V + jet production at the LHC: ELECTROWEAK PRECISION · Outline 1 Introduction 2 Status of Theory...

V + jet production at the LHC:ELECTROWEAK PRECISION

Tobias Kasprzik

In collaboration with A. Denner, S. Dittmaier and A. Mück

Karlsruhe Institute of Technology (KIT),Institut für Theoretische Teilchenphysik (TTP)

JHEP 0908 (2009) 075, JHEP 1106 (2011) 069

Workshop on electroweak corrections for LHC physics,24-26 September 2012, Durham

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Tobias Kasprzik (KIT) V + jet production at the LHC 25/9/2012, Durham 1 / 20

Outline

1 Introduction

2 Status of Theory PredictionsQCD CorrectionsElectroweak Corrections

3 Details of the CalculationsVirtual CorrectionsReal Corrections

4 Numerical Results

5 Combination of QCD and EW Corrections

6 Summary & Conclusions


Introduction – W/Z + Jets at the LHC

Vector bosons almost always produced together with additionalQCD radiation

V + jets production: pp→ W/Z + n jets

Wq

g gggq′

eν

g

g

eW

νq′

q

Q Q

Proper understanding of SM physicsStudyjet dynamicsin QCDBackgrounds to various signatures (leptons + jets +/ET) predicted bynew-physicsmodels

SUSY-particle pair productionSingle-graviton production (1 jet +/pT

) → νℓνℓ + jet


Introduction – W/Z + Jets at the LHC

Vector bosons almost always produced together with additionalQCD radiation

V + jets production: pp→ W/Z + n jets

Wq

g gggq′

eν

g

g

eW

νq′

q

Q Q

Proper understanding of SM physicsStudyjet dynamicsin QCDBackgrounds to various signatures (leptons + jets +/ET) predicted bynew-physicsmodels

SUSY-particle pair productionSingle-graviton production (1 jet +/pT

) → νℓνℓ + jet

High-precision theoretical predictions necessary!


W/Z + jet(s) at the LHC – QCD Corrections

W/Z + n jetsmulti-leg processes, high jet multiplicity→ demanding calculations, high computational effort

NLO corrections matched with partonshowers for W/Z + jet[Alioli et al. 2010] andW + 1/2/3 jets production[Sherpa+MC@NLO: Hoeche,

Krauss, Schönherr, Siegert 2012]

Resummation effects known for V-bosonproduction at small[Bozzi et al. 2008; Berge, Nadolsky,

Olness 2006;. . .] and largepT [Becher, Lorentzen, Schwartz 2012,

. . .]

NLO corrections to W + 1/2/3/4(/5) jetsand Z + 1/2/3/4 jets known[BlackHat+Sherpa,

Rocket+MCFM,many others. . .]

→ W + 5 jets: First 2 → 6 NLOprediction for hadron colliders!

Automation of NLOcomputations[OpenLoops, GoSam, HELAC-NLO,

MadLoop/aMC@NLO, . . .]

200 300 400 500 600 700 800 900 1000

10-4

10-3

10-2

dσ /

dHT

[ pb

/ G

eV ]

LONLO

200 300 400 500 600 700 800 900 1000H

T [ GeV ]

0.5

1

1.5

2LO / NLO NLO scale dependence

W- + 4 jets + X

BlackHat+Sherpa

LO scale dependence

pT

jet > 25 GeV, | η jet

| < 3

ET

e > 20 GeV, | ηe

| < 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

[Berger et al.: arXiv:1009.2338 [hep-ph]]


V + jet Production at High EnergiesSudakov Logarithms

High-energy limit

s, |t|, |u| ≫ M2V , s ∼ |t| ∼ |u|

→ bosons have to be produced at largepT

EW corrections at high energies dominated byuniversal large logarithms

∝ αL ln2L(MV/√

s) (LL) ,

∝ αL ln2L−1(MV/√

s) (NLL) , . . .

at theL-loop levelSizable negative correctionsat NLO at largepT

Change of signgoing from LL to NLL (to NNLL . . .)→ substantial cancellations possible!


