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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.thphys.uni-heidelberg.de/~schumann/

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

http://www.sherpa-mc.de

Disclaimer

These lectures will not cover:Heavy-ion collisionsSpecific aspects of heavy-flavour physicsBeyond the Standard Model physicsmost of the details, derivations, ...

Recommended reading:

Ellis, Stirling & Webber

“QCD and Collider Physics”

Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 8, 1 (1996)

Sjostrand, Mrenna & Skands

“PYTHIA 6.4 Physics and Manual”

JHEP 0605 (2006) 026

... papers cited on the way

arXiv:

hep-ph

/0603

175v

2 12

May

2006

Preprint typeset in JHEP style - HYPER VERSION hep-ph/0603175

LU TP 06–13

FERMILAB-PUB-06-052-CD-T

March 2006

PYTHIA 6.4 Physics and Manual

Torbjorn Sjostrand

Department of Theoretical Physics, Lund University,

Solvegatan 14A, S-223 62 Lund, Sweden

E-mail: [email protected]

Stephen Mrenna

Computing Division, Simulations Group, Fermi National Accelerator Laboratory,

MS 234, Batavia, IL 60510, USA


Peter Skands

Theoretical Physics Department, Fermi National Accelerator Laboratory,

MS 106, Batavia, IL 60510, USA


Abstract: The Pythia program can be used to generate high-energy-physics ‘events’,

i.e. sets of outgoing particles produced in the interactions between two incoming particles.

The objective is to provide as accurate as possible a representation of event properties in

a wide range of reactions, within and beyond the Standard Model, with emphasis on those

where strong interactions play a role, directly or indirectly, and therefore multihadronic

final states are produced. The physics is then not understood well enough to give an exact

description; instead the program has to be based on a combination of analytical results

and various QCD-based models. This physics input is summarized here, for areas such

as hard subprocesses, initial- and final-state parton showers, underlying events and beam

remnants, fragmentation and decays, and much more. Furthermore, extensive information

is provided on all program elements: subroutines and functions, switches and parameters,

and particle and process data. This should allow the user to tailor the generation task to

the topics of interest.

The code and further information may be found on the Pythia web page:

http://www.thep.lu.se/∼torbjorn/Pythia.html.

Keywords: Phenomenological Models, Hadronic Colliders, Standard Model, Beyond

Standard Model.

– 1 –



Outline Lecture 1

Motivation/Introduction

LHC challenges: highest energies & highest multiplicitiesA prototypical LHC event: the simulators point of viewThe case for Monte Carlo event generators

Basic Monte Carlo techniquesThe Hit-or-Miss method

importance samplingthe multi-channel approach

The Veto Algorithm

Hard-Process generation

The partonic hadron-hadron cross-section formulaMulti-leg tree-level matrix elementsOne-loop matrix-element calculations



Hadron-collision experiments

identify & measure all particles coming from individual pp clashes

⇒ to be confronted with hypotheses for the underlying physics



Hadron-collision experiments

identify & measure all particles coming from individual pp clashes



The LHC challenge

Objectives for the LHC era

reveal the mechanism of EWSB [discovery of the Higgs?, alternatives?]

search for physics beyond the SM: weak scale SUSY, ED, W’ & Z’, ...

Higgs Huntingobvious production & decay channels buried in QCD backgroundssearch for rare decays like h→ γγlook for associated production modes, e.g. hjj , W /Zh, tth

signals & backgrounds to be understood at high precision

Searching for New Physicslarge cross sections for producing new colored statessubsequent decays into SM final states + Xgeneric signals: #-leptons + #-jets + E/T

SM backgrounds: V+jets, VV+jets, tt+jets, QCD jets new physics encoded in energies, flavours, edges

Typically searches in (rare) multi-particle / multi-jet final states!

Detailed understanding of QCD jet production indispensable!



