We consider QCD radiative corrections to Standard Model Higgs boson
production in association with a W boson in hadron collisions. We present a
fully exclusive calculation up to next-to-next-to-leading order (NNLO) in QCD
perturbation theory. To perform this NNLO computation, we use a recently
proposed version of the subtraction formalism. Our calculation includes
finite-width effects, the leptonic decay of the W boson with its spin
correlations, and the decay of the Higgs boson into a bbbar pair. We present
selected numerical results at the Tevatron and the LHC.Comment: 7 pages, 2 figure

Ferrera, G.

Grazzini, M.

Tramontano, F.

English

arXiv

We consider QCD radiative corrections to standard model Higgs-boson production in association with a W boson in hadron collisions. We present a fully exclusive calculation up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. To perform this NNLO computation, we use a recently proposed version of the subtraction formalism. Our calculation includes finite-width effects, the leptonic decay of the W boson with its spin correlations, and the decay of the Higgs boson into a bb¯ pair. We present selected numerical results at the Tevatron and the LHC

Ferrera, G

Grazzini, M

Tramontano, F

ZORA

Associated Higgs-W-Boson production at hadron colliders: a fully exclusive QCD calculation at NNLO

We consider QCD radiative corrections to Standard Model Higgs boson production in association with a W boson in hadron collisions. We present a fully exclusive calculation up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. To perform this NNLO computation, we use a recently proposed version of the subtraction formalism. Our calculation includes finite-width effects, the leptonic decay of the W boson with its spin correlations, and the decay of the Higgs boson into a bbbar pair. We present selected numerical results at the Tevatron and the LHC

G. Ferrera

M. Grazzini

F. Tramontano

AIR Universita degli studi di Milano

Associated Higgs-W-boson production at hadron colliders : a fully exclusive QCD calculation at NNLO

Giancarlo Ferrera

Massimiliano Grazzini

Francesco Tramontano

Crossref

Associated Higgs-
                    
                      W

We consider QCD radiative corrections to standard model Higgs-boson production in association with a W boson in hadron collisions. We present a fully exclusive calculation up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. To perform this NNLO computation, we use a recently proposed version of the subtraction formalism. Our calculation includes finite-width effects, the leptonic decay of the W boson with its spin correlations, and the decay of the Higgs boson into a bb̄ pair. We present selected numerical results at the Tevatron and the LHC

