]

10-4

10-3

10-2

10-1

100

101

dσ/d

p T [p

b/G

eV]

CDF 2000e

+e

-g (scaled)

pT(e+e

-) @ Tevatron Run1

0 5 10 15 20pT [GeV]

5

10

15

20

25

30

dσ/d

p T [p

b/G

eV]

∣∣∣∣Mqq→e+e−g

∣∣∣∣2 ∼ ∣∣∣∣Mqq→e+e−∣∣∣∣2 αS (µ2

R )

p2T

σpp→e+e−g

∼ σpp→e+e−αS (µ2

R ) logpmaxT

pminT

|M|2 factorise in IR limes (universal) large logs need to be resummed to all orders



QCD Bremsstrahlung

accelerated charges radiate

QED: electrons (charged) emit photons

QCD: quarks (coloured) emit gluons

but, gluons coloured as well gluons emit gluons

QCD radiation enhanced in the infra-red: soft / collinear emissions

real-emission matrix elements factorize in collinear limit [universal]

|t| = |p2b|, z = Eb/Ea t = p2

a , z = Eb/Ea

dσn+1 = dσndt

tdzαS

2πPba(z)

iteration / Markov process

parton shower MC



Parton Shower: Toy Model

one particle species G only, starting scale t = tmax

GG

G

∝ PGG (z)dPG = PGG (z)

dt

tdz

given t→ I (t) =

∫ z+(t)

z−(t)

dzPGG (z)

probability of no-branching between tmax and t < tmax

PG ,no−branch(t, tmax) = exp

−tmax∫t

dt ′

t ′I (t ′)

→ ordering parameter t

probability for branching to occur at t < tmax

dPG ,branch

dt= −dPG ,no−branch

dt= I (t) exp

−tmax∫t

dt ′

t ′I (t ′)

lends itself to simulation, parton cascade



Parton Shower: Toy Model

a simple shower algorithm

determine scale of next emission by solving

# = exp

−tmax∫t

dt ′

t ′I (t ′)

for t

select energy fraction z according to PGG (z)

construct kinematics of emitted particle

reset tmax = t and start afresh

The full QCD picture

Pqq, Pgq, Pgq, Pgg , αS(z , t), choice of evolution variable [coherence effects]

shower has to stop at some infra-red cut-off to ∼ O(1GeV2)

below perturbative approach no-longer applies

invoke hadronization model



The QCD Parton Shower picture

Shower evolution as a probabilistic processconstruct explicitely the initial- & final-state partons history/fatesuccessive branching of incoming and outgoing legsencoded in QCD evolution of PDFs and Fragmentation Functions exclusive partonic final states with Ptot = Phard · PIS · PFS

What are Parton Showers good for?evolve parton ensemble from high- to low scale t0 ∼ O(1GeV2) link the hard process to universal hadronization models

in turn resummation of large kinematical logarithms [to (N)LL accuracy]

model intra-jet energy flows: jets become multi-parton objects



Parton Shower in real QCDQCD evolution of PDFs (Fragmentation Functions)

∂fa(z, t)

∂ log(t/t0)=

∫ ζmax

z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)− fa(z, t)

∫ ζmax

ζmin

dζ∑b=q,g

Kba(ζ, t)

Kba(ζ, t) - evolution kernels of the scheme IR factorization scheme e.g. αs/2π Pba(ζ)

Kba(ζ, t)IR→ 1

σ(n)a (Φn)

dσ(n+1)b (ζ, t; Φn)

d log(t/t0) dζ

ζ, t - splitting, evolution variable separate resolved from unresolved emissions

∆a(t0, t) = exp

−∫ t

t0

dt

t

∫ ζmax

ζmin

dζ∑b=q,g

Kba(ζ, t)

∂

∂ log(t/t0)

fa(z, t)

∆a(t0, t)=

1

∆a(t0, t)

∫ ζmax

z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)

fa(z, t) = ∆a(t0, t)fa(z, t0) +

t∫t0

dt

t

∆(t0, t)

