MITP/13-004 PreprinttypesetinJHEPstyle-PAPERVERSION OUTP-13-005 + Electroweak W W jj prodution at NLO in QCD − matched with parton shower in the POWHEG-BOX 3 1 0 2 n a J Barbara J¨ager 8 PRISMA Cluster of Excellence & Institute of Physics, Johannes Gutenberg University, ] 55099 Mainz, Germany h E-mail: [email protected] p - p Giulia Zanderighi e h Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, University of Oxford, UK [ E-mail: [email protected] 1 v 5 9 Abstract:We present an implementation of electroweak W+W−jj production at hadron 6 colliders inthePOWHEGframework,amethodthatallowstheinterfacingofanext-to-leading 1 . order QCD calculation with parton shower Monte Carlo programs. We provide results for 1 0 both, fully and semi-leptonic decay modes of the weak bosons, taking resonant and non- 3 resonant contributions and spin correlations of the final-state particles into account. To 1 : illustrate the versatility of our implementation, we provide phenomenological results for v two representative scenarios with a light and with a heavy Higgs boson, respectively, and i X in a kinematic regime of highly boosted gauge bosons. The impact of the parton shower r a is found to depend on the setup and the observable under investigation. In particular, distributions related to a central-jet veto are more sensitive to these effects. Therefore the impact of radiation by the parton shower on next-to-leading order predictions should be assessed carefully on a case-by-case basis. Keywords: POWHEG, NLO, QCD, SMC. Contents 1. Introduction 1 2. Technical details 2 2.1 Next-to-leading order QCD corrections to VBF W+W−jj production 2 2.2 The POWHEG BOX implementation 4 3. Phenomenological results 6 3.1 Results at 8 TeV 7 3.1.1 Fully leptonic decay mode 7 3.1.2 Semi-leptonic decay mode 11 3.2 Semi-leptonic decay mode with boosted kinematics 13 4. Conclusions 14 1. Introduction With the discovery of a new particle that is compatible with the postulated Higgs boson at theCERNLargeHadronCollider(LHC)[1,2]andevidenceforitsexistenceattheFermilab Tevatron [3], high-energy physics has entered a new era. To clarify whether this particle with a mass of about 125 GeV indeed is the CP-even, spin-zero Higgs boson predicted by the Standard Model (SM), a determination of its properties, such as its couplings to gauge bosons and fermions, spin and CP properties, and decay width, is indispensable [4–6]. Inthis context, electroweak vector bosonfusion(VBF) processes play a crucialrole [7– 10]. Higgs production via VBF mainly proceeds via the scattering of quarks by the ex- change of weak gauge bosons in the t-channel that subsequently radiate a Higgs boson. Because of the color singlet nature of the weak gauge boson exchange, gluon radiation in the central-rapidity region is strongly suppressed. The scattered quarks typically give rise to two well-separated jets in the forward regions of the detector, while the decay products of the Higgs boson tend to be located at central rapidities, in between the two tagging jets. These characteristic features of VBF reactions help to distinguish them from a priori overwhelming QCD backgrounds. Higgs production via VBF has been considered in the H γγ, H τ+τ−, and the fully leptonic H WW(∗) decay modes in the most recent → → → analyses of the ATLAS [1] and CMS collaborations [2]. Clearly, a precise knowledge of each signal and background process is essential for quantitative results, in particular if one aims at performing coupling measurements. In this article, we focus on electroweak W+W− production in association with two tagging jets, pp W+W−jj. This process contains both, the signal-type contributions → – 1 – from the VBF-induced production of a Higgs boson that subsequently decays into a pair of weak bosons, and the irreducible background from the continuum W+W− production via VBF. To maintain unitarity, both contributions to the full W+W−jj final state at order (α4) have to be taken into account, even though in experimental analyses selection O cuts may be imposed to diminish the impact of the unwanted background coming from the W+W− continuum. Inordertobesttunetheselectioncuts,itisthenclearlydesirabletobe abletosimulatetheVBF-inducedW+W−jj productionattheHiggsresonanceaswellasin the W+W− continuum in a common setup, taking both types of contributions