EW Corrections to V + jet Production

On-Shell W/Z production with one QCD jet:

Purely weak corrections to on-shellZ + jet production known, includingNLL and NNLL approximationsatone loop[Kühn, Kulesza, Pozzorini, Schulze 2005]

Full O(α) + leading 2-loopcorrectionsknown for on-shell W +jet production[Kühn, Kulesza, Pozzorini, Schulze 2007/08;

Hollik, TK, Kniehl 2008]

NNLO = NLO + 2-loop NLLNLL and NNLL considered at oneloopTypical negative one-loop SudakovlogsNLL two-loop corrections lead to ashift of ∼ 10% at highestpT

NNLL/LO − 1

NLL/LO − 1

NLO/LO − 1

NNLO/LO − 1

(c) W−

pT [GeV]

200018001600140012001000800600400200

0.00

-0.10

-0.20

-0.30

-0.40

NNLL/LO − 1

NLL/LO − 1

NLO/LO − 1

NNLO/LO − 1

(b) W+

0.00

-0.10

-0.20

-0.30

-0.40

LO

(a)W−

W+

dσ dpT

[pb/

GeV

]

101

100

10−1

10−2

10−3

10−4

10−5

10−6

[Kühn et al.: arXiv:0708.0476 [hep-ph]]


EW Corrections to V + jet Production (II)

Next step:Compute full NLO EW corrections to

pp → W + jet → νℓℓ + jet ,

pp → Z/γ∗ + jet → ℓ+ℓ−/νℓνℓ + jet

in the SM [Denner, Dittmaier, TK, Mück 2009/11]

Include leptonic decays:X Final-state leptons phenomenologically accessibleX Investigate effects due to final-state photon radiation

Include off-shell effects:X Investigate distribution ofmℓℓ (NC) andmT,ℓℓ (CC)

→ Search for new resonances in the off-shell tailsChallenges:=⇒ Consistent treatment of finite gauge-boson width!=⇒ Demanding 2→ 3 computation in the full SM (many scales, pentagon diagrams,

infrared singularities,. . .)Tobias Kasprzik (KIT) V + jet production at the LHC 25/9/2012, Durham 7 / 20

Virtual EW Corrections to pp→ ℓℓ + jetOverview – 1PI Insertions

Self-energyinsertions:

q

g

l

l

q

q

q

Z/γq

g

l

l

q

Z/γZ/γ

q

q

g

l

l

q

q

q

Z/γ q

g

l

l

q

Z/γ

Z/γq

Triangleinsertions:

q

g

l

l

q

q

Z/γq

g

l

l

q

q

Z/γq

g

l

l

q

q

Z/γ

q

g

l

l

q

qZ/γ

q

g

l

l

q

qZ/γ

q

g

l

l

q

qZ/γ

Box and pentagoninsertions:

q

g

l

l

q

q

q

g

l

l

q

qq

g

l

l

q

Z/γq

g q

l

l


Virtual EW Corrections pp→ ℓℓ + jet (II)Some details

Pentagon Contributions atO(α3αs)

q

g

l

l

q

q

Z/γ

q

l

Z/γ

q

g

l

l

q

q

Z/γ

q

l

Z/γ

q

g

l

l

q

q′

W

q′

νl

W

The fine-structure constant is defined in theGµ scheme:�

�α(0) → αGµ =

√2GµM2

Wπ

(

1− M2W

M2Z

)

, δZe → δZe − 12∆r

Loops calculated usingComplex-Mass Scheme[Denner, Dittmaier, Roth, Wieders 2005]

Reduction of pentagons directly to boxes avoiding small Gram determinants[Denner, Dittmaier 2003, 2005]

Need to calculate scalar one-loop 4-point integrals with complex masses[Denner,

Dittmaier 2010]


The Complex-Mass Scheme (CMS)

A problem with unstable particlesNaive implementation of finite width in gauge-boson propagator:

−igµν

q2 − M2W + iǫ

→ −igµν

q2 − M2W + iMWΓW

ΓW includes Dyson summation of self energies, mixing of perturbative orders→ might destroy gauge invariance (even at leading order!)


The Complex-Mass Scheme (CMS)

A problem with unstable particlesNaive implementation of finite width in gauge-boson propagator:

−igµν

q2 − M2W + iǫ

→ −igµν

q2 − M2W + iMWΓW

ΓW includes Dyson summation of self energies, mixing of perturbative orders→ might destroy gauge invariance (even at leading order!)