TRAMONTANO, FRANCESCO

Archivio della ricerca - Università degli studi di Napoli Federico II

Associated Higgs-W-Boson Production at Hadron Colliders:A Fully Exclusive QCD Calculation at NNLOGiancarlo Ferrera,1 Massimiliano Grazzini,2,* and Francesco Tramontano31Dipartimento di Fisica e Astronomia, Universita` di Firenze and INFN,Sezione di Firenze, I-50019 Sesto Fiorentino, Florence, Italy2Institut fu¨r Theoretische Physik, Universita¨t Zu¨rich, CH-8057 Zu¨rich, Switzerland3Theory Group, Physics Department, CERN, CH-1211 Geneva 23, Switzerland(Received 11 July 2011; published 7 October 2011)We consider QCD radiative corrections to standard model Higgs-boson production in association with aW boson in hadron collisions. We present a fully exclusive calculation up to next-to-next-to-leading order(NNLO) in QCD perturbation theory. To perform this NNLO computation, we use a recently proposedversion of the subtraction formalism. Our calculation includes finite-width effects, the leptonic decay ofthe W boson with its spin correlations, and the decay of the Higgs boson into a b b pair. We presentselected numerical results at the Tevatron and the LHC.DOI: 10.1103/PhysRevLett.107.152003 PACS numbers: 12.38.BxThe search for the Higgs boson or its alternatives intheories beyond the standard model (SM) is the key en-deavor of current high-energy colliders. The Tevatron hasrecently excluded at the 95% C.L. a SM Higgs boson in themass range 158<mH < 173 GeV [1]. At the LHC theHiggs-boson search has now started. If the LHC will con-firm the Tevatron exclusion, the attention will move to thelow mass region, where the Higgs-boson search is moredifficult.One of the most important production mechanisms of alight Higgs boson at hadron colliders is the so-calledHiggs-strahlung process, i.e., the associated productionof the Higgs boson together with a vector boson V(V ¼ W; Z). At the Tevatron, this is the main searchchannel in the low mass region, mH & 140 GeV, sincethe lepton(s) from the decay of the vector boson providethe necessary background rejection. At the LHC, thisproduction channel has been considered less promising,due to the large backgrounds. Recent studies [2] haveindicated that at large transverse momenta, employingmodern jet reconstruction and decomposition techniques,WH and ZH production can be recovered as promisingsearch modes for a light Higgs boson at the LHC.In order to fully exploit this channel it is important tohave accurate theoretical predictions for the productioncross section and the associated distributions. Theoreticalpredictions with high precision demand in turn detailedcomputations of radiative corrections. The next-to-leadingorder (NLO) QCD corrections to VH production are thesame as those of the Drell-Yan process [3]. Beyond NLO,the QCD corrections differ from those to the Drell-Yanprocess [4] by contributions where the Higgs boson cou-ples to the gluons through a heavy-quark loop. (In the caseof ZH production there are also gluon-gluon-inducedterms where both the Z and H bosons couple to a heavy-quark loop [5].) The impact of these additional terms is,however, expected to be rather small. Using the classicalresult of Ref. [4], the computation of the NNLO inclusivecross section has been completed in Ref. [5]. Also, NLOelectroweak corrections have been evaluated [6].The effect of NNLO QCD radiative corrections on theinclusive cross section is relatively modest [5]. However, itis important to study how QCD corrections impact theaccepted cross section and the relevant kinematicaldistributions. This is particularly true when severe selec-tion cuts are applied, as it typically happens in Higgs-boson searches.The evaluation of higher-order QCD radiative correc-tions to hard-scattering processes is well known to be ahard task. The presence of infrared singularities at inter-mediate stages of the calculation does not allow a straight-forward implementation of numerical techniques. Inparticular, fully differential calculations at the NNLO in-volve a substantial amount of conceptual and technicalcomplications [7–12]. In eþe collisions, NNLO differen-tial cross sections are known only for two [13,14] and threejet production [15,16]. In hadron-hadron collisions, fullydifferential cross sections have been computed only in thecases of Higgs-boson production by gluon fusion [17–19]and of the Drell-Yan process [20–22].In this Letter we focus on WH production and wepresent the fully exclusive NNLO QCD computation forthis process. The calculation is performed by using thesubtraction formalism of Ref. [18], and it is based onan extension of the numerical program of Ref. [21]. Weinclude finite-width effects, the leptonic decay of theW boson, with its spin correlations, and the decay ofthe Higgs boson into a b b pair. Only diagrams in whichthe Higgs boson is radiated by a W boson are considered;i.e., we neglect the contributions in which the Higgs bosoncouples to a heavy-quark loop. Comparing our results tothose of Ref. [23], where NLO predictions for WH þ jet,PRL 107, 152003 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending7 OCTOBER 20110031-9007=11=107(15)=152003(4) 152003-1  2011 American Physical Societyincluding these additional diagrams, are presented, weexpect the neglected contributions to be at the 1% levelor smaller. When no cuts are applied, and theW and H areproduced on shell, our numerical results agree with thoseobtained with the program VH@NNLO [5].In the following we present an illustrative selectionof numerical results for WH production at the Tevatronand the LHC. We consider u; d; s; c; b quarks in theinitial state and we use the (unitarity constrained)Cabibbo-Kobayashi-Maskawa matrix elements Vud ¼0:974 28, Vus ¼ 0:2253, Vub ¼ 0:003 47, Vcd ¼ 0:2252,Vcs ¼ 0:973 45, Vcb ¼ 0:0410 from the Particle DataGroup (PDG) 2010 [24]. As for the electroweak couplings,we use the so-called G scheme, where the input parame-ters are GF, mZ, mW . In particular we use the valuesGF¼1:16637105 GeV2, mZ ¼ 91:1876 GeV, mW ¼80:399 GeV, andW ¼ 2:085 GeV. Throughout the Letter,we consider a SM Higgs boson with mass mH ¼ 120 GeVand width H ¼ 3:47 MeV [25]. We compute the H ! b bdecay at tree level in the massless approximation, and wenormalize the Hb b Yukawa coupling such that the branch-ing ratio is BRðH ! b bÞ ¼ 0:649 [25]. We use the