consistently into account at the highest level of precision that is currently attainable for this class of reactions [11–16]. Accomplishing this goal is the major purpose of this work. Building on existing next-to-leading order (NLO)QCDcalculations for weak boson pair productionvia VBF [11], we aim at providing an interface between the NLO-QCD calculation and parton shower programs such as HERWIG [17,18] or PYTHIA [19] to allow for precise, yet realistic and flexible simulations of W+W−jj production processes at hadron colliders. To this end we develop an implementation of electroweak W+W−jj production in the context of the POWHEG BOX [20], a framework for matching dedicated NLO-QCD calculations with public parton-shower programs [21,22]. We consider both the fully-leptonic and the semi-leptonic decay modes of the W bosons. We describe the technical details of our implementation in Sec. 2. Section 3 contains samplephenomenologicalresultsforafewrepresentativesetups,wheretheW bosonsdecay either fullyleptonically orsemi-leptonically. Inthelastcase, weconsideralsoakinematical regimewheretheW bosonsareproducedhighlyboosted. Thecodehasbeenmadeavailable inthepublicrepositoryofthePOWHEG BOXatthewebsitehttp://powhegbox.mib.infn.it. Our conclusions are given in Sec. 4. 2. Technical details 2.1 Next-to-leading order QCD corrections to VBF W+W−jj production The calculation of the next-to-leading order (NLO) QCD corrections to VBF W+W−jj productionwithfullyleptonicdecayshasfirstbeenaccomplishedinRef.[11]andispublicly available intheframeworkoftheVBFNLOpackage[23]. Weextractedthematrixelementsat Born level, the real emission and the virtual corrections from that reference and adapted them to the format required by the POWHEG BOX. In addition, we are providing matrix elements for the semi-leptonic decays of the weak bosons. Electroweak W+W−jj production with fully leptonic decays in hadronic collisions mainly proceeds via the scattering of two (anti-)quarks by the exchange of weak bosons in the t-channel, which in turn emit W bosons that may decay into lepton-neutrino pairs, c.f. Fig. 1 (a). Furthermore, diagrams with one or both of the weak bosons being emitted off a quark line occur, c. f. Fig. 1 (b), as well as t-channel configurations with non-resonant ℓ+νℓℓ′−ν¯ℓ′ productioninaddition tothetwo jets, c.f.Fig.1(c). Inprinciple,thesamefinal state may arise from quark-antiquark annihilation diagrams with weak-boson exchange in the s-channel and subsequent decay of one of the gauge bosons into a pair of jets. Such contributions have been shown to be negligible [15,24] in regions of phase space – 2 – d d d d d d e+ e+ νµe− ν¯µµ− νee+ νµe− ν¯ µ ν¯ u u µ u u u u (a) (b) (c) Figure 1: Resonant(a,b)andnon-resonant(c)samplediagramsforthe partonicsubprocessdu e+ν µ−ν¯ du at leading order. → e µ where VBF processes are searched for experimentally, and will therefore be disregarded throughout. For subprocesses with identical quark-flavor combinations, in addition to the t-channel topologies one encounters u-channel exchange diagrams, which we include in our calculation. Their interference with the t-channel diagrams is however strongly suppressed once typical VBF selection cuts are applied, and will therefore be neglected here. In the following, we will refer to the electroweak production process pp e+ν µ−ν¯ jj e µ → within the above-mentioned approximations as “fully leptonic VBF W+W−jj ” produc- tion, even though we include contributions from non-resonant diagrams that do not arise from the decay of a W+W−jj intermediate state. Final states related to one of the weak bosons in pp W+W−jj decaying into a massless quark-antiquark and the other one into → a lepton-neutrino pair are referred to as “semi-leptonic”. In analogy to the fully leptonic decay mode,forsemi-leptonicVBFW+W−jj productionwetake double-,single-andnon- resonant diagrams into account and neglect s-channel contributions as well as interference effects between identical quarks of the VBF production process. In addition, we disregard interference effects between the decay quarks and the quarks of the VBF production pro- cess. Decays into massive quarks are not taken into account. For a recent reference on the impact of quark masses in semi-leptonic H WW⋆ decays, see, e.g., Ref. [25]. Represen- → − tative diagrams for the partonic subprocess