Monte Carlo Tools Frank Krauss Institute for Particle Physics - - PowerPoint PPT Presentation

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Monte Carlo Tools

Frank Krauss

Institute for Particle Physics Phenomenology Durham University

GGI, 24.&26.9.2007

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Topics of the lectures

1

Lecture 1: Tour through Event Generators

Hard physics simulation: Parton Level event generation Dressing the partons: Parton Showers Soft physics simulation: Hadronization Beyond factorization: Underlying Event 2

Lecture 2: Higher Orders in Monte Carlos

Some nomenclature: Anatomy of HO calculations Merging vs. Matching Thanks to the other Sherpas: T.Gleisberg, S.H¨

• che, S.Schumann, F.Siegert, M.Sch¨
• nherr, J.Winter;
• ther MC authors: S.Gieseke, K.Hamilton, L.Lonnblad, F.Maltoni, M.Mangano, P.Richardson,

M.Seymour, T.Sjostrand, B.Webber, . . . .

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Simulation’s paradigm

Basic strategy

Divide event into stages, separated by different scales.

Signal/background:

Exact matrix elements.

QCD-Bremsstrahlung:

Parton showers (also in initial state).

Multiple interactions:

Beyond factorization: Modeling.

Hadronization:

Non-perturbative QCD: Modeling.

Sketch of an event

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Today’s lecture: Higher Orders in Monte Carlos

Which higher orders? Some anatomy First attempts: ME corrections Higher orders in rate: MC@NLO Higher orders through extra emission: Merging A new shower formulation

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event Higher Orders

Nomenclature

Specifying higher-order corrections: γ∗ → hadrons

In general: NnLO ↔ O(αn

s )

But: only for inclusive quantities

(e.g.: total xsecs like γ∗ →hadrons).

Counter-example: thrust distribution

In general, distributions are HO. Distinguish real & virtual emissions: Real emissions → mainly distributions, virtual emissions → mainly normalization.

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event Higher Orders

Nomenclature

Anatomy of HO calculations: Virtual and real corrections

NLO corrections: O(αs) Virtual corrections = extra loops Real corrections = extra legs UV-divergences in virtual graphs → renormalization But also: IR-divergences in real & virtual contributions Must cancel each other, non-trivial to see: N vs. N + 1 particle FS, divergence in PS vs. loop

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event Higher Orders

Nomenclature

Cancelling the IR divergences: Subtraction method

Total NLO xsec: σNLO = σBorn +

• dDk|M|2

V +

• d4k|M|2

R

IR div. in real piece → regularize:

• d4k|M|2

R →

• dDk|M|2

R

Construct subtraction term with same IR structure:

• dDk (|M|2

R − |M|2 S) =

• d4k|M|2

RS = finite.

Possible:

• dDk|M|2

S = σBorn

• dDk| ˜

S|2, universal | ˜ S|2.

• dDk|M|2

V + σBorn

• dDk| ˜

S|2 = finite (analytical)

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event Higher Orders

Nomenclature

State-of-the-art NLO calculations: General strategy

Construct Born + 1st order terms Subtraction term: Born term × (analytical) divergences

Evaluate loop term analytically - perform cancellation

Monte Carlo separately over subtracted real emission and virtual+subtraction term

Limitations

So far only loops with ≤ 5 propagators under full control

= ⇒ in general, only 2 → 3 processes at NLO

Soft/collinear corners maybe still badly described

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event Higher Orders

Nomenclature

Resummation: Basic idea

Observation: Universal soft & collinear divergences @ all orders Cutting them produces universal logarithms. Universality = ⇒ resummation of leading logs @ all orders possible. Improves behavior in soft/collinear regions of phase space. Example: Thrust distribution. Nomenclature: LL, NLL, NNLL, . . . . Limitation due to mixing with finite pieces @ some NnLL. Leading logs also in parton shower (=resummation!!)

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event Higher Orders

Orders in ME and PS

ME vs. PS

Matrix elements good for: hard, large-angle emissions; take care of interferences. Parton shower good for: soft, collinear emissions; resums large logarithms. Want to combine both! Avoid double-counting.

