Transverse Momentum Resummation for Higgs Production at Hadron

Colliders

Chong Sheng LiSchool of Physics, Peking University

2012 海峡两岸粒子物理与宇宙学研讨会

2012-05-08, 重庆邮电大学

Based on recent work with J.Wang, H.T. Li, Zhao Li, and C.P.Yuan

Higgs mechanism: the spontaneous breakdown of a gauge symmetry by a self-interacting scalar field, which thereby lends mass to gauge bosons

Large Hadron Collider (LHC)

LHC Results from ATLAS 4.9 fb−1

ATLAS-CONF-2011-163

LHC Results from CMS 4.8 fb−1

arXiv:1202.1487, arXiv:1202.1997, arXiv:1202.1488

Status of Higgs Production in the SM• An accurate prediction of the Higgs boson production is crucial to discover or

exclude certain Higgs boson mass regions.

• The main production mechanism of the SM Higgs boson at hadron colliders is gluon fusion through a heavy-quark loop.

1978

LO, Georgi,Glashow

1991,1993,1995 2002

NLO, Dawson,Djouadi,

Spira,Zerwas,

NNLO Harlander,Kilgore,

Anastasiou, Melnikov,

NNLL+NLOpT Resummation, Catani, Grazzini

2005,2007

NNNLL+NNLO Resummation in

SCET, Neubert, L.L.Yang

2008

Differential NNLO, Anastasiou, Melnikov,

Catani, Grazzini

2003-2006

NLL+NLO pT

Resummation in SCET

2008-now

NNLL+NNLO pT Resummation

our work

pT Resummation in SCETRecently, the soft-collinear effective theory (SCET) has been used widely to discuss the transverse momentum distribtution.

PRD 72,114020(2005)

Y.Gao,C.S.Li,J.Liu No numerical results NLL

PLB625 (2005)253 A.Idilbi,X.Ji,F.Yuan No numerical results NLL

PRD 83,053007(2011)

S. Mantry,F.Petriello Has numerical results for Higgs production

NLL

EPJC(2011)71:1665 T. Becher, M.Neubert Has numerical results for Z production

NNLL

arXiv:1111.4996 M. Garcia, A. Idilbi,… No numerical results NLL

arXiv:1202.0814 J. Chiu, A.Jain,... No numerical results NLL

Collinear Anomaly Rapidity Renormalization Group

Transverse momentum distribtution

ResBos: Resummation for Bosons• ResBos can calculate the resummed soft gluon contributions  in unpolarized

Drell-Yan-like processes at hadron-hadron colliders.

• ResBos is a useful tool for studying electroweak gauge bosons and Higgs bosons at the Tevatron and the LHC.

• ResBos includes not only QCD resummation for low qT region but also higher order effect in high qT region, with spin correlations included via gauge invariant set of matrix elements.

Soft Gluon Resummation• In hadron colliders, if the final states are colorless,

the transverse momentum of them vanish due to total momentum conservation. The cross section can be well predicted by fixed-order perturbative calculations.

• But in the small qT region, the fixed-order is not reliable any more since it suffers from the large soft gluon radiation contributions.

Resummation is to resum systematically these large contributions to all orders.

Soft Gluon Resummation FormulaThe resummation formula for inclusive differential cross section for gg → H can be written as

Born cross sectionQuark mass effects Narrow width approximation

Containing large logarithms Matching termNon-perturbative effects

Soft Gluon Resummation FormulaThe dominant effects at small qT are encoded in

C function

where the S denote the Sudakov exponent controlled by A, B functions,

Soft Gluon Resummation FormulaTo obtain the C function, we use the equation

Soft Gluon Resummation Formula

Soft Gluon Resummation Formula

Notice

From virtual corrections

Soft Gluon Resummation FormulaA G function similar to the C function is also included in ResBos this time.

with

This function appears only for the gluon initiated process.

S. Catani, Nucl.Phys. B845, 297 (2011)

Total Cross Section for gg → H

Increase by 8% (6%) Agree in 3%, but small uncertainty

pT distribution of Higgs

enhanced by 20% suppressed by 20%

Here

Effects of including G functions

The difference is small

Non-perturbative Coefficients Uncertainty

The uncertainty is obvious only in the small qT region

Summary