Theoretical Modelling

Monte Carlo Event Generators

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Hard interactionexact matrix elements |M|2

QCD bremsstrahlungparton showers in the initial and final state

Multiple Interactionsbeyond factorization: modelling

Hadronizationnon-perturbative QCD: modelling

Hadron Decaysphase space or effective theories

⇒ stochastic simulation of pseudo data⇒ fully exclusive hadronic final states⇒ direct comparison with experimental data, e.g. ATLAS, CMS, LHCb, DØ, CDF

modulo detector simulation

Herwig, Pythia, Sherpa



The case for Monte Carlo generators

theoretical & experimental studies of complex multi-particle physics

large flexibility of physical quantities that can be assessed

disseminate ideas from theorists to experimentalists

Applications I: theorists/experimentalists

predict event rates and topologies ⇒ can estimate feasibility

simulate possible backgrounds ⇒ can devise analysis strategies

Applications II: experimentalists [supplemented with detector simulation]

study detector requirements ⇒ can optimize detector/trigger design

study detector imperfections ⇒ can evaluate acceptance corrections

study detector response ⇒ can unfold data to particle level




new analysis techniques

Searching for the boosted Higgs[Butterworth et al. Phys. Rev. Lett. 100 (2008) 242001]

consider pp → Vh with h→ bb

focus on Higgs with phT > 200 GeV

use subjet info to reduce QCD BG

pp → Vh with h→ bb resurrected

desperate new physics searches

New Physics in all-jet final states[Cilic, S., Son JHEP 0904 (2009) 128]

consider pp → π8π8 → 4jets

fight QCD 4jet background

mass window criterion for jet pairs

discovering color octets seems feasible




The Atlas simulation framework [arXiv:1005.4568]



↘

LHC data is coming!

We are here!



Basic Monte Carlo techniques



Basic Monte Carlo techniques

“Spatial” problems: without memory

What is the volume of a given body?

Pick a random point, with equal probability in this area.

What is the integrated cross section of a given process?

Pick an event at random, according to the differential cross section.

“Temporal” problems: have memory

Financial systems: What is the probability for a stock to have price X attime t, given the price Y at t0?

Parton shower: What is the probability for a parton to branch at a scale Q,given that it was created at a scale Q0?

In particle physics often combined problems

What is the probability for a parton to branch at Q, with the daughters sharingthe mother momentum in some specific way?



Basic Monte Carlo techniques: “Spatial” problems

Assume function f (x) in range xmin ≤ x ≤ xmax,where f (x) ≥ 0 everywhere(in practise x is multi-dimensional)

Two standard tasks

1 Calculate (approximatively)

I =

xmax∫xmin

f (x ′)dx ′ = (xmax − xmin)〈f (x)〉

' IN = (xmax − xmin)1

N

N∑i=1

f (xi )± (xmax − xmin)

√〈f 2〉 − 〈f 〉2

N

Example: integrated cross section from the differential one

2 Select x at random according to f (x)

Example: given probability distribution from quantum mechanics

↙random points ∈ [xmin, xmax ]




Select x according to f (x)

as P(x) ∼f (x)∫0

dy = f (x)

equivalent to uniform selection of (x , y) in areaxmin ≤ x ≤ xmax & 0 ≤ y ≤ f (x)

x∫

xmin

f (x ′)dx ′ = #

xmax∫

xmin

f (x ′)dx ′

Analytical solution

known primitive function F (x) and inverse F−1

F (x)− F (xmin) = #(F (xmax)− F (xmin)) = #Atot

x = F−1(F (xmin) + #Atot)

Example: f (x) = e−x for x ≥ 0

F (x) = 1− e−x

1− e−x = # x = − ln(#)




The Hit-or-Miss method: basics

f (x) ≤ fmax in xmin ≤ x ≤ xmax

1 select x = xmin + #1(xmax − xmin)

2 select y = #2fmax

3 if y ≤ f (x) accept point [Nacc++, Ntry++]

if y > f (x) reject point [Nfail++, Ntry++]

As a byproduct the integral is given by:

I =

xmax∫

xmin

f (x)dx ' (xmax − xmin)fmaxNacc

Ntry= Atot

Nacc

Ntry

with its relative variance approaching:

δI

I−→ 1√

Nacc




Example: Battleships

Can we do better?