αs vs. Log

resummed in PS exact ME LO 5jet, but also NLO 4jet

L αn

m NLL exact ME LO 4jet

4 4 4 4 4 5 5 5 5 5 5 5

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Correcting the parton shower

Example: e+e− → q¯ qg

ME :

• +
• 2

PS :

• 2

+

• 2

0.2 0.4 0.6 0.8 1

1

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

2

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ME over PS

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Correcting the parton shower

Practicalities of ME-corrections

Obviously, ME < PS is not always fulfilled. Could enhance PS expression by a (large) factor. Question: Efficiency of the approach? Therefore: realized in few processes only: Best-known: ee → q¯ q, q¯ q → V , t → bW

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

MC@NLO

S.Frixione, B.R.Webber, JHEP 0206 (2002) 029 S.Frixione, P.Nason, B.R.Webber, JHEP 0308 (2003) 007

Basic principles

Want:

NLO-Normalization and first (hard) emission correct, Soft emissions correctly resummed in PS.

Method:

Modify subtraction terms for real infrared divergences, use first order parton shower-expression, this is process-dependent!

In practise much more complicated. Implemented for DY, W -pairs, gg → H, Q-pairs.

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

MC@NLO

Example results: W -pairs @ Tevatron

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

PowHEG

• P. Nason, JHEP 0411 (2004) 040
• S. Frixione, P. Nason and C. Oleari, arXiv:0709.2092 [hep-ph]

Basic idea:

For k⊥-ordered showers, generate hardest emission through

dσ = ¯ B(φN)dφN

• ∆(φN, Q0) + ∆(φN, k(N+1)

⊥

)R(φN+1) B(φN) dφ1

• with modified Sudakov form factor

∆(φN, p⊥) = exp

• −
• dφ1

R(φN+1) B(φN) ϑ(k(N+1)

⊥

− p⊥)

• ,

where k⊥ is the transverse momentum w.r.t. its emitter.

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

PowHEG, cont’d

• P. Nason, JHEP 0411 (2004) 040
• S. Frixione, P. Nason and C. Oleari, arXiv:0709.2092 [hep-ph]

Basic idea:

Get norm correct through

¯ B(φN) = B(φN) + Vfin(φN) +

• dφ1 [R(φN+1) − C(φN+1) + . . . ]

Advantage: Shower-independent caveat: k⊥- vs. angular ordered shower Advantage: No extra manipulation of NLO needed. Operational mode: Produce parton-level events with 1st emission, hand-over to your preferred shower etc..

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

S.Catani, F.K., R.Kuhn and B.R.Webber, JHEP 0111 (2001) 063 F.K., JHEP 0208 (2002) 015

Basic principles

Want:

All jet emissions correct at tree level + LL, Soft emissions correctly resummed in PS

Method:

Separate Jet-production/evolution by Qjet (k⊥ algorithm). Produce jets according to LO matrix elements re-weight with Sudakov form factor + running αs weights, veto jet production in parton shower.

Process-independent implementation.

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

n-jet rates @ NLL

S.Catani et al. Phys. Lett. B269 (1991) 432

At NLL-Accuracy

R2(Qjet) = ˆ ∆q(Ec.m., Qjet) ˜2 R3(Qjet) = 2∆q(Ec.m., Qjet) · Z dq " αs(q)Γq(Ec.m., q) ∆q(Ec.m., Qjet) ∆q(q, Qjet) ∆q(q, Qjet)∆g (q, Qjet) #

Sudakov weights

Example: γ∗ → q¯ qg

WSud = αs (q) αs (Qjet) · ∆q(Ec.m., Qjet) ∆q(Ec.m., Qjet) ∆q(q, Qjet) ∆q(q, Qjet)∆g (q, Qjet)

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Algorithm as scale-setting prescription

Example: p⊥ distribution of jets @ Tevatron Consider exclusive W + 1- and W + 2-jet production

Comparison with MCFM; J.Campbell and R.K.Ellis, Phys. Rev. D 65 (2002) 113007 in : F.K., A.Sch¨ alicke, S.Schumann and G.Soff, Phys. Rev. D 70 (2004) 114009

20 40 60 80 100 120 140 160 180 pT (jet) [GeV] 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

1/σ dσ/dpT [1/GeV] MCFM NLO Sherpa LO

Wj @ Tevatron

PDF: cteq6l Cuts: pT

lep|<1

pT

jet|<2

pT

∆Rjj> 1.0 20 40 60 80 100 120 140 160 180 pT (first jet) [GeV] 10

• 4

10

• 3

10

• 2

10

• 1

1/σ dσ/dpT [1/GeV] MCFM NLO Sherpa LO

Wjj @ Tevatron

20 40 60 80 100 pT (second jet) [GeV] 10

• 4

10

• 3

10

• 2

10

• 1

1/σ dσ/dpT [1/GeV] PDF: cteq6l pT

jet|<2

Cuts: pT

lep|<1

pT

∆Rjj> 1.0

Sherpa = tree-level matrix elements with αs scales and Sudakov form factors.

