NLO QCD corrections to WZjj production at the...

INSTITUT FUR THEORETISCHE PHYSIK

NLO QCD corrections to WZjj production at the LHC

Francisco Campanario, Matthias Kerner, LE Duc Ninh, Dieter Zeppenfeld |Windows on the universe, Aug 2013, Quy Nhon

www.kit.eduKIT – Universitat des Landes Baden-Wurttemberg undnationales Forschungszentrum in der Helmholtz-Gemeinschaft

Outline

VVjj production (with leptonic decays) at the LHC: motivation

WZjj @ NLO QCD : some calculational details

Numerical results

Summary

LE Duc Ninh –Windows on the universe, Aug 2013, Quy Nhon2/17

VVjj production at the LHC: why?

Motivation:Sensitive to VV → VV scattering, quartic quage-boson couplings.Important background for new physics searches.WVjj with one charged lepton unobserved: background to W +W + jj production.

Classification at LO: 2 mechanismsEW mechanism (vector boson fusion, VBF): σEW ∝ α6

QCD mechanism: σQCD ∝ α2sα

Interference: color and kinematically suppressed. can be neglected for a-few-percent precision measurements at the LHC.

VVjj production at the LHC: why?

Motivation:Sensitive to VV → VV scattering, quartic quage-boson couplings.Important background for new physics searches.WVjj with one charged lepton unobserved: background to W +W + jj production.

Classification at LO: 2 mechanismsEW mechanism (vector boson fusion, VBF): σEW ∝ α6

QCD mechanism: σQCD ∝ α2sα

Interference: color and kinematically suppressed. can be neglected for a-few-percent precision measurements at the LHC.

What have been done at NLO QCD?

EW mechanism (VBF): consider QCD corrections to each quark lines separately pentagons at most.

W +W− jj : [Jager, Oleari, Zeppenfeld, 2006]ZZjj : [Jager, Oleari, Zeppenfeld, 2006]W±Zjj : [Bozzi, Jager, Oleari, Zeppenfeld, 2007]W +W + jj /W−W− jj : [Jager, Oleari, Zeppenfeld, 2009], [Denner, Hosekova, Kallweit, 2012], goodagreement!

QCD mechanism: two quark lines are not independent hexagons at most.W +W + jj /W−W− jj : [Melia, Melnikov, Rontsch, Zanderighi, 2010], [Campanario, Kerner, LDN,Zeppenfeld (to be published)]W +W− jj : [Melia, Melnikov, Rontsch, Zanderighi, 2011], [Greiner, Heinrich, Mastrolia, Ossola, et al,2012]W±Zjj : [Campanario, Kerner, LDN, Zeppenfeld, 2013]ZZjj : not done

all VBF processes and QCD W +W +jj /W−W−jj , W±Zjj are included in VBFNLOprogram. Available soon.

VBF vs. QCD background: a Higgs example[Rainwater, hep-ph/9908378]

LHC√

s = 14 TeV, pTj ≥ 20 GeV, |ηj | < 5, ∆Rjj ≥ 0.7,|ηγ | < 2.5, ∆Rjγ ≥ 0.7;ηj,min + 0.7 < ηγ < ηj,max − 0.7, ηj1ηj2 < 0

solid: VBFdashed: QCD

The two tagging jets are more separated in VBF than in QCD background!

pp → W±Zjj: QCD mechanism

The problem

+ . . .

Q: What is the NLO QCD correction to this process?

A: Before answering this question, some classifications are needed.

LO: subprocesses

2-quark lines [4q]: q1 + q2 → q3 + q4 + (WV )

76 subprocesses (2 generations).12 crossings.

1-quark line [2g]: q1 + q2 → g + g + (WV )

14 subprocesses (2 generations).7 crossings.

4 QCD gauge invariant groups: 4q(W ), 4qWV , 2g(W ), 2gWV .

NLO calculation: theory

vs. practice

dσNLO = dσvirt2→N + dσreal

2→N+1.

Both terms are IR divergent. The sum is finite for IR-safe observables (e.g. jetdistributions)

Real: IR divergences can be separated using Catani-Seymour dipole subtractionmethod.

Virtual: 1-loop amplitude is, unfortunately, much more complicated than tree-levelone. Use Feynman-diagram and tensor reduction methods. The most difficult part.

NLO calculation: theory vs. practice

dσNLO = dσvirt2→N + dσreal

2→N+1.