∆(t0, t)

ζmax∫z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)

∆(t0, t) probability for evolving from t0 to t without branching [Sudakov Form Factor]




∂fa(z, t)

∂ log(t/t0)=

∫ ζmax

z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)− fa(z, t)

∫ ζmax

ζmin

dζ∑b=q,g

Kba(ζ, t)


Kba(ζ, t)IR→ 1

σ(n)a (Φn)


d log(t/t0) dζ


∆a(t0, t) = exp

−∫ t

t0

dt

t

∫ ζmax

ζmin

dζ∑b=q,g

Kba(ζ, t)

∂

∂ log(t/t0)

fa(z, t)

∆a(t0, t)=

1

∆a(t0, t)

∫ ζmax

z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)

fa(z, t) = ∆a(t0, t)fa(z, t0) +

t∫t0

dt

t

∆(t0, t)

∆(t0, t)

ζmax∫z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)





∂fa(z, t)

∂ log(t/t0)=

∫ ζmax

z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)− fa(z, t)

∫ ζmax

ζmin

dζ∑b=q,g

Kba(ζ, t)


Kba(ζ, t)IR→ 1

σ(n)a (Φn)


d log(t/t0) dζ


∆a(t0, t) = exp

−∫ t

t0

dt

t

∫ ζmax

ζmin

dζ∑b=q,g

Kba(ζ, t)

∂

∂ log(t/t0)

fa(z, t)

∆a(t0, t)=

1

∆a(t0, t)

∫ ζmax

z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)

fa(z, t) = ∆a(t0, t)fa(z, t0) +

t∫t0

dt

t

∆(t0, t)

∆(t0, t)

ζmax∫z

dζ

ζ

∑b=q,g

Kba(ζ, t) fb(z

ζ, t)




Parton Shower in real QCD

Initial- and Final-State Parton Showers

Starting from dσ, generate more radiation

P(IS)no, a(z , t, t′) =

∆a(t0, t′) fa(z , t)

∆a(t0, t) fa(z , t′)& P(FS)

no, a(t, t′) =∆a(t0, t

′)

∆a(t0, t)

+ accounts for multiple soft/collinear emissions resummation of large logs

+ exclusive radiation pattern/ hard cross section preserved

− lacks hard/large angle emissions

− leading-colour contributions only

0 25 50 75 100 125 150 175 200pT [GeV]

10-4

10-3

10-2

10-1

100

101

dσ/d

p T [p

b/G

eV]

CDF 2000e

+e

-g (scaled)

pT(e+e

-) @ Tevatron Run1

0 5 10 15 20pT [GeV]

5

10

15

20

25

30

dσ/d

p T [p

b/G

eV]

0 25 50 75 100 125 150 175 200p

T [GeV]

10-4

10-3

10-2

10-1

100

101

dσ/d

p T [

pb/G

eV]

CDF 2000CS show. + Py 6.2 had.CS show. + Py 6.2 had. (enhanced start scale)

0 5 10 15 20p

T [GeV]

5

10

15

20

25

30

dσ/d

p T [

pb/G

eV]



Subtraction formalism based ShowersCatani–Seymour local subtraction term∫

m+1

dσA =∑

dipoles

∫m

dσB ⊗∫

1

dVdipole

→ universal dipole term←spin- & color correlation

Ansatz: Complete factorisation through

projection onto leading term in 1/Nc

spin averaged dipole terms Vdipole → 〈Vdipole〉

Shower Algorithm

color connected emitter–spectator ’dipoles’

subsequent branchings of type II, IF, FI, FF

exact momentum mappings invertable

emissions ordered in k2⊥

i j k

m-parton LO-ME Splitting operator

4 2e

m-parton state splitting operator

pi pk

(pi pj )(pk pj )=

pi pk

(pi pj )(pi + pk )pj

+pi pk

(pk pj )(pi + pk )pj

Dipole subtraction based: Dinsdale et al. Phys. Rev. D 76 (2007) 094003, Krauss, S. JHEP 0803 (2008) 038