Martin-Stirling-Thorne-Watt 2008 (MSTW2008) [26] sets ofparton distributions, with densities and S evaluated ateach corresponding order [i.e., we use (nþ 1) loop S atNnLO, with n ¼ 0; 1; 2]. The central values of the renor-malization and factorization scales are fixed to the valueR ¼ F ¼ mW þmH.We start the presentation of our results by consideringWH production at the Tevatron (p p collisions atﬃﬃsp ¼1:96 TeV). We use the following cuts (see, e.g., Ref. [27]).We require the charged lepton to have transverse momen-tum plT > 20 GeV and pseudorapidity jlj< 2, andthe missing transverse momentum of the event to fulfilpmissT > 20 GeV. Jets are reconstructed with the kT algo-rithm with R ¼ 0:4 [28]. We require exactly two jets withpT > 20 GeV and jj< 2, and at least one of them has tobe a b jet, with jj< 1.In Table I we report the accepted cross section (through-out the Letter the errors on the values of the cross sectionsand the error bars in the plots refer to an estimate of thenumerical errors in the Monte Carlo integration) at LO,NLO, and NNLO in the case of three different scalechoices around the central value F ¼ R ¼ mW þmH.The impact of NLO (NNLO) corrections ranges fromþ13% to þ30% ( 1% to þ4%), depending on the scalechoice. The scale dependence is at the level of about1%both at NLO and NNLO.In Fig. 1 we show the transverse-momentum spectrum ofthe dijet system at LO, NLO, NNLO. The lower panel ofthe figure shows the NNLO to NLO ratio. We see that theshape of the spectrum is rather stable, when going fromNLO to NNLO, within the statistical uncertainties.We now consider WH production at the LHC (ﬃﬃsp ¼14 TeV). We follow the selection strategy of Ref. [2] (seealso [29]): the Higgs boson is searched for at large trans-verse momenta through its decay into a collimated b b pair.We require the charged lepton to have plT > 30 GeVand jlj< 2:5, and the missing transverse momentumof the event to fulfil pmissT > 30 GeV. We also require theW boson to have pWT > 200 GeV. Jets are reconstructedwith the Cambridge-Aachen algorithm [30], with R ¼ 1:2.One of the jets (fat jet) must have pJT > 200 GeV andjJj< 2:5 and must contain the b b pair. There shouldnot be other jets with pT > 20 GeV and jj< 5.In Table II we report the corresponding accepted crosssections at LO, NLO, and NNLO.We see that the impact ofNLO and NNLO corrections is negative and larger than atTABLE I. Cross sections for p p! WH þ X ! llb bþ X at the Tevatron. The applied cutsare described in the text. (fb) LO NLO NNLOF ¼ R ¼ ðmW þmHÞ=2 4:266 0:003 4:840 0:005 4:788 0:013F ¼ R ¼ mW þmH 3:930 0:003 4:808 0:004 4:871 0:013F ¼ R ¼ 2ðmW þmHÞ 3:639 0:002 4:738 0:004 4:908 0:010FIG. 1 (color online). Transverse-momentum spectrum of thedijet system for p p! WHþ X ! lb bþ X at the Tevatron atLO (dots), NLO (dashes), and NNLO (solid). The applied cutsare described in the text.PRL 107, 152003 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending7 OCTOBER 2011152003-2the Tevatron. The NLO (NNLO) effect ranges from52%to 36% ( 6% to 19%), depending on the scalechoice. The scale dependence goes from about 13% atNLO to about 6% at NNLO. The NLO and NNLOaccepted cross sections are compatible within the scaleuncertainties.In Fig. 2 we show the transverse-momentum spectrum ofthe fat jet at LO, NLO, and NNLO. The lower panel showsthe NNLO to NLO ratio. We see that the shape of thedistribution is relatively stable when going from NLO toNNLO.We add a few comments on the different impact of QCDradiative corrections at the Tevatron and at the LHC [31].At the Tevatron, the invariant mass of the WH system isMWH mW þmH. The typical scale of the accompanyingQCD radiation is of the order of about h1 ziMWH, whereh1 zi ¼ h1M2WH=s^i is the average distance from thepartonic threshold. The effect of the veto on additional jetsis thus marginal if the jet veto scale pvetoT is of the order ofh1 ziMWH. In this case the perturbative expansion ap-pears under good control. The situation at the LHC isdifferent in two respects. First, the invariant mass of theWH system is larger, due to the high pT required for theW and the Higgs-boson candidate. Second, the typicaldistance from the partonic threshold is larger, i.e., h1 ziis larger than at the Tevatron, due to the increasedﬃﬃsp. As aconsequence, a stringent veto on the radiation recoilingagainst the WH system spoils the cancellation of theinfrared singularities in real and virtual corrections, andcontributions enhanced by the logarithm of the ratioð1 zÞMWH=pvetoT are definitely relevant. We have checkedthat the reduction in the accepted cross section is in fact dueto the jet veto, the impact of QCD corrections being positiveif the jet veto is removed.We have illustrated a calculation of the NNLO crosssection for WH production in hadron collisions. The calcu-lation is implemented in a parton level event generator andallows us to apply arbitrary kinematical cuts on theW andHdecay products as well as on the accompanying QCD radia-tion. We have studied the impact of NNLOQCD correctionsin two typical cases at the Tevatron and the LHC. At theTevatron, the perturbative expansion appears under goodcontrol. At the LHC, by searching for events where theHiggs boson is boosted at high pT , the impact of QCDcorrections is more sizable, and the stability of the fixed-order calculation is challenged. More detailed studies, alongthe lines of Refs. [32,33], are needed in order to assess therelevance of these fixed-order perturbative result.We are grateful to Rikkert Frederix for allowing us tocross-check our NLO results for WH þ jet with those ofthe numerical program of Ref. [23]. We thank RobertHarlander for sending us a version of VH@NNLO, andStefano Catani, Nicolas Greiner, and Stefano Pozzorinifor helpful discussions and comments on the manuscript.We also thank Craig Group, Tom Junk, and GiacintoPiacquadio for discussions on the experimental analysisat the Tevatron and the LHC. This work has been supportedin part by the European Commission through the‘‘LHCPhenoNet’’ Initial Training Network PITN-GA-2010-264564.*On leave from: INFN, Sezione di Firenze, SestoFiorentino, Florence, Italy.[1] T. 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Associated Higgs-W-Boson Production at Hadron Colliders: A Fully Exclusive QCD Calculation at NNLO

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