�

�

�

�

→ CMS universal solution thatrespects gauge invariance

is valid in all phase-space regions

Straightforward implementation:

LO: M2V → µ2

V = M2V − iMVΓV , cos2 ΘW =

µ2W

µ2Z

, V = W, Z

NLO:Complex renormalization:L0 → L + δL, bare (real) Lagrangian unchanged!Evaluate loop integrals with complex masses


Real EW Corrections to pp→ ℓℓ + jetInfrared Singularities

Real photon radiation atO(αsα3): q g → ℓ−ℓ+ + q + γ

q

g

l

l

q

γ

q

q Z/γ

q

g

l

lq

γ

q

Z/γ

q q

g

l

l

q

γ

qZ/γ

q

q

g

ll

q γq

lZ/γq

g

l

lq

γ

q

lZ/γ

q

g

l

l

q γ

q

q

Z/γq

g

l

lq

γ

Z/γ

q

q

q

g

l

l

q

γ

q

Z/γ

q

q

g

ll

q γ

q

Z/γ

l

q

g

l

l

qγ

q

Z/γ

l

Soft singularitiesdue to soft photonsInitial-state collinear singularities due to collinear photon radiationoffinitial-state quarks→ renormalization of PDFsFinal-statecollinear singularities due to photon-radiation off final-state leptonsand quarks

−→ Dipole subtraction for photon radiation off fermions [Dittmaier 1999]


Final-State Radiation

We allow for fully exclusive treatment of FS photon radiation:

dressed electrons (rec.):recombination of collinearelectron–photon configurations→ large lnme terms cancel

bare muons: exclusive treatment of collinear muon–photonconfigurations→ enhancement of corrections due to large lnmµ terms

quark → photon fragmentation: exclusive treatment of collinearparton(q, g)–photon configurations to separate V + jet from V + photon→ residual lnmq terms absorbed in the perturbative part of arenormalizedphoton fragmentation function[Buskulic et al. 1996; Glover, Morgan 1994; Denner, Dittmaier, Gehrmann, Kurz 2010]

Dq→γ(zγ) =αQ2

q

2πPq→γ(zγ)

(

lnm2

q

µ2F

+ 2 lnzγ + 1

)

+ DALEPH,MSq→γ (zγ , µF)

Non-perturbative partDALEPH,MSq→γ (zγ , µF) determined by the ALEPH experiment

at CERNTobias Kasprzik (KIT) V + jet production at the LHC 25/9/2012, Durham 12 / 20

Technical Framework

Tools for numerical evaluation: Two completely different implementations!

SD (Freiburg), TK (Karlsruhe)Virtuals: FeynArts-1.0 [Küblbeck, Böhm, Denner],

Algebraical reduction: in-houseMathematica routines

Real emission:amplitudes worked out by hand

Numerical integration: Vegas [Lepage]

AD (Würzburg), AM (Aachen)Virtuals & real emission: FeynArts-3.2/FormCalc-3.1 [Hahn]

Fortran code generated automatically byPole [Meier, Mück]

Numerical integration: Pole interface toLusifer [Dittmaier, Roth]

(Vegas-improved)


Numerical Results (I) – Z + jet production

Distribution of the invariant mass mℓℓ =√

(pℓ+ + pℓ−)2

δvarQCD,veto

δµ=MZ

QCD,veto

δvarQCD

δµ=MZ

QCD

mℓℓ[GeV]

δ[%]

1401201008060

60

40

20

0

−20

−40

δµ+µ−

EW

δrecEW

mℓℓ [GeV]

δ[%]

1401201008060

120

100

80

60

40

20

0

−20

σµ+µ−

full,veto

σµ+µ−

full

σ0

pp → ℓ+ℓ−+jet (+γ)√

s = 14 TeV

mℓℓ [GeV]

dσ/dmℓℓ [pb/GeV]

1401201008060

100

10

1

0.1

0.01

Typical Breit–Wigner shape of the LO distributionFinal-state photon radiation systematically shifts events to smallermℓℓ

→ huge positive correctionscorrections to total cross section still small (−5%)Note: QCD corrections uniform and of expected size


Numerical Results (II) – Compare Z and W Cross Sections

Distribution of the transverse massmT,ℓℓ =√

2pT,ℓ+pT,ℓ−(1− cosφℓℓ)

W-PRODUCTION CROSS SECTION:

δvarQCD,veto

δµ=MZ

QCD,veto

δvarQCD

δµ=MZ

QCD

pp → W+ + jet (+jet)

mT,ℓℓ/MV

δ[%]

1.41.31.21.110.90.80.70.6

60

40

20

0

−20

−40

δµ+µ−

EW,W

δrecEW,W

pp → W+ + jet (+γ)

mT,ℓℓ/MV

δ[%]

1.41.31.21.110.90.80.70.6

10

5

0

−5

−10

−15

−20

σ0(W−)

σ0(W+)

pp → V + jet (+γ)√

s = 14 TeV

mT,ℓℓ [GeV]

dσ/dmT,ℓℓ [pb/GeV]