Antenna subtraction based: Krauss, Winter JHEP 0807 (2008) 040, Giele et al. Phys. Rev. D 78 (2008) 014026



Parton Showers at work

Dijet azimuthal decorrelation [Krauss, S. JHEP 0803 (2008) 038, DØ data Phys. Rev. Lett. 94 (2005) 221801]

∆φ dijet (rad)

1/σ

dije

t dσ

dije

t / d∆φ

dije

t

pT max > 180 GeV (×8000)

130 < pT max < 180 GeV (×400)

100 < pT max < 130 GeV (×20)

75 < pT max < 100 GeV

LO

NLO

NLOJET++ (CTEQ6.1M)

µr = µf = 0.5 pT max

DØ

10-3

10-2

10-1

1

10

102

103

104

105

π/2 3π/4 π

only the two leading jets need to be reconstructed strong test of the initial- and final-state radiation pattern



Parton Showers at work

Dijet azimuthal decorrelation [Krauss, S. JHEP 0803 (2008) 038, DØ data Phys. Rev. Lett. 94 (2005) 221801]

π/2 3π/4 π

∆φdijet

(rad)

10-3

10-2

10-1

100

101

102

103

104

105

1/σ

dij

et dσ

dij

et/d∆φ

dij

et

75 < pTmax

< 100 GeV

100 < pTmax

< 130 GeV (x20)

130 < pTmax

< 180 GeV (x400)

pTmax

> 180 GeV (x8000)

∆φdijet

distribution @ Tevatron Run II

points: D0 data 2005

histo: CS show. + Py 6.2 had.

only the two leading jets need to be reconstructed strong test of the initial- and final-state radiation pattern



Combining ME & PS

Problem: QCD MEs and PS deal with the same physics!double counting of phase-space configurations

unpopulated phase-space regions

Aim: Consistent description of real QCD emissions!proper description of soft/collinear and hard emissions

combine QCD matrix elements of different parton multiplicity with showers

[CKKW: Catani et al. ’01, MLM: Mangano et al. ’01, CKKW-L: Lonnblad ’01]

Construction criteria:describe few hardest emissions through full matrix elements

Kba(z, t) →1

dσ(n)a (Φn)

dσ(n+1)b

(z, t; Φn)

d log(t/t0) dz

preserve shower-evolution equation i.e. logarithmic accuracy

avoid double counting or empty phase-space regions

slice emission phase space by parton-separation criterion Qba(z, t)



Combining ME & PS: sneak preview

Drell-Yan pT distribution [Krauss,Schalicke, S., Soff Phys. Rev. D 70 (2004) 114009]

/ GeV Z

P0 20 40 60 80 100 120 140 160 180 200

10-3

10-2

10-1

1

10pt Z

Z + 0 jet

Z + 1 jet

Z + 2 jet

Z + 3 jet

CDF

Ge

Vp

b

/

dPσ

d

/ GeV Z

P0 5 10 15 20 25 30 35 40 45 50

G

eV

pb

/

d

Pσd

1

10

pt Z

Z + 0 jet

Z + 1 jet

Z + 2 jet

Z + 3 jet

CDF



Solution part 1: Slicing the phase space

Phase-space separation

KPSba (z , t) = Kba(z , t) Θ

[Qcut − Qba(z , t)

]← shower regime

KMEba (z , t) = Kba(z , t) Θ

[Qba(z , t)− Qcut

]← matrix-element regime

⇒ Qba(z , t) has to identify logarithmically enhanced phase-space regions

Consequences

Sudakov form factor and shower no-branch probabilities factorize

∆a(t0, t) = ∆PSa (t0, t) ∆ME

a (t0, t)

P(IS)no, a(z, t, t′) = P(IS) PS

no, a (z, t, t′) P(IS) MEno, a (t, t′) =

∆PSa (t0, t

′) fa(z, t)

∆PSa (t0, t) fa(z, t′)