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Vetoing the shower

WVeto = ( 1 + Z Ec.m.

Qjet

dq Γq(Ec.m., q) + Z Ec.m.

Qjet

dq Γq(Ec.m., q) Z q

Qjet

dq′ Γq(Ec.m.q′) + · · · )2 = ( exp Z Ec.m.

Qjet

dq Γq(Ec.m., q) !)2 = ∆−2

q

(Ec.m., Qjet)

= ⇒ Cancels dependence on Qjet.

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Independence on Qjet

Example: p⊥ of W in p¯ p → W + X @ Tevatron

in F.K., A.Sch¨ alicke, S.Schumann and G.Soff, Phys. Rev. D 70 (2004) 114009

Qjet = 10 GeV Qjet = 30 GeV Qjet = 50 GeV

/ GeV

W

p 20 40 60 80 100 120 140 160 180 [ pb/GeV ]

W

/dp σ d

• 2

10

• 1

10 1 10

2

10 SHERPA

W + X W + 0jet W + 1jet W + 2jets W + 3jets

/ GeV

W

p 20 40 60 80 100 120 140 160 180 [ pb/GeV ]

W

/dp σ d

• 2

10

• 1

10 1 10

2

10 SHERPA

W + X W + 0jet W + 1jet W + 2jets W + 3jets

/ GeV

W

p 20 40 60 80 100 120 140 160 180 [ pb/GeV ]

W

/dp σ d

• 2

10

• 1

10 1 10

2

10 SHERPA

W + X W + 0jet W + 1jet W + 2jets W + 3jets

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with other codes

p⊥ of W -bosons & jets in p¯ p → W + X @ Tevatron pW

⊥

p1st jet

⊥

[ GeV ]

W

p 20 40 60 80 100 120 140 160 180 200 [ 1/GeV ]

w

/dp σ d σ 1/

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10

Sherpa PYTHIA MC@NLO

(first jet) [ GeV ]

T

p 20 40 60 80 100 120 140 160 180 [ 1/GeV ]

T

/dp σ d σ 1/

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10

Sherpa PYTHIA MC@NLO

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with other codes

p⊥ of W -bosons & jets in p¯ p → W + X @ Tevatron p2nd jet

⊥

p3rd jet

⊥

(second jet) [ GeV ]

T

p 20 40 60 80 100 120 140 160 [ 1/GeV ]

T

/dp σ d σ 1/

• 4

10

• 3

10

• 2

10

• 1

10

Sherpa PYTHIA MC@NLO

(third jet) [ GeV ]

T

p 20 40 60 80 100 120 [ 1/GeV ]

T

/dp σ d σ 1/

• 4

10

• 3

10

• 2

10

• 1

10

Sherpa PYTHIA MC@NLO

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with data from Tevatron

p⊥ of Z-bosons in p¯ p → Z + X

Data from CDF, Phys. Rev. Lett. 84 (2000) 845

/ GeV

Z

P 20 40 60 80 100 120 140 160 180 200 10

• 3

10

• 2

10

• 1

1 10

pt Z Z + 0 jet Z + 1 jet Z + 2 jet CDF

GeV pb / dP σ d / GeV

Z

P 5 10 15 20 25 30 35 40 45 50 GeV pb / dP σ d 1 10

pt Z Z + 0 jet Z + 1 jet Z + 2 jet CDF

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with data from Tevatron

Jet rates in p¯ p → Z + X

(D0-Note 5066)

1 2 3 4 5 6 1 10

2

10

3

10

4

10 1 2 3 4 5 6 1 10

2

10

3

10

4

10

data w/stat error data w/stat & sys error Pythia range stat Pythia range stat & sys

D0 RunII Preliminary Jet Multiplicity

• Nr. of Events

1 2 3 4 5 6 0.2 1 2 3 4

Jet Multiplicity Data / PYTHIA

1 2 3 4 5 6 1 10

2

10

3

10

4

10 1 2 3 4 5 6 1 10

2

10

3

10

4

10

data w/stat error data w/stat & sys error Sherpa range stat Sherpa range stat & sys

D0 RunII Preliminary Jet Multiplicity

• Nr. of Events

1 2 3 4 5 6 0.2 1 2 3 4

Jet Multiplicity Data / SHERPA

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with data from Tevatron

Jet spectra (1st jet) in p¯ p → Z + X

(D0-Note 5066)

