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QCD resummation in Higgs Boson Plus Jet Production

Feng Yuan Lawrence Berkeley National Laboratory

Ref: Peng Sun, C.-P. Yuan, Feng Yuan, PRL 113, 232001 (2014);

PRL114, 202001 (2015); arXv: 1506.06170.

Outlines

Dijet correlation from Tevatron and LHC Soft gluon resummation

Collins-Soper-Sterman Higgs boson plus Jet production

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Dijet production at the hadron colliders

Most abundant events Almost back-to-back De-correlation comes

Hard gluon jetSoft gluon radiation

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Beautiful data from Tevatron/LHC

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ATLAS, PRL11

QCD calculations Fixed order calculations

divergent around π, where soft gluon radiation dominate

All order resummation is needed to understand the physics around here Two separate scales PT>>qT

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Leading PT

Total qT≈PTSin(Δϕ)

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Sudakov Large Double Logarithms Differential cross section depends on Q1, where

Q2>>Q12>>2

QCD

We have to resum these large logs to make reliable predictions QT: Dokshitzer, Diakonov, Troian, 78; Parisi Petronzio,

79; Collins, Soper, Sterman, 85 Threshold: Sterman 87; Catani and Trentadue 89

Sudakov, 1956

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How Large of the Resummation effects

ResumResum

NLONLOKulesza, Sterman, Vogelsang, 02

Z/γ*

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Collins-Soper-Sterman Resummation (PT,Q)=H(Q) f1(k1T,Q) f2(k2T, Q) S(T) Large Logs are resummed by solving

the energy evolution equation of the TMDs

K and G obey the renormalization group eq.

(Collins-Soper 81, Collins-Soper-Sterman 85)

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CSS Formalism (Drell-Yan)

The large logs will be resummed into the exponential form factor

A,B,C functions are perturbative calculable A: Sudakov double logs B: anomalous dimension C: hard coefficients

f1,f2 are integrated PDFs(Collins-Soper-Sterman 85)

Dijet production is different

Final states carry colorSoft gluon radiation will contribute

Jet algorithm will enter into the calculations as wellOnly out of cone radiation contributes to the

imbalance between the two jets

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Dijet (Leading Double Logs-A)

Power counting: each incoming parton contributes to a half of the associated color factor

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Banfi-Dasgupta-Delenda, PLB 2008Mueller-Xiao-Yuan, PRD 2013

A(1)=(Cp1+Cp2)/2

Next-to-leading Logs (NLL) Jet size-dependence (Banfi-Dasgupta 2004)

Matrix form (Kidonakis-Sterman 1997)

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Sun,C.-P. Yuan, F. Yuan, PRL 2014

D: color-factor for the jetR: jet size

One-loop: Soft and collinear gluon

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VirtualEllis-Sexton 86

Jet (Narrow Jet Approx.)Jager-Stratmann-Vogelsang 2004

SoftInitial state

SoftFinal state (out of jet cone)

Cross checks Divergences cancelled out between

virtual, jet, sot contributions (dimension regulation applied)

Final results :double logs, single logs, ..

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Quark channel: qiqjqiqj

Compared to full calculations

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Leading PT

Total qT≈PTSin(Δϕ)

full LO: Nagy 2002, NLOJET++ D0 kinematics

Sun, Yuan, FY,PRL 113, 232001 (2014)

Compared to the data

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D0 data

Full NLO: Nagy 2002, NLOJET++

NLL Resummation:Sun,C.P.Yuan, F.Yuan, PRL2014

Sun, Yuan, FY;PRL 113, 232001 (2014)

At the LHC

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Sun, Yuan, FY, 1506.06170.

Higgs Boson plus Jet Production

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Higgs Boson plus Jet Production One of the major channels to study Higgs

boson coupling to SM particles Already data from LHC In particular, Higgs boson plus two jets

with large rapidity separation to study HWW coupling

As compared to dijet, it is much simpler, and a complete one-loop calculation possible

Jet and soft gluon radiation

Virtual graphs been calculated before

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One-loop results

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Resummation

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Importance of the resummation

qT: total transverse momentum of the Higgs boson and the jet

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Sun, Yuan, FY,PRL114, 202001 (2015)

Azimuthal angular correlation

Φ: azimuthal angle between the Higgs boson and the jet

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Sun, Yuan, FY,PRL114, 202001 (2015)

Further applications Higgs boson PT distribution in associated

with jet production

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Boughezal et al,1504.07922,1505.03893

Resummation willbe important in thePcut regionWork in progress

Higgs boson plus two jets

Vector boson fusion and gluon-gluon fusion

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Competing mechanism

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Campbell et al,hep-ph/0608194

QCD resummation

It’s a tough calculation However, in the most interesting channel,

two jets are produced forward-backward (+y,-y), we can simplify the derivation

No color-matrix needed, although there are two jets in the final stateSimilar to the Mueller-Navelet dijet

Mueller-Xiao-Yuan, working in progress

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Similar to W/Z and inclusive Higgs production (Collins-Soper-Sterman)

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We are working on numerics,…

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Summary Soft gluon resummation for jet production

and jet plus weak boson production can be performed, and these effects are important

Improvements can be made to extend the narrow jet approximation and study jet size dependence carefully

Extend to W/Z and jet production, many data to test the formalism

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TMD factorization and resummation

TMD evolution

Soft factor

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Final results at NLL

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Factorization breaking effects

In collinear calculations, it appears at αs3 corrections, will

affect A(3) coefficient

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Collins-Qiu 07

Factorizable,A(1)

Non-perturbative form factor

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W(b) for gluon-gluon channelfor typical LHC kinematics withtwo different non-perturbative inputs