∆MEa (t0, t

′)

∆MEa (t0, t)

need to constrain shower emissions to Q < Qcut

matrix elements need to be reweighted [made exclusive quantities]

→ think of ME’s as predetermined shower emissions, truncated shower



Solution part 2: Defining PS histories

Interpret ME as if produced by PS

Identify most likely splittingacc. to PS branching probability

Combine partons into mother partonacc. to inverse PS kinematics

Continue until 2→ 2 core process

shower specific cluster algorithm

predetermined shower emissions

PS starts at core processcan radiate “between” ME emissions

ME branchings must be respectedevolution-, splitting- & angular variable preserved

truncated shower

Example branching history

NNLO

cluster once

find some t

NLO

t

cluster twice

find some t′

LOt′

t



Solution part 3: Truncated shower

Assume ME splittings at t and t ′ > t

Shower emission below Qcut

t′Q > Qcut

tQ > Qcut

tQ < Qcut

> >

emission accepted

large-angle soft emissions

soft color coherence

approx. in CKKW only

Shower emission above Qcut

↔ N3LOLO

t′

t entire event is rejected

Sudakov suppression PMEno, a(t, t ′)

to be described by ME instead

σtot preserved at LO



Matrix Elements and Parton Showers: ME⊕PS

How to attach shower to an N-parton ME?

The emerging algorithm [Hoche, Krauss, S., Siegert JHEP 0905 (2009) 053]

ME legs pre-determined shower emissionsdetermined by clustering inverse to the shower

→ pseudo shower history for MEs

PS starts off a reconstructed 2→ 2 corecan radiate gluons off “intermediate” lines→ Truncated Shower

ME branchings must be respectedevolution-, splitting- & angular variables k2

⊥, z, φ preserved

veto event if shower emission above Qcut

preserves the log-accuracy of the shower

implementations

Sherpa-1.2 [Hoche, Krauss, S., Siegert JHEP 0905 (2009) 053]

Herwig for e+e− [Hamilton, Richardson, Tully JHEP 0911 (2009) 038]

pseudo shower history

NNLO

cluster once

find k2⊥;z;φ

NLO

k2⊥

cluster twice

find k′2⊥ ;z′;φ′

LOk′2⊥

k2⊥

Truncated ShowerQ < Qcut Q > Qcut

N3LOLO

k′2⊥

k2⊥



ME⊕PS: facts & figures

Qcut and/or Nmax variation should affect σtot only beyond (N)LL

Example: DY-pair production σtot @ Tevatron

Nmax0 1 2 3 4 5 6

Qcut

20 GeV192.6(1)

191.0(3) 190.5(4) 189.0(5) 189.4(7) 188.2(8) 189.9(10)30 GeV 192.3(2) 192.7(2) 192.6(3) 192.9(3) 192.7(3) 193.2(3)45 GeV 193.6(1) 194.4(1) 194.3(1) 194.4(1) 194.6(2) 194.4(1)

LO

Nmax = 6

Nmax = 5

Nmax = 4

Nmax = 3

Nmax = 2

Nmax = 1

20 30 45

0.96

0.98

1.0

1.02

1.04

Qcut/GeV

σ/

σ(LO)

“merging systematics” of σtot < ±3%




Jet rates and -spectra improved compared to pure PS simulationdue to exact real emission ME’s

Example: DY-pair production σe+e−+NjetCDF Data: PRL 100 (2008) 102001

b

b

b

Nmax = 0

Nmax = 1

Nmax = 2

Nmax = 3

datab

10 1

10 2

10 3

10 4

σ(N

jet)

(scaledto

firstbin)

1 2 3

0.6

0.8

1

1.2

1.4

Njet

MC/data

Note: σtot preserved but big effectson rare events!

e+ e−e+

e− e+ e−

e+ e−e+

e− e+ e−

e+ e−e+

e− e+ e− e+ e−

Qcut = 30 GeV




Variation of Qcut should affect distributions only beyond (N)LLbut Qcut must be in range where PS approximation is valid