Basic Monte Carlo techniques: “Spatial” problemsThe Hit-or-Miss method: importance sampling

f (x) ≤ g(x) in xmin ≤ x ≤ xmax

and G (x) =x∫

xmin

g(x ′)dx ′ & G−1(y) are simple

1 select x = according to distribution g(x)

2 select y = #g(x)



Example: f (x) = xe−x and g(x) = Ne−x/2

f (x)

g(x)=

xe−x/2

N

!≤ 1→ find maximum

d

dx

(f (x)

g(x)

)=

1

N

(1− x

2

)e−x/2 !

= 0 x = 2

normalize such that g(2) = f (2) N = 2/e

from G (x) ∼ 1− e−x/2 = #1

x = −2 ln(#1)y = #2g(x) = #22e−(1+x/2)




The Hit-or-Miss method: multi-channel approach

f (x) ≤ g(x) =N∑i=1

αigi (x) in xmin ≤ x ≤ xmax,

where all gi are “nice”, αi ≥ 0 &N∑i=1

αi = 1

1 select i with relative probability αi

xmax∫

xmin

gi (x′)dx ′

2 select x according to gi (x)

3 select y = #g(x) = #N∑i=1

αigi (x)



5 adjust apriori weights αi to minimize variance

self-adaptive multi-channel Monte Carlo



Basic Monte Carlo techniques: “Temporal” problems

The radioactive decay problem

known probability f (t) that something will happen at time t

[nucleus decays, parton branches, transistor fails]

something happens at t only if it didn’t happen at t ′ < t

Define: N(t): probability that nothing happend until t [N(0) = 1]

P(t) = −dN(t)/dt = f (t)N(t): probability for decay at time t

Solution:

N(t) = exp

−

t∫

0

f (t ′)dt ′

P(t) = f (t) exp

−

t∫

0

f (t ′)dt ′

naıve answer P(t) = f (t) modified by exponential suppression

in parton-shower picture, N(t) is called the Sudakov form factor



Basic Monte Carlo techniques: “Temporal” problems

If F (t) and F−1 exist: Standard solution to find “decay” time tt∫

0

P(t ′)dt ′ = N(0)− N(t) = 1− exp {−(F (t)− F (0))} = 1−#

t = F−1(F (0)− ln(#))

The Veto Algorithm

if f (t) has no simple F (t) or F−1: use “nice” g(t) ≥ f (t)

1 start with i = 0 and t0 = 0

2 increment i and select ti = G−1(G (ti−1)− ln(#1))

3 if f (ti )/g(ti ) ≤ #2 go back to step 2

otherwise, keep ti as “decay” time

next step only depends on the very previous one

Markov chain process



Basic Monte Carlo techniques: Summary

use Monte Carlo to perform integrals and sample distributions

only need few points to estimate feach additional point increases accuracy

techniques generalize to many dimensions

typical LHC phase space ∼ d3~p × 100’s particleserror scales as 1/

√N vs. 1/N2/d or 1/N4/d (Trapezoidal or Simpson’s Rule)

suitable for complicated integration regions

kinematic cuts or detector cracks

can sample distributions where exact solutions cannot be found

Veto Algorithm applied to parton shower



Hard-Process generation



The partonic hadron-hadron cross section

proton bound state of quarks and gluons

universal probability distributionof finding parton a with momentum pa = xaPfa(xa, µ

2F )→ Parton Density Function

↪→ partonic CM energy: s = xaxbspp



The partonic hadron-hadron cross section

�'

&

$

%|Mqq→e+e−|2

γ∗/Z0

fq(xq , µ2F ) fq(xq, µ

2F )

proton bound state of quarks and gluons

universal probability distributionof finding parton a with momentum pa = xaPfa(xa, µ

