Transverse Momentum Resummation for Higgs Production at Hadron Colliders Chong Sheng Li School of Physics, Peking University 2012 海峡两岸粒子物理与宇宙学研讨会 , 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

LHC Results from CMS 4.8 fb −1 arXiv: , arXiv: , arXiv:

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 LO, Georgi,Glashow 1991,1993, NLO, Dawson,Djouadi, Spira,Zerwas, NNLO Harlander,Kilgore, Anastasiou, Melnikov, NNLL+NLO pT Resummation, Catani, Grazzini 2005,2007 NNNLL+NNLO Resummation in SCET, Neubert, L.L.Yang 2008 Differential NNLO, Anastasiou, Melnikov, Catani, Grazzini NLL+NLO pT Resummation in SCET 2008-now NNLL+NNLO pT Resummation our work

pT Resummation in SCET Recently, 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.LiuNo numerical resultsNLL PLB625 (2005)253A.Idilbi,X.Ji,F.YuanNo numerical resultsNLL PRD 83,053007(2011)S. Mantry,F.PetrielloHas numerical results for Higgs production NLL EPJC(2011)71:1665T. Becher, M.NeubertHas numerical results for Z production NNLL arXiv: M. Garcia, A. Idilbi,…No numerical resultsNLL arXiv: J. Chiu, A.Jain,...No numerical resultsNLL Collinear AnomalyRapidity 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 Formula The resummation formula for inclusive differential cross section for gg → H can be written as Born cross sectionQuark mass effectsNarrow width approximation Containing large logarithms Matching termNon-perturbative effects

Soft Gluon Resummation Formula The 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 Formula To obtain the C function, we use the equation

Soft Gluon Resummation Formula

Notice From virtual corrections

Soft Gluon Resummation Formula A 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