50 100 150 200 250 300 350 1 10

2

10

3

10 50 100 150 200 250 300 350 1 10

2

10

3

10

data w/stat error data w/stat & sys error Pythia range stat Pythia range stat & sys

D0 RunII Preliminary jet [GeV]

st

1

T

p

• Nr. of Events

50 100 150 200 250 300 350 0.2 1 2 3 4

jet [GeV]

st

1

T

p Data / PYTHIA

50 100 150 200 250 300 350 1 10

2

10

3

10 50 100 150 200 250 300 350 1 10

2

10

3

10

data w/stat error data w/stat & sys error Sherpa range stat Sherpa range stat & sys

D0 RunII Preliminary jet [GeV]

st

1 p

• Nr. of Events

50 100 150 200 250 300 350 0.2 1 2 3 4

jet [GeV]

st

1

T

p Data / SHERPA

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with data from Tevatron

Jet spectra (2nd jet) in p¯ p → Z + X

(D0-Note 5066)

20 40 60 80 100 120 140 160 180 1 10

2

10

3

10 20 40 60 80 100 120 140 160 180 1 10

2

10

3

10

data w/stat error data w/stat & sys error Pythia range stat Pythia range stat & sys

D0 RunII Preliminary jet [GeV]

nd

2

T

p

• Nr. of Events

20 40 60 80 100 120 140 160 180 0.2 1 2 3 4

jet [GeV]

nd

2

T

p Data / PYTHIA

20 40 60 80 100 120 140 160 180 1 10

2

10

3

10 20 40 60 80 100 120 140 160 180 1 10

2

10

3

10

data w/stat error data w/stat & sys error Sherpa range stat Sherpa range stat & sys

D0 RunII Preliminary jet [GeV]

nd

2

T

p

• Nr. of Events

20 40 60 80 100 120 140 160 180 0.2 1 2 3 4

jet [GeV]

nd

2

T

p Data / SHERPA

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with data from Tevatron

Jet spectra (3rd jet) in p¯ p → Z + X

(D0-Note 5066)

20 40 60 80 100 120 1 10

2

10 20 40 60 80 100 120 1 10

2

10

data w/stat error data w/stat & sys error Pythia range stat Pythia range stat & sys

D0 RunII Preliminary jet [GeV]

rd

3

T

p

• Nr. of Events

20 40 60 80 100 120 0.2 1 2 3 4

jet [GeV]

rd

3

T

p Data / PYTHIA

20 40 60 80 100 120 1 10

2

10 20 40 60 80 100 120 1 10

2

10

data w/stat error data w/stat & sys error Sherpa range stat Sherpa range stat & sys

D0 RunII Preliminary jet [GeV]

rd

3

T

p

• Nr. of Events

20 40 60 80 100 120 0.2 1 2 3 4 5

jet [GeV]

rd

3

T

p Data / SHERPA

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with data from Tevatron

Azimuthal correlation (∠1.jet,2.jet) in p¯ p → Z + X

(D0-Note 5066)

0.5 1 1.5 2 2.5 3 50 100 150 200 250 0.5 1 1.5 2 2.5 3 50 100 150 200 250

data w/stat error data w/stat & sys error Pythia range stat Pythia range stat & sys

D0 RunII Preliminary (jet,jet) φ ∆

• Nr. of Events

0.5 1 1.5 2 2.5 3 0.2 1 2 3 4

(jet,jet) φ ∆ Data / PYTHIA

0.5 1 1.5 2 2.5 3 50 100 150 200 250 0.5 1 1.5 2 2.5 3 50 100 150 200 250

data w/stat error data w/stat & sys error Sherpa range stat Sherpa range stat & sys

D0 RunII Preliminary (jet,jet) φ ∆

• Nr. of Events

0.5 1 1.5 2 2.5 3

0.2 1 2 3 4

(jet,jet) φ ∆ Data / SHERPA

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Extrapolation to LHC: Jets

p⊥ of jets in inclusive Z+jets Influence of more jets. Displayed here: x-sections. Difference in shape & x-sec.