2F )→ Parton Density Function

factorization in hard and soft component (resummed in PDFs)

σpp→Xpart(s;µ2R, µ

2F) ≡

∑ab

∫dxadxb fa(xa, µ

2F)fb(xb, µ

2F) dσab→Xpart(s; {pX}, µ2

R, µ2F)

soft/collinear QCD emissions summed in fa(xa, µ2F) σ is inclusive!

hard production process described through

dσab→Xpart(s; {pX}, µ2R, µ

2F) ≡ |Mab→Xpart(s; {pX}, µ2

R, µ2F)|2 dΦX

↪→ from model Lagrangian, e.g. LSM , LMSSM , ...

allows for probabilistic generation of partonic events {pX} the center piece of each event need to model transition of partons to hadrons: Xpart → Xhad



The Hard Process: setting the scene

σpp→Xn =∑

ab

∫dxadxb fa(xa, µ

2F)fb(xb, µ

2F) |Mab→Xn |2 dΦn

generic features

high-dimensional phase space dim[Φn ] = 3n − 4

|Mab→Xn |2 wildly fluctuating over Φn

steep parton densities [parametrization]

state-of-the-art

tradionally based on LO 2→ 2 only

now dedicated 2→ n tree-level codes

extract Feynman rules from Lagrangian Lgenerate compact expressions for |M|2flexible phase-space integrators

↪→ ALPGEN, AMEGIC, COMIX, HELAC, MADGRAPH

automation of one-loop corrections on the way

L(B)SM

↓

↓|Mn|2dΦn

�fZ ′

µ

f

1




σpp→Xn =∑

ab

∫dxadxb fa(xa, µ

2F)fb(xb, µ


generic features


dΦn = δ4

(pa + pb −

n∑

i=1

pi

)n∏

i=1

d3~pi(2π)32Ei

↪→ subject to non-trivial cuts �pa

pb

. . .

p1p2

pn−1

pn



state-of-the-art






L(B)SM

↓

↓|Mn|2dΦn

�fZ ′

µ

f

1




σpp→Xn =∑

ab

∫dxadxb fa(xa, µ

2F)fb(xb, µ


generic features



competing resonances [Breit-Wigner]enhanced phase-space regionsmomentum correlationsnumber of diagrams ∼ n! [costly]


state-of-the-art






L(B)SM

↓

↓|Mn|2dΦn

�fZ ′

µ

f

1




σpp→Xn =∑

ab

∫dxadxb fa(xa, µ

2F)fb(xb, µ


generic features




10-4

10-3

10-2

10-1 1

x

0

0.5

1

1.5

2

2.5

3

3.5

4

xf(

x,Q

2)

u-quark

u-quarkgluon (*0.05)

Q2=(100 GeV)

2

MRST2002NLO

state-of-the-art






L(B)SM

↓

↓|Mn|2dΦn

�fZ ′

µ

f

1




σpp→Xn =∑

ab

∫dxadxb fa(xa, µ

2F)fb(xb, µ


generic features




state-of-the-art






L(B)SM

↓

↓|Mn|2dΦn

�fZ ′

µ

f

1



Phase-Space integration: a look into the tool box

build-up suitable channels during amplitude generation

|M|2 ≡∣∣∣∣∣

k∑

i=1

Ai

∣∣∣∣∣

2

=k∑

i=1

|Ai |2 +∑

i 6=j

AiA†j

phase-space map for each topology |Ai |2

�4

1

2

3=⇒

dΦ4 ∝ dφ12,34 d cos θ12,34

×ds12 dφ1,2 d cos θ1,2

×ds34 dφ3,4 d cos θ3,4

with sij = (pi + pj)2

use suitable distributions

use adaptive multi-channel technique to combine channels



Phase-Space integration: a look into the tool box

Example: Breit-Wigner propagator – particle with mass M and width Γ

mapping

s = MΓ tan ρ+ M2

ds = MΓ sec2 ρ dρ

yields

I =

smax∫

smin

ds

(s −M2)2 + M2Γ2

=

ρmax∫

ρmin

MΓ sec2 ρ dρ

M2Γ2 tan2 ρ+ M2Γ2

=1

MΓ

ρmax∫

ρmin

dρ δI = 0

60 70 80 90 100√s [GeV]