Example: All-jets pT ’s in DY-pair production CDF Data: PRL 100 (2008) 102001

b

bbb

bb

b

b

b

b

b

Qcut = 20GeV

Qcut = 30GeV

Qcut = 45GeV

datab

10−1

1

10 1

10 2

dσ/d

p⊥(jet)forN

jet≥

1

50 100 150 200 250 300 350 400

0.6

0.8

1

1.2

1.4

p⊥(jet) [GeV]

MC/data

b

b

b

b

b

b

b

Qcut = 20GeV

Qcut = 30GeV

Qcut = 45GeV

datab

10−1

1

10 1

10 2

dσ/d

p⊥(jet)forN

jet≥

2

50 100 150 200 250 300

0.6

0.8

1

1.2

1.4

p⊥(jet) [GeV]

MC/data

Nmax = 5 Nmax = 5


http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=eprint+0711.3717


Matching Parton Showers with NLO: NLO⊕PS

Objectives:

Born observable (e.g. total rate) accurate to NLO

first/hardest emission according to real emission

further collinear/soft emissions according through shower

→ resolve double counting for the first/hardest emission

→ preserve log-resummation of the shower scheme

The MC@NLO approach

[Frixione, Webber JHEP 0206 (2002) 029]

modified subtraction in σNLO

O(αS) shower exp. removed

shower specific

first emission gets corrected

implemented for Herwig shower

many processes [also BSM]

The POWHEG approach

[Nason JHEP 0411 (2004) 040]

dσB → dσB to get NLO rate

hardest shower emission from σR

vetoed & truncated shower

used with Pythia/Herwig

Powheg-Box

recently automated in Sherpa



Matching Parton Showers with NLO calculations

Example: top-pairs @ LHC

[Frixione et al. JHEP 0308 (2003) 007]

Example: Z − pT @ Tevatron

[Hoche et al. arXiv:1008.5399]

[DØ data arXiv:1006.0618]

b bbbbb

b

b

b

b

b

b

b

DØ datab

POWHEG

ME+PS (1-jet) × 1.2LO+PS × 1.2

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1Z boson pT

1/

σd

σ/dp⊥(Z

)

0 50 100 150 200 250 300

0.6

0.8

1

1.2

1.4

p⊥(Z) [GeV]

MC/data



Pull the rabbit: MEnloPS

Objective: combine virtues of ME⊕PS & NLO⊕PS MEnloPS

inclusive rate accurate to NLOhigher emissions from tree-level matrix elementsall supplemented/combined with parton showers

Hamilton, Nason JHEP 1006 (2010) 039

jet multiplicities in pp → W− + X @ LHC

Hoche et al. arXiv:1009.1127

2nd jet pT in gg → h → ττ + X @ LHC

MENLOPS (3-jet)ME+PS (3-jet) × 2.1POWHEG

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Transverse momentum of second jet

dσ/dp⊥(jet

2)[pb/GeV

]

10 2 10 3

0.6

0.8

1

1.2

1.4

p⊥(jet 2) [GeV]

Ratio



Pull the rabbit: MEnloPS

Objective: combine virtues of ME⊕PS & NLO⊕PS MEnloPS

inclusive rate accurate to NLOhigher emissions from tree-level matrix elementsall supplemented/combined with parton showers

Hamilton, Nason JHEP 1006 (2010) 039

jet multiplicities in pp → W− + X @ LHC

Hoche et al. arXiv:1009.1127

2nd jet pT in gg → h → ττ + X @ LHC

MENLOPS (3-jet)ME+PS (3-jet) × 2.1POWHEG

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Transverse momentum of second jet

dσ/dp⊥(jet

2)[pb/GeV

]

10 2 10 3

0.6

0.8

1

1.2

1.4

p⊥(jet 2) [GeV]