1201101009080706050

50

40

30

20

10

0





W AND Z-PRODUCTION CROSS SECTION:

δvarQCD,veto

δµ=MZ

QCD,veto

δvarQCD

δµ=MZ

QCD

pp → Z + jet (+jet)

mT,ℓℓ/MV

δ[%]

1.41.31.21.110.90.80.70.6

60

40

20

0

−20

−40

δµ+µ−

EW,Z

δrecEW,Z

δµ+µ−

EW,W

δrecEW,W

pp → Z + jet (+γ)

mT,ℓℓ/MV

δ[%]

1.41.31.21.110.90.80.70.6

10

5

0

−5

−10

−15

−20

σ0(W−)

σ0(W+)

σ0(Z)

pp → V + jet (+γ)√

s = 14 TeV

mT,ℓℓ [GeV]


1201101009080706050

50

40

30

20

10

0





W AND Z-PRODUCTION CROSS SECTION:

δvarQCD,veto

δµ=MZ

QCD,veto

δvarQCD

δµ=MZ

QCD

pp → Z + jet (+jet)

mT,ℓℓ/MV

δ[%]

1.41.31.21.110.90.80.70.6

60

40

20

0

−20

−40

δµ+µ−

EW,Z

δrecEW,Z

δµ+µ−

EW,W

δrecEW,W

pp → Z + jet (+γ)

mT,ℓℓ/MV

δ[%]

1.41.31.21.110.90.80.70.6

10

5

0

−5

−10

−15

−20

σ0(W−)

σ0(W+)

σ0(Z)

pp → V + jet (+γ)√

s = 14 TeV

mT,ℓℓ [GeV]


1201101009080706050

50

40

30

20

10

0

σ(W+)/σ(Z) ∼ 5Phase-space-dependent EW corrections 100% bigger in Z-boson production(two leptons in the final state!)QCD corrections of similar size for W and Z production


Numerical Results (III): Z + jet production

Z+jet production, leading-jet transverse momentum

Huge QCD corrections at highpT,jet

→ events at NLO dominated by tree-level Z + 2 jets production

Jet vetostabilizes corrections; reduction of scale dependence

Large negative EW correctionsat highpT,jet due to universal Sudakov logs


Numerical Results (IV) – Single-Jet Production

Monojet production, missing transverse momentum

Moderate QCD corrections, constantK-factor forvariable scalechoice→ jet veto leads to amoderateshift (-20%), no distortion of process signature

Assume factorization of EW correctionsfor this particularobservable


Combination of QCD and EW Corrections

Task: Include EW corrections in comparison with experimental data

(DY: Additive combination of NLO EW + NNLO QCD inFEWZ [Li, Petriello 2012])

ChallengeHow to combine our NLO EW corrections with a “state-of-the-art”QCD Monte Carlo (N(N)LO, parton-shower, resummation,hadronization,. . .)

Compute mixed QCD×EW corrections⇒ difficult, requires involved 2-loop computationsEW correctionsdominated by Sudakov logsattributed to hard process,QCD correctionsdominated by soft and collinear radiation⇒ factorized ansatzmay be well justified

dσbestQCD×EW

dpT,Z= (1 + δEW(pT,Z))

dσbestQCD

dpT,Z�

�

�

�

Caveat: Factorized ansatz will fail for observables whichare dominated by hard QCD radiation (Z + 2 jets at LO)!⇒ veto hard back-to-back jets


EW Corrections at the Tevatron

Our predictions have been included in the analysis of Tevatron data[http://www-cdf.fnal.gov/physics/new/qcd/QCD.html]

[GeV/c]ll→ZT

p30 40 50 100 200 300

[fb

/ (G

eV/c

)]ll

→Z T

/dp

σd

-110

1

10

210

310

410

CDF Run II Preliminary

1 jet≥) + -l+ l→*(γZ/2 > 25 GeV/cl

T| < 1.0; plη; |µl = e,

2.1≤| jet 30 GeV/c, |Y≥ jet

Tp

-1 CDF Data L = 9.64 fb

Systematic uncertainties

NLO EW⊗ NLO QCD

MSTW2008NLO PDF

)-lT + P

+lT + PT

j PjΣ (

21 = TH

21 =

0µ

arXiv:1103.0914

Dat

a / T

heor

y

1

1.5

NLO LOOPSIM+MCFMn

NLO MCFM

/20

µ = µ ; 0

µ = 2µ

[GeV/c]ll→ZT

p30 40 50 100 200 300

0.8

1

1.2

1.4 NLO EW⊗ NLO QCD

NLO QCD

δEW ∼ 5% atpT,Z = 300 GeVOnset of Sudakov logs visible at the TevatronEW correctionscrucialat the LHC