0.00

0.25

0.50

1

(s-M2)2+M

2Γ

2



Matrix-Element generation: a look into the tool box

Helicity amplitudes [e.g. Hagiwara, Zeppenfeld Nucl. Phys. B 274 (1986) 1]

express amplitudes Ai in terms of spinor products u(pi , λi )u(pj , λj)

for assigned helicities & momenta Ai ’s just complex numbers

can perform the sum of amplitudes before squaring

Feynman-diagram based

factor out common pieces

2→ 6 is feasible

Recursive approaches

exponential growth of complexity

2→ 8− 10 doable

n−1

n−2

2

1

Jµ =

n−1∑

i=2

i+2i+1

ii−1

1 2

n−1 n−2

V3

+

n−2∑

i=2j>i

j

j−1

i+2

i+1

1 2 i−1 i

n−1 n−2 j+2 j+1

V4



Tree-level matrix elements: state-of-the-art

LHC cross sections [√

s =14 TeV, generic cuts] [Gleisberg, Hoche JHEP 0812 (2008) 039]

σpp→XpartNumber of jets

Process + n QCD jets Order 0 1 2 3 4 5 6

e+νe [pb] α2EMα

nS 5434(5) 1274(2) 465(1) 183.0(6) 77.5(3) 33.8(1) 14.7(1)

e+e− [pb] α2EMα

nS 723.5(4) 187.9(3) 69.7(2) 27.14(7) 11.09(4) 4.68(2) 2.02(2)

e+e− + bb [pb] α2EMα

n+2S

18.86(3) 6.78(2) 3.10(5) 1.536(9) 2.47(2) 1.28(2)

tt [pb] αn+2S

754.8(8) 745(1) 518(1) 309.8(8) 170.4(7) 89.2(4) 44.4(4)

bb [µb] αn+2S

471.2(5) 8.83(2) 1.813(8) 0.459(2) 0.150(1) 0.0531(5) 0.0205(4)

σpp→XpartNumber of jets

Process + n QCD jets Order 0 1 2 3 4 5 6 7 8

pure jets [µb] αnS – – 331.0(4) 22.72(6) 4.95(2) 1.232(4) 0.352(1) 0.1133(5) 0.0369(3)

parton-level event generation

+ fully differential [{pXpart} any distribution can be studied]

+ full momentum/spin correlations

+ theory/pheno analyses

− limited in final-state multiplicity [factorial growth of Feynman diagrams / phase-space maps]

− not directly observable / measurable

− Leading-Order dependence on µ2F & µ2

R

NLO QCD precision desirable



Hard Processes at Next-to-Leading Order QCD

The need for higher precision

derive exclusion bounds from a given measurement

non-observation of a given hypothesis, e.g. light Higgs, BSM modelcrucial to know the corresponding production cross sections preciselyderive limits on particle masses, model parameters

counting experiments to extract certain parameters, couplings

stop mass bounds from Tevatron[from the early days, T. Plehn private communication]

10-1

1

100 110 120 130 140 150

∆MLO

∆MNLO

σNLO

σLO

: µ=[m(t)/2 , 2m(t)]

: µ=[m(t)/2 , 2m(t)]

m(t1) [GeV]

σ(pp– → t

1t−

1 + X) · BR(t

1t−

1 → ee + ≥ 2j) [pb]

CDF 95% C.L. upper limit (prel.)

m(χ1o)=m(t

1)/2

Higgs coupling extraction

σ(gg → h→ γγ) ∼ ΓgΓγΓ

σ(gg → h→WW ∗) ∼ ΓgΓW

Γ

σ(qq → qqh, h→ ττ) ∼ ΓW ΓτΓ

...