du cs¯µ ν¯ du can be obtained by replacing µ → the e+ν in Fig. 1 with cs¯ pairs. Similarly, some diagrams for the partonic subprocess e − − du sc¯µ ν¯ du are obtained by replacing the µ ν¯ in Fig. 1 with sc¯ pairs. We note, µ µ → however, that some additional diagrams that, because of the absence of a photon-neutrino coupling, do not occur for the e+ν µ−ν¯ jj final state have to be computed for each of the e µ semi-leptonic decay modes. The NLO-QCD corrections to fully leptonic VBF W+W−jj production comprise real- emission contributions with one extra parton in the final state and the interference of one- loop diagrams with the Born amplitude. Within our approximations, for the latter only self-energy, triangle, box, andpentagon corrections toeithertheupperorthelower fermion linehavetobeconsidered. Thefinitepartsofthesecontributionsareevaluatednumerically by means of a Passarino-Veltman-type tensor reduction that is stabilized by means of the methods of Refs. [26,27]. The numerical stability is monitored by checking Ward identities at every phase-space point. The real-emission contributions are obtained by attaching a gluon in all possible ways to the tree-level diagrams discussed above. Crossing-related di- agrams with a gluon in the initial state are also taken into account. Infrared singularities – 3 – emerging in both, real-emission and virtual contributions, at intermediate steps of the cal- culation, are taken care of via the Frixione-Kunszt-Signer subtraction approach [28] that is provided by the POWHEG BOX framework. For semi-leptonic VBF W+W−jj production, QCD corrections to the W hadronic decay are implemented only in the shower approxima- tion. We remark, however, that most shower Monte Carlo programs describe the dressing of hadronic W decays with QCD radiation accurately, since they have been fit to LEP2 data. The NLO-QCD corrections are thus of the same form as those for the fully leptonic final state, but hadronic decays include the inclusive (α ) QCD correction to the decay s O vertex. 2.2 The POWHEG BOX implementation For the implementation of VBFW+W−jj productionin theframework of thePOWHEG BOX we proceed in analogy to Refs. [16,29]. Because of the larger complexity of the current process, however, some further developments are necessary. As an input, the POWHEG BOX requires a list of all independent flavor structures of the Born and the real emission processes, the Born amplitude squared, the real-emission amplitude squared, the finite parts of the virtual amplitudes interfered with the Born, the spin- and the color-correlated Born amplitudes squared. Because of the simple color structure of VBF processes the latter are just multiples of the Born amplitude itself, while the spin-correlated amplitudes vanish entirely. For the fully leptonic decay modes, the LO amplitudes squared, the virtual and the real-emission contributions are extracted from Ref.[11], as describedin theprevioussection. For semi-leptonic decays of theweak bosons, appropriate modifications of the matrix elements are performed. Subtraction terms do not need to be provided explicitly, but are computed by the POWHEG BOX internally. Due to the specialcolor structureofVBFprocesses, withinourapproximations thereisnointerference between radiation off the upper and the lower fermion lines. This information has to be passed to thePOWHEG BOXby assigninga tag toeach quarkline, as explained in somedetail in Refs. [16,30]. The tags are taken into account by the POWHEG BOX when singular regions for the generation of radiation are identified. Similarly to the case of electroweak Zjj production [29], in the Born cross section for electroweak W+W−jj production collinear q qγ configurations can arise when a t- → channelphotonof low virtuality is exchanged. Suchcontributions areconsidered tobepart of the QCD corrections to pγ W+W−jj and not taken into account here. To effectively → removesuchcontributionsevenbeforeVBFcutsareapplied,weintroduceacut-offvariable Q2 = 4 GeV2 for the virtuality of the t-channel exchange boson. Contributions from γ,min configurations with avirtuality Q2 below this cutoff valuearedroppedpriortophase-space integration. We checked that, within the numerical accuracy of the program, predictions do not change when the cut-off variable is increased to 10 