Summary & Conclusions

We have calculated the full NLO EW correctionsto off-shell V+jet production and single-jet production at

the LHC:

Consistent treatment of the vector-boson resonance using theComplex-Mass SchemeAll off-shell effects includedNon-collinear-safe treatmentof final-state photon radiation fromleptons possibleCalculationfully differentialPredictions for Z+jet productionimplemented in CDF analysis:http://www-cdf.fnal.gov/physics/new/qcd/QCD.html

Future Work:Publish monojet results!Combination of EW and QCD correctionsCompare our results to LHC data


Summary & Conclusions

We have calculated the full NLO EW correctionsto off-shell V+jet production and single-jet production at

the LHC:

Consistent treatment of the vector-boson resonance using theComplex-Mass SchemeAll off-shell effects includedNon-collinear-safe treatmentof final-state photon radiation fromleptons possibleCalculationfully differentialPredictions for Z+jet productionimplemented in CDF analysis:http://www-cdf.fnal.gov/physics/new/qcd/QCD.html

Future Work:Publish monojet results!Combination of EW and QCD correctionsCompare our results to LHC data

Thank You!Tobias Kasprzik (KIT) V + jet production at the LHC 25/9/2012, Durham 20 / 20

NLO Electroweak Corrections – IR-Safe Observables

Infrared SingularitiesOccur in real bremsstrahlung corrections as well as in loop diagrams

Have to be regularized to make them calculable!

Mass regularization for IR singularities: include small fermion massesmℓ, mq

and an infinitesimal photon massλ (Neglect regulator masses in non-singularparts of the calculation!)

combine virtual and real corrections→ ln(λ) dependence drops out.Initial-state collinear singularities absorbed into PDFsFinal-state collinear singularities give rise toln(mℓ) andln(mq) terms in the crosssection.

Important: Proper definition of observables!




Collinear photon-quark pair:

Photon-quark recombination to get rid of unphysicalln(mq) terms

Photon-gluon recombination will lead to soft gluon pole!

Way out: Distinguish Z+jet from Z+γ events→ discard events withzγ =

Eγ

Eq+Eγ> 0.7→ residual logs absorbed inrenormalized photon

fragmentation function [Buskulic et al. 1996; Glover, Morgan 1994; Denner, Dittmaier, Gehrmann, Kurz 2010]

�

�

�

Dq→γ(zγ) =

αQ2q

2πPq→γ(zγ)

(

lnm2

q

µ2F

+ 2 lnzγ + 1

)

+DALEPH,MSq→γ (zγ , µF)

Non-perturbative partDALEPH,MSq→γ (zγ , µF) determined by the ALEPH experiment

at CERN




A collinear e± + γ pair cannot bedistinguished experimentally→ recombination necessary→ ln(me) drops out (KLN theorem)

collinear-safe observable

A collinear µ± + γ pair can bedistinguished experimentally→ no recombination necessary→ ln(mµ) survives→ physical contributions!→ enhanced corrections!

non-collinear-safe observable

We have worked out thedipole subtractionformalism for non-collinear-safe observables andvarious QED splittings.[Dittmaier, Kabelschacht, TK 2008]


EW Input Schemes – Definition ofα

α(0): On-shell definition in the Thomson-limit (zero momentum transfer)

u(p)ΓAeeµ (p, p)u(p)

∣

∣

p2=m2e= e(0)u(p)γµu(p) , α(0) = e(0)2/4π

α(MZ) obtained via renormalization-group running from 0 to weak scaleMZ

α(MZ) =α(0)

1− ∆α(MZ), ∆α(MZ) = ΠAA

f 6=t(0) − ReΠAAf 6=t(M

2Z)

αGµ defined through the Fermi constant related to the muon lifetime

αGµ =

√2GµM2

Ws2w

π=

α(0)

1− ∆r

∆r includes corrections to muon lifetime not contained in QED-improved Fermimodel

light-fermion mass logs contained inΠAAf 6=t(0) resummed in effective

couplingsα(MZ) and αGµ


V + jet production at the LHC: ELECTROWEAK PRECISION · Outline 1 Introduction 2 Status of Theory...

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Transcript of V + jet production at the LHC: ELECTROWEAK PRECISION · Outline 1 Introduction 2 Status of Theory...