Γi ∼ giih, Γg ∼ gtth theoretical uncertainties dominate

systematics reduced for σ ratios



Hard Processes at Next-to-Leading Order QCDAnatomy of NLO QCD calculations

�γ∗/Z0

�γ∗/Z0

�γ∗/Z0

σNLO2→n =

∫

n+1

d(d)σR +

∫

n

d(d)σV +

∫

n

d(4)σB

real-emission σR IR divergent

(UV renormalized) virtual-corrections σV IR divergent

for IR safe observables sum is finite

Dipole subtraction method [Catani, Seymour Nucl. Phys. B 485 (1997) 291]

σNLO2→n =

∫

n+1

[d(4)σR−d(4)σA

]+

∫

n

[d(4)σB +

∫

loop

d(d)σV+

∫

1

d(d)σA

]

ε=0

subtraction terms yield local approximation for the real emission process

describe the amplitude in the soft & collinear limits [1/ε and 1/ε2 poles]∫

n+1

d(d)σA =∑

dipoles

∫

n

d(d)σB ⊗∫

1

d(d)Vdipole

↪→ universal dipole terms←↩spin- & color correlations



Hard Processes at Next-to-Leading Order QCD

The emerging picture

σNLO2→n =

∫

n+1

[d(4)σR−d(4)σA

]+

∫

n

[d(4)σB +

∫

loop

d(d)σV+

∫

1

d(d)σA

]

ε=0

Monte-Carlo codes

all the tree-level bits

subtraction of singularities∗

efficient phase-space integration

One-Loop codes

Loop amplitudes, i.e. 2<(AVA†B)

Loop integration

1/ε, 1/ε2 coefficients & finite terms

∗ automatedCatani-Seymour subtraction in:

Amegic/Sherpa [Gleisberg, Krauss Eur. Phys. J. C 53 (2008) 501]

MadDipole/MadGraph [Frederix, Gehrmann, Greiner JHEP 1006 (2010) 086]

Helac [Czakon, Papdopoulos, Worek JHEP 0908 (2009) 085]

Frixione-Kunszt-Signer subtraction [Nucl. Phys. B 467 (1996) 399] in:

MadFKS/MadGraph [Frederix et al. JHEP 0910 (2009) 003]



Hard Processes at Next-to-Leading Order QCDExample: W + 3jets @ NLO

real emission corrections:

g

q

gg g

qν

g

e

q′ q′

g

ν

Q

Q

e

q ′

q

ν

Q2Q1

Q1

Q2

e

one-loop corrections:

q

q′ν

e

g

Q Qg

q

q′ν

e

g

g g

q′

qν

e

g

g

q

g q′

g

g

ν

e

qν

e

Q Q

q′

g



Hard Processes at Next-to-Leading Order QCDExample: W + 3jets @ NLO

real emission corrections:

g

q

gg g

qν

g

e

q′ q′

g

ν

Q

Q

e

q ′

q

ν

Q2Q1

Q1

Q2

e

one-loop corrections:

q

q′ν

e

g

Q Qg

q

q′ν

e

g

g g

q′

qν

e

g

g

q

g q′

g

g

ν

e

qν

e

Q Q

q′

g

recently calculated using BlackHat+Sherpa[Berger et al. Phys. Rev. Lett. 102 (2009) 222001, Phys. Rev. D 80 (2009) 074036 ]

BlackHat: on-shell methods for one-loop amplitudes [arXiv:0808.0941]

Sherpa:

real-emission processesCatani–Seymour subtraction termsphase-space integration

⇒ also completed: Z/γ∗ + 3jets [arXiv:1004.1659] & W + 4jets [arXiv:1009.2338]