Both terms are IR divergent. The sum is finite for IR-safe observables (e.g. jetdistributions)

Real: IR divergences can be separated using Catani-Seymour dipole subtractionmethod.

Virtual: 1-loop amplitude is, unfortunately, much more complicated than tree-levelone. Use Feynman-diagram and tensor reduction methods. The most difficult part.

Counting diagrams: 2 generations

LO: 4840

NLO real emission: 79784

NLO virtual: 116896 (up to 6-point rank 5)

This calculation can be done with:

good classifications: effective currents V → l1l2, V → l1l2l3l4, building blocks(hexlines, penlines, . . .), . . .

use crossing symmetry (to a minimum extent to reduce computing time):subprocesses are not completely independent (diagrams share common parts).two independent calculations:

manual implementation using VBFNLO frameworkmore automated approach using HELAS/MadGraph, FeynArts, FormCalcloop integrals: 2 different codes

numerical instabilities in the virtual part: difficult gauge tests

Counting diagrams: 2 generations

LO: 4840

NLO real emission: 79784

NLO virtual: 116896 (up to 6-point rank 5)

This calculation can be done with:

good classifications: effective currents V → l1l2, V → l1l2l3l4, building blocks(hexlines, penlines, . . .), . . .

use crossing symmetry (to a minimum extent to reduce computing time):subprocesses are not completely independent (diagrams share common parts).two independent calculations:

manual implementation using VBFNLO frameworkmore automated approach using HELAS/MadGraph, FeynArts, FormCalcloop integrals: 2 different codes

numerical instabilities in the virtual part: difficult gauge tests

Numerical instabilities: gauge test

BN = T Nµ ε

µ(k), εµ → kµ,

1/q + /k

=1/q−

1/q + /k

T Nµ kµ −AN−1 = 0,

Q = 1−AN−1

T Nµ kµ

if Q < ε : accept the point.

if Q > ε : use quadruple precision,

Q < ε ? accept or discard points.

610 510 410 310 210 110 1

σ2.65

3 jj+Xµ+µeν+ e→pp

QCD virtual

2 = 10ε deviation off σBand: 2

Results: inclusive cuts

0µ/µ

110 1 10

[ fb ]

= 14TeVs

µ±µeν± e→pp

[Campanario, Kerner, LDN, Zeppenfeld, arXiv: 1305.1623]

pT ,j > 20 GeV, |ηj | < 4.5, Ranti−ktjj = 0.4, Rjl > 0.4;

pT ,l > 20 GeV, |ηl | < 2.5, Rll > 0.4, Ml+ l− > 15 GeV.

Dynamic scale: µF = µR = µ0 =(∑

jet pT ,jet +√

p2T ,W + m2

W +√

p2T ,Z + m2

pT ,V (mV ) are reconstructed from leptons, jets pass all cuts.

speed: 1% statistical errorin 2.5h on a normal PC(Intel i5-3470) with 1 core.

Distributions of leading jets

[ fb/T

= 14TeVs

jj+Xµ+µeν

+ e→pp

[ TeV ]T,j

p0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

[ fb/T

= 14TeVs

jj+Xµ+µeν

+ e→pp

[ TeV ]jjm0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

scale uncertainty: significantly reduced

K factor (NLO/LO): 0.6–1 in a large range

regular NLO QCD corrections (as expected)

Summary

VVjj is a special class of processes: sensitive to VV → VV scatterings, quarticgauge couplings, background for new physics searches, ...

Two mechanisms: EW (VBF), QCD, interference effects are very small.For WZjj with leptonic decays, QCD mechanism:

K factor: from 0.6–1 with a dynamic scale choice for many distributionsscale uncertainty: from 50% at LO to 5% at NLO for inclusive cross section

Virtual amplitude: difficult part, gauge tests are good to deal with numericalinstabilities.

The code will be available in the next release of the VBFNLO program.

Thank you!

Dipole subtraction method

∫N+1

dσrealN+1(p)JN+1(p) =

∫N+1

(dσrealN+1(p)JN+1(p)−

∑i,j

SNij (pij )JN

ij (pij )

∫N+1

∑i,j

SNij (pij )JN

ij (pij )︸︷︷︸PK+I

0dx∫

∑j 6=a

SNaj (x , p)JN

a (x , p) + (a↔ b) (2)

∑i,j

SNij (p)JN (p). (3)

The Jet function: a cut, a histogram, PDF(Q), αs(Q), ...IR safety: JN → JN+1 in the IR singular limits.