Ratio



Summary: Parton Showers & Matching with Fixed Order

exclusive generation of multiple emissions

guided by QCD evolution equations

Multijet ME-PS merging sustainable approach to describe multijet events

hard emissions through exact tree-level matrix elements(intra) jet evolution through truncated QCD parton showers

complementary ansatz: showers matched to NLO matrix elements

latest: combination of both approaches MEnloPS

ultimate goal: combine NLO for different multiplicities plus showers



Leaving the perturbative ground:

The Underlying Event & Hadronization



The Underlying Event: remnant-remnant interactions

Definition: An attempteverything but the hard interaction including showers & hadronization→ soft & hard remnant-remnant interactions

Beyond factorization: Multiple-Parton Interactions

σ2→2QCD(p2

T ,min) =

s/4∫p2T,min

dp2T

dσ2→2QCD (p2

T )

dp2T

=

∫ ∫ ∫ s/4

p2T,min

dxadxbdp2T fa(xa, p

2T )fb(xb, p

2T )

dσ2→2QCD

dp2T

∼ α2S(p2

T )

p4T

for low pT ,min: 〈σ2→2QCD(p2

T ,min)/σNDpp 〉 = 〈n〉 > 1

there might be many interactions per event Pn =〈n〉nn!

e−〈n〉

strong dependence on cut-off pT ,min energy dependent!



The Underlying Event: remnant-remnant interactions

Definition: An attempteverything but the hard interaction including showers & hadronization→ soft & hard remnant-remnant interactions

Beyond factorization: Multiple-Parton Interactions

σ2→2QCD(p2

T ,min) =

s/4∫p2T,min

dp2T

dσ2→2QCD (p2

T )

dp2T

=

∫ ∫ ∫ s/4

p2T,min

dxadxbdp2T fa(xa, p

2T )fb(xb, p

2T )

dσ2→2QCD

dp2T

∼ α2S(p2

T )

p4T

for low pT ,min: 〈σ2→2QCD(p2

T ,min)/σNDpp 〉 = 〈n〉 > 1

there might be many interactions per event Pn =〈n〉nn!

e−〈n〉

strong dependence on cut-off pT ,min energy dependent!



Experimental Evidence

direct: DPS in γ + 3jets

CDF Phys. Rev. D56 (1997) 3811

indirect: jet shapes

r/R 0 0.2 0.4 0.6 0.8 1

(r/R

)

Ψ

0

0.2

0.4

0.6

0.8

1

CDF Run II Preliminary

-1 Data L = 1.7 fb

Pythia Tune A

Pythia w/o UE

Pythia Tune DW

ee + jets→Z2

< 116 GeV/cee66 < M

| < 1e1

η > 25 GeV, |eT

E

| < 2.8e2

η| < 1 || 1.2 < |e2

η|

| < 2.1jet

> 30 GeV/c, |yjetT

p

R(e,jet) > 0.7∆

Statistical uncertainties only



Multiple Interactions: A simple modelSjostrand, Zijl Phys. Rev. D 36 (1987) 2019

hard process defines scale pT ,hard

generate sequence of additional 2→ 2 QCD scatterings ordered in pT

P(pT ) =1

σND

dσ2→2QCD

dp2T

exp

−p2T,hard∫p2T

1

σND

dσ2→2QCD

dp2′T

dp2′T

with σ2→2

QCD regulated according to

dσ2→2QCD

dp2⊥→

dσ2→2QCD

dp2⊥× p4

⊥(p2⊥ + p2

⊥0)2

α2S (p2⊥ + p2

⊥0)

α2S (p2⊥)