50 100 150 200 250 300 pT (first jet) [GeV] 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

1/σ dσ/dpT [1/GeV] MC@NLO Pythia Sherpa e

+e

• j + X @ LHC

20 40 60 80 100 120 140 pT (second jet) [GeV] 10

• 4

10

• 3

10

• 2

10

• 1

1/σ dσ/dpT [1/GeV] MC@NLO Pythia Sherpa Sherpa 2jet e

+e

• j + X @ LHC

20 40 60 80 100 pT (third jet) [GeV] 10

• 4

10

• 3

10

• 2

10

• 1

1/σ dσ/dpT [1/GeV] MC@NLO Pythia Sherpa Sherpa 2jet Sherpa 3jet e

+e

• j + X @ LHC
• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with other merging algorithms: MLM

p⊥ of jets in inclusive W +jets at Tevatron

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Combining MEs & PS

Comparison with other merging algorithms: MLM

p⊥ of jets in inclusive W +jets at LHC

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Further developments of parton showers

Shower based on Catani-Seymour splitting kernels

First discussed in: Z.Nagy and D.E.Soper, JHEP 0510 (2005) 024.

Catani-Seymour dipole subtraction terms as universal framework for QCD NLO calculations. Factorization formulae for real emission process: Full phase space coverage & good approx. to ME. Currently implemented into SHERPA by S.Schumann.

Example: final-state final-state dipoles splitting: ˜ pij + ˜ pk → pi + pj + pk variables: yij,k =

pi pj pi pj +pi pk +pj pk ,

zi =

pi pk pi pk +pj pk

consider qij → qi gj : Vqi gj ,k(˜ zi , yij,k) = CF 

2 1−˜ zi +˜ zi yij,k − (1 + ˜

zi ) ff

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Further developments of parton showers

Shower based on Catani-Seymour splitting kernels

Results for e+e− → hadrons

1-Thrust @ LEP1

SHERPA SHERPA

DELPHI 96 CS show. + Py 6.2 had.

1/N dN/d(1-T)

• 3

10

• 2

10

• 1

10 1 10

2

10

1-Thrust @ LEP1

(MC-data)/data

• 0.2
• 0.1

0.1 0.2 1-T 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Major @ LEP1

SHERPA SHERPA

DELPHI 96 CS show. + Py 6.2 had.

1/N dN/dM

• 1

10 1 10

Major @ LEP1

(MC-data)/data

• 0.2
• 0.1

0.1 0.2 M 0.1 0.2 0.3 0.4 0.5 0.6

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Further developments of parton showers

Shower based on Catani-Seymour splitting kernels

Results for e+e− → hadrons

@ LEP1

2

Durham 2-jet rate R

SHERPA

DELPHI CS show. + Py 6.2 had.

2

R 0.2 0.4 0.6 0.8 1

@ LEP1

2

Durham 2-jet rate R

(MC-data)/data

• 0.2
• 0.1

0.1 0.2 )

cut Durham

(y

10

log

• 4
• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

@ LEP1

3

Durham 3-jet rate R

SHERPA

DELPHI CS show. + Py 6.2 had.

3

R 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

@ LEP1

3

Durham 3-jet rate R

(MC-data)/data

• 0.2
• 0.1

0.1 0.2 )

cut Durham

(y

10

log

• 4.5
• 4
• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5
• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Further developments of parton showers

Shower based on Catani-Seymour splitting kernels

Results for p¯ p → ℓ+ℓ−

25 50 75 100 125 150 175 200

pT [GeV]

10

• 4

10

• 3

10

• 2

10

• 1

10 10

1

dσ/dpT [pb/GeV]

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

+e

• ) @ Tevatron Run1

5 10 15 20 pT [GeV] 5 10 15 20 25 30 dσ/dpT [pb/GeV]

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Further developments of parton showers

Shower based on Catani-Seymour splitting kernels

Results for p¯ p → jets

200 400 600 800 1000 1200 1400

Mdijet [GeV]

1e-08 1e-07 1e-06 1e-05 1e-04 1e-03 1e-02 1e-01

d

3σ / dMdijetdη1dη2 [nb/GeV] D0 99 CS show. + Py 6.2 had.

Dijet invariant mass @ Tevatron Run I

cuts: |ηj| < 1.0 Rjj > 0.7 π/2 3π/4 π

∆φdijet (rad)

10

• 3

10

• 2

10

• 1

10 10

1

10

2

10

3

10

4

10

5

1/σdijet dσdijet/d∆φdijet

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.