An easy mistake: in Eq. (1), set αNs (Q) = αN+1

s (Q): the result is finite, BUT wrong(almost correct) because the integrated part 6= the subtraction part.If we do JN = JN+1 in Eq. (1), then PK term will get more complicated. [arXiv:0802.1405]

Dipole subtraction method

∫N+1

dσrealN+1(p)JN+1(p) =

∫N+1

(dσrealN+1(p)JN+1(p)−

∑i,j

SNij (pij )JN

ij (pij )

∫N+1

∑i,j

SNij (pij )JN

ij (pij )︸︷︷︸PK+I

0dx∫

∑j 6=a

SNaj (x , p)JN

a (x , p) + (a↔ b) (2)

∑i,j

SNij (p)JN (p). (3)

The Jet function: a cut, a histogram, PDF(Q), αs(Q), ...IR safety: JN → JN+1 in the IR singular limits.

An easy mistake: in Eq. (1), set αNs (Q) = αN+1

s (Q): the result is finite, BUT wrong(almost correct) because the integrated part 6= the subtraction part.If we do JN = JN+1 in Eq. (1), then PK term will get more complicated. [arXiv:0802.1405]

Tree-level, virtual and real matchingPartonic level:

dσIsoft + dσvirt

soft = 0,

dσIcoll + dσvirt

coll = 0,

dσPKcoll 6= 0.

Hadronic level:

dσNLO = dσtree + dσvirt + dσreal,

PDFNLO ⊗ dσNLO =

∫dx1

∫dx2fa(x1,Q)fb(x2,Q)dσNLO + δPDF(dσtree, 1/ε),

dσPK ≡ dσPK (1/ε) + δPDF(dσtree, 1/ε) : finite

Default matching: PDF and dσreal are defined in the conventionaldimensional-regularization scheme (CDR), AND MS scheme.Virtual: use ’t Hooft-Veltman (HV) scheme (external momenta in 4D)

dσvirtHV = dσvirt

CDR, αHVs = αCDR

Dimensional regularization scheme (DRS) independence [Catani, Seymour, Trocsanyi 1997]:

dσtree + dσvirt + dσI : /∈ DRS at partonic level!

4 flavors (no b/t) or 5 flavors (b and t loop): αs , PDF, tree, virtual, real.

dσIsoft + dσvirt

soft = 0,

dσIcoll + dσvirt

coll = 0,

dσPKcoll 6= 0.

Hadronic level:

PDFNLO ⊗ dσNLO =

∫dx1

dσvirtHV = dσvirt

CDR, αHVs = αCDR

dσIsoft + dσvirt

soft = 0,

dσIcoll + dσvirt

coll = 0,

dσPKcoll 6= 0.

Hadronic level:

PDFNLO ⊗ dσNLO =

∫dx1

Default matching: PDF and dσreal are defined in the conventionaldimensional-regularization scheme (CDR), AND MS scheme.

Virtual: use ’t Hooft-Veltman (HV) scheme (external momenta in 4D)

dσvirtHV = dσvirt

CDR, αHVs = αCDR

dσIsoft + dσvirt

soft = 0,

dσIcoll + dσvirt

coll = 0,

dσPKcoll 6= 0.

Hadronic level:

PDFNLO ⊗ dσNLO =

∫dx1

dσvirtHV = dσvirt

CDR, αHVs = αCDR

Fermion loops

Include V decays:

εµ(k , λ)→ Jµeff/(k2 −M2V + iMV ΓV ), Or

gµν = −∑

λ=−1,0,1

εµ(k , λ)ε∗ν(k , λ) +kµkν

k2︸︷︷︸=0

kµF1γµ(a + bγ5)F2 = 0, since : m1 = m2 = 0 (no Goldstones).

Fermion loop with γ5: anomaly free (need both b and t)g*

2.5 generations not OK (we cannot decouple the top quark).

Fermion loops

Include V decays:

εµ(k , λ)→ Jµeff/(k2 −M2V + iMV ΓV ), Or

gµν = −∑

λ=−1,0,1

εµ(k , λ)ε∗ν(k , λ) +kµkν

k2︸︷︷︸=0

kµF1γµ(a + bγ5)F2 = 0, since : m1 = m2 = 0 (no Goldstones).

Fermion loop with γ5: anomaly free (need both b and t)g*

2.5 generations not OK (we cannot decouple the top quark).

NLO QCD corrections to WZjj production at the...

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