[parameter pT,0 ≈ 2 GeV]

further featuresimpact parameter dependence [typically double Gaussian]

central collisions more active, Pn broader than Poissonian

use rescaled PDFs taking into account used up momentum Pn narrower than Poissonian

attach parton showers/hadronization



The Underlying Event: comparison to Tevatron data

Ncharged vs. p⊥,jet1 in different ∆φ regions w.r.t the leading jet

SHERPASHERPASHERPASHERPASHERPA

Min Bias Run IJet20 Run I

Sherpa w/o MIPYTHIA w/ MI

Sherpa w/ MI

in

1 G

eV

bin

Ch

arg

ed

N

1

2

3

4

5

6

7

8

9

10

Track Finding Efficiency: 0.92

>0.5T

p |<1.0η|Theory / Data - 1


>0.5T



>0.5T



>0.5T



>0.5T



>0.5T



>0.5T



>0.5T


-0.2

-0.10

0.1

0.2

GeV T, jet1

P

0 5 10 15 20 25 30 35 40 45 50

SHERPASHERPASHERPASHERPASHERPA

Min Bias Run IJet20 Run I

Sherpa w/o MIPYTHIA w/ MI

Sherpa w/ MI

in

1 G

eV

bin

Ch

arg

ed

N

0.5

1

1.5

2

2.5

3

3.5

4


>0.5T



>0.5T



>0.5T



>0.5T



>0.5T



>0.5T



>0.5T



>0.5T


-0.2

-0.10

0.1

0.2

GeV T, jet1

P

0 5 10 15 20 25 30 35 40 45 50



From partons to hadrons: Hadronization Models

Objectives: dynamical hadronization of multi-parton systemscapture main non-perturbative aspects of QCDuniversality→ robust extrapolation to new machines, higher energies

→ should not depend on specifics of the hard process

model (un)known decays of (un)known hadrons→ hadron multiplicities, meson/baryon ratios→ decay branching fractions

→ hadron-momentum distibutions

Lund string fragmentation

implemented in Pythia

Cluster-hadronization model

implemented in Herwig & Sherpa



From partons to hadrons: Cluster-Hadronization Model

Cluster-formation model

Cluster-decay model

features

preconfinement [colour neighboring partons after shower close in phase space]

parametrization of primary-hadron generation

locality and universality



From partons to hadrons: Cluster-Formation Model



From partons to hadrons: Cluster-Decay Model



Point of reference: LEP @√s = 91.2 GeV

particle multiplicities: Herwig++[Gieseke et al. JHEP 0402 (2004) 005]

Particle Measured LEP Herwig++

All Charged 20.924 ± 0.117 20.814

γ 21.27 ± 0.6 22.67

π0 9.59 ± 0.33 10.08

ρ(770)0 1.295 ± 0.125 1.316

π± 17.04 ± 0.25 16.95

ρ(770)± 2.4 ± 0.43 2.14η 0.956 ± 0.049 0.893ω(782) 1.083 ± 0.088 0.916

η′(958) 0.152 ± 0.03 0.136

K0 2.027 ± 0.025 2.062

K∗(892)0 0.761 ± 0.032 0.681

K∗(1430)0 0.106 ± 0.06 0.079

K± 2.319 ± 0.079 2.286

K∗(892)± 0.731 ± 0.058 0.657φ(1020) 0.097 ± 0.007 0.114

p 0.991 ± 0.054 0.947

∆++ 0.088 ± 0.034 0.092

Σ− 0.083 ± 0.011 0.071Λ 0.373 ± 0.008 0.384

Σ0 0.074 ± 0.009 0.091

Σ+ 0.099 ± 0.015 0.077

Σ(1385)± 0.0471 ± 0.0046 0.0312∗Ξ− 0.0262 ± 0.001 0.0286

Ξ(1530)0 0.0058 ± 0.001 0.0288∗Ω− 0.00125 ± 0.00024 0.00144

... ... ...

event shapes: Sherpa[Sherpa unpublished]

T = max|n|=1

∑i n · pi∑i |pi |

b

b bbbbbbbb

bb

bb

b

b

b

b

b

b

DELPHI datab

Njet = 2

Njet = 3

Njet = 4

Njet = 5

Sherpa1.2.110−3

10−2

10−1

1

10 1

1− Thrust

Nd

σ/d(1

−T)

0 0.1 0.2 0.3 0.4 0.5

0.6

0.8

1

1.2

1.4

1− T

MC/data



Summary: Monte Carlo event generators for the LHC

Stochastic simulation of exclusive events

Hard Processes at Fixed Order

Initial- & Final-State Parton Showers

Underlying Event/Multiple Interactions

Hadronization

...

produce exclusive events at the rate produced in nature

Ptot = PHard · PShower · PUE · PHadronization · PDecays · PQED



First LHC tests passed ...