• F. Krauss

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Further developments of parton showers

Shower based on Catani-Seymour splitting kernels

Results for p¯ p → jets

• 4
• 2

2 4

η3

0.02 0.04 0.06 0.08

1/σ dσ/dη3

CDF 94 (detector level) CS show. + Py 6.2 had.

normalised distribution of η3 @ Tevatron Run I

∆Rjj > 0.7, |η1|, |η2| < 0.7 |φ1-φ2| < 2.79 rad ET1 > 110 GeV, ET2 > 10 GeV

• π/2
• π/4

π/4 π/2

α

0.01 0.02 0.03 0.04 0.05 0.06

1/σ dσ/dα

CDF 94 (detector level) CS show. + Py 6.2 had.

normalised distribution of α @ Tevatron Run I

∆Rjj > 0.7, |η1|, |η2| < 0.7 1.1 < ∆R23 < π |φ1-φ2| < 2.79 rad ET1 > 110 GeV, ET2 > 10 GeV

• F. Krauss

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying Event

Multiple parton scattering?

Hadrons = extended objects! No guarantee for one scattering only. Running of αS = ⇒ preference for soft scattering.

• F. Krauss

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying Event

Evidence for multiple parton scattering

Events with γ + 3 jets:

Cone jets, R = 0.7, ET > 5 GeV; |ηj| <1.3; “clean sample”: two softest jets with ET < 7 GeV;

σDPS = σγjσjj

σeff ,

σeff ≈ 14 ± 4 mb.

CDF collaboration, Phys. Rev. D56 (1997) 3811.

• F. Krauss

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying Event

Definition(s)

• 1

Everything apart from the hard interaction including IS showers, FS showers, remnant hadronization.

2

Remnant-remnant interactions, soft and/or hard. = ⇒ Lesson: hard to define

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying event

Model: Multiple parton interactions

To understand the origin of MPS, realize that σhard(p⊥,min) =

s/4

• p2

⊥,min

dp2

⊥

dσ(p2

⊥)

dp2

⊥

> σpp,total for low p⊥,min. Here:

dσ(p2 ⊥) dp2 ⊥

=

1

R dx1dx2dˆ tf (x1, q2)f (x2, q2) d ˆ

σ2→2 dp2 ⊥

δ “ 1 − ˆ

tˆ u ˆ s

” (f (x, q2) =PDF, ˆ σ2→2 =parton-parton x-sec)

σhard(p⊥,min)/σpp,total ≥ 1 Depends strongly on cut-off p⊥,min (Energy-dependent)!

• F. Krauss

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying event

Old Pythia model: Algorithm, simplified

T.Sjostrand and M.van Zijl, Phys. Rev. D 36 (1987) 2019.

Start with hard interaction, at scale Q2

hard.

Select a new scale p2

⊥

(according to f =

dσ2→2(p2 ⊥) dp2 ⊥

with p2

⊥ ∈ [p2 ⊥,min, Q2])

Rescale proton momentum

(“proton-parton = proton with reduced energy”).

Repeat until below p2

⊥,min.

May add impact-parameter dependence, showers, etc.. Treat intrinsic k⊥ of partons (→ parameter) Model proton remnants (→ parameter)

• F. Krauss

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying Event

In the following: Data from CDF, PRD 65 (2002) 092002, plots partially from C.Buttar

Observables

• ∆φ

∆φ ∆φ ∆φ

• η

η η η

• η

η η η

• F. Krauss

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying event

Hard component in transverse region

• η

η η η

• η

η η η

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying event

Energy extrapolation

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Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Underlying event

General facts on current models

No first-principles approach for underlying event:

Multiple-parton interactions: beyond factorization Factorization (simplified) = no process-dependence in use of PDFs.

Models usually based on xsecs in collinear factorization: dσ/dp⊥ ∝ p4−8

⊥

= ⇒ strong dependence on cut-off pmin

⊥ .

“Regularization”: dσ/dp⊥ ∝ (p2

⊥ + p2 0)2−4, also in αS.

Model for scaling behavior of pmin

⊥ (s) ∝ pmin ⊥ (s0)(s/s0)λ, λ =?

Two Pythia tunes: λ = 0.16, λ = 0.25.

Herwig model similar to old Pythia and SHERPA New Pythia model: Correlate parton interactions with showers, more parameters.

• F. Krauss

IPPP Monte Carlo Tools

Orientation ME corrections MC@NLO CKKW New Showers Underlying Event

Summary & outlook

Summary: QCD & simulation tools

Many interesting signals at LHC “spoiled” by QCD. Need to understand & describe QCD to high precision. Time to improve & validate essential tools is now! New methods of merging of ME& PS extremely powerful. Different, complementary aspects w.r.t. MC@NLO. Important: educated choice which tool to use! Important: know your Monte Carlo! Important: know the assumptions!

• F. Krauss

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