NLO QCD calculations: W + 3jets

BlackHat+Sherpa: Tevatron results [Phys. Rev. D 80 (2009) 074036]

consider W → eν and SISCone jets with E nth-jetT > 25 GeV & R=0.4

# of jets CDF LO NLO

1 53.5± 5.6 41.40(0.02)+7.59−5.94 57.83(0.12)+4.36

−4.00

2 6.8± 1.1 6.159(0.004)+2.41−1.58 7.62(0.04)+0.62

−0.86

3 0.84± 0.24 0.796(0.001)+0.488−0.276 0.882(0.005)+0.057

−0.138

20 40 60 80 100 120 140 160 180 200

10-4

10-3

10-2

10-1

100

dσ

/ d

ET [

pb /

GeV

]

LONLOCDF data

20 40 60 80 100 120 140 160 180 200

Second Jet ET [ GeV ]

0.5

1

1.5

2 LO / NLOCDF / NLO

NLO scale dependence

W + 2 jets + X

BlackHat+Sherpa

LO scale dependence

ET

jet > 20 GeV, | η

jet | < 2

ET

e > 20 GeV, | η

e | < 1.1

ET

/ > 30 GeV, MT

W > 20 GeV

R = 0.4 [siscone]

√s = 1.96 TeV

µR = µ

F = E

T

W

20 30 40 50 60 70 80 90

10-3

10-2

10-1

dσ

/ d

ET [

pb /

GeV

]

LONLOCDF data

20 30 40 50 60 70 80 90

Third Jet ET [ GeV ]

0.5

1

1.5

2 LO / NLOCDF / NLO

NLO scale dependence

W + 3 jets + X

BlackHat+Sherpa

LO scale dependence

ET

jet > 20 GeV, | η

jet | < 2

ET

e > 20 GeV, | η

e | < 1.1

ET

/ > 30 GeV, MT

W > 20 GeV

R = 0.4 [siscone]

√s = 1.96 TeV

µR = µ

F = E

T

W



NLO QCD calculations: W + n-jets

BlackHat+Sherpa: LHC predictions for√s = 7 TeV [arXiv:1009.2338]

Number of jetsσpp→e−νe+n−jets 1 2 3 4

σLO [pb] 264.4(0.2)+22.6−21.4 73.14(0.09)+20.81

−14.92 17.22(0.03)+8.07−4.95 3.81(0.01)+2.44

−1.34

σNLO [pb] 331(1)+15−12 78.1(0.5)+1.5

−4.1 16.9(0.1)+0.2−1.3 3.56(0.03)+0.08

−0.30

50 100 150

10-4

10-3

10-2

10-1

100

dσ

/ d

pT [

pb /

GeV

]

LONLO

50 100 150

First Jet pT [ GeV ]

0.5

1

1.5

2

LO / NLO

50 100 150

50 100 150

Second Jet pT [ GeV ]

50 100 150

50 100 150

Third Jet pT [ GeV ]

50 100 150

10-4

10-3

10-2

10-1

100

50 100 150

Fourth Jet pT [ GeV ]

0.5

1

1.5

2

NLO scale dependence BlackHat+SherpaLO scale dependence

pT

jet > 25 GeV, | η

jet | < 3

ET

e > 20 GeV, | η

e | < 2.5

ET

ν > 20 GeV, M

T

W > 20 GeV

R = 0.5 [anti-kT]

√s = 7 TeV

µR = µ

F = H

T

^ ’ / 2

W- + 4 jets + X



Hard Process generation: Summary

Automated tools to generate and evaluate tree-level amplitudes

compact matrix-element expressionsefficient phase-space integrators

Enormous progress in automating NLO calculations

modularity of the problemautomated subtraction terms + improved loop methodsW /Z + 3jets, W + 4jets with BlackHat+Sherpatt + 2jets with Helac-NLO [Bevilacqua et al. Phys. Rev. Lett. 104 (2010) 162002]

ttbb with Helac-NLO [Bevilacqua et al. JHEP 0909 (2009) 109]

e+e− → 5jets with MadFKS/MadGraph [Frederix et al. arXiv:1008.5313 [hep-ph]]



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