Dijet Mass (GeV)200 400 600 800

|<1.

3)η

|<0.

7)/N

(0.7

<|η

N(|

0.5

1

1.5 CMS Preliminary = 7 TeVs

(M<838 GeV)-1Data 120 nbNLONLO+Non-Pert. CorrectionNLO UncertaintyPYTHIA6PYTHIA6 x NLO/LO

dijetϕ∆

dijet

ϕ∆

dd

N

N1

310

210

110

1

10

210

)3

200 GeV (x10≥ T

max p

)2 200 GeV (x10≤ T

max p≤ 120

120 GeV (x10)≤ T

max p≤ 90

90 GeV≤ T

max p≤ 70

)GENSMR Herwig++ (

)GENSMR Pythia 6 (

)GENSMR MadGraph (

= 7 TeVs@ pp

1L = 72 nb

1.1≤|y|

CMS Preliminary

/2π /3π2 /6π5 π

η-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

η/d

chdN

0

1

2

3

4

5

6

7

8Data 7 TeVPYTHIA-6 D6TPYTHIA-6 DWPYTHIA-6 P0PYTHIA-6 CWPYTHIA-8

CMS preliminary

> 3 GeV/cT

leading track-jet p

> 0.5 GeV/c)T

charged particles (p



LHC data is coming!

Frigate Monte Carlo



Aside: Logarithmic accuracy Catani–Seymour shower

Catani–Seymour Shower Sudakov form factor

∆CSq (µ2,Q2) = exp

−∫ Q2

µ2

dk2T

k2T

αS(λRk2T )

π

[CF log

(Q2

k2T

)− 3

2CF + . . .

]

∆CSg (µ2,Q2) = exp

−∫ Q2

µ2

dk2T

k2T

αS(λRk2T )

π

[CA log

(Q2

k2T

)− 1

6(11CA − 2nf ) + . . .

]Analytic QCD Sudakov form factor

∆QCDa (µ2,Q2) = exp

−∫ Q2

µ2

dk2T

k2T

[Aa(αS(k2

T )) log

(Q2

k2T

)+ Ba

(αS(k2

T ))]

Aa(αS ) =∞∑n=1

(αS

π

)nA

(n)a and Ba(αS ) =

∞∑n=1

(αS

π

)nB

(n)a

a=q: A(1)q = CF , B

(1)q = − 3

2CF , A

(2)q = 1

2CFK , with K = CA

(67

18− π2

6

)− 5nf

9

q=g: A(1)g = CA, B

(1)g = − 1

6(11CA − 2nf ), A

(2)g = 1

2CAK

set λR = exp(−K/2β0) = exp(− 67−3π2−10nf /3

33−2nf

)[Catani et al. Nucl. Phys. B 349 (1991) 635]



Aside: Phase-space slicing

The proposed measure [example final-state splitting]

Q2ij = 2 pipj min

k 6=i,j

2

C ki,j + C k

j,i

; C ki,j =

pipk

(pi + pk )pj− m2

i

2 pipjif j = g

1 else

→ minimize over color partners k

IR limitae

soft limit: pj = λq, λ → 0

1

Q2ij

→ 1

2λ2

1

2 pi qmaxk 6=i,j

[pipk

(pi + pk ) q− m2

i

2 piq

]quasi-collinear limit: k⊥ → λk⊥, m → λm

1

Q2ij

→ 1

2λ2

1

p 2ij −m2

i −m2j

(Ci,j + Cj,i

); Ci,j =

z

1− z− m2

i

2 pipjif j = g

1 else

measure correctly identifies enhanced phase-space regions



Documents

Monte Carlo Event Generators for the LHC - uni-mainz.de