GeV2. Toimprovetheefficiencyoftheprogram,inadditionweareemployingaso-calledBorn- suppression factor F(Φ ) that vanishes whenever a singular region of the Born phase space n Φ is approached. In the POWHEG BOX, the underlying Born kinematics is then generated n – 4 – according to a modified B¯ function, B¯ = B¯(Φ )F(Φ ). (2.1) supp n n For VBF W+W−jj production, at Born level, singular configurations related to the ex- change of a photon of low virtuality in the t-channel are characterized by low transverse momentumofanoutgoingparton. Itisthereforeadvantageous toapplyaBorn-suppression factor that damps such configurations. Following the prescription of Ref. [29], we are using p2 2 p2 2 T,1 T,2 F(Φ ) = , (2.2) n p2 +Λ2 p2 +Λ2 T,1 ! T,2 ! withthep denotingthetransversemomentaofthetwooutgoingpartonsoftheunderlying T,i Born configuration, and Λ= 10 GeV. Electroweak W+W− production in association with two jets contains contributions fromVBF-inducedHiggs productionwithsubsequentdecay intoapairofweakbosons,and from continuum W+W− production via VBF. These two types of contributions populate different regions of phase space: The Higgs resonance exhibits a pronounced peak where the invariant mass of the decay leptons and neutrinos, M , is equal to the Higgs mass, decay whereas the WW continuum is distributed over a broad range in M . In order to decay optimize the efficiency of the phase space integration, in the case of a light Higgs boson with a narrow width we have split our simulation into two contributions, dependingon the value of M in the underlying Born configuration. In the region decay m n Γ < M < m +n Γ , n = 50, (2.3) H H decay H H − · · our results are then dominated by the sharp Higgs resonance, whereas for other values of M results are fully dominated by the broad WW continuum. Even though both decay phase space regions contain contributions from all Feynman diagrams, for simplicity we refer to the region of Eq. (2.3) as “Higgs resonance” and to the complementary region as “WW continuum”. We note that, because of the presence of two neutrinos, the invariant mass distribu- tion cannot be fully reconstructed in experiment in the fully leptonic decay mode. The separation we perform is of purely technical nature and serves the only purpose of im- proving the convergence of the phase space integration. To obtain meaningful results for the full VBF W+W−jj final state, the two contributions therefore have to be added, and results are independent of the choice of n in Eq. (2.3). Still, it is interesting to observe the differences of some characteristic distributions in these two regions. Figure 2 shows the azimuthal angle separation of the two charged leptons after only basic transverse mo- mentum cuts of p > 25 GeV are applied on the two hardest jets that are reconstructed T,j via the anti-k algorithm [31,32] in the rapidity range y < 4.5, with R > 0.4. As is T j evident, in the Higgs resonance region the leptons tend to be close in azimuthal angle, as they arise from the decay of two weak bosons that stem from a Higgs boson of spin zero. In the continuum region, no such correlation exists between the decay leptons, resulting in a completely different shape of the angular distribution [33]. Should one wish to enhance – 5 – 1.4 WW continuum Higgs resonance 1.2 ] b f [ φ ll 1 d σ/ 0.8 d 0.6 0.4 0.2 0 0.5 1 1.5 2 2.5 3 φ ll Figure 2: Azimuthal angle separation of the two charged leptons at NLO-QCD accuracy for the Higgs resonance and the W+W− continuum region. See text for more details. the Higgs contributions with respect to the full VBF W+W−jj cross section, clearly one would make use of this feature. In order to validate the complete implementation of VBF W+W−jj production in the POWHEG BOX,wehaveperformedvariouschecks. TheLOandreal-emission matrixelements for each class of subprocesses have been compared at the amplitude level to MadGraph- generated code [34,35]. We found agreement at the level of 12 significant digits. With the user-supplied LO and real-emission matrix elements squared, the POWHEG BOX itself tests whether the real-emission cross section approaches all soft and collinear limits correctly. This provides a useful check on the relative normalization of the Born and real-emission amplitudes squared as well as on the flavor summation. For the fully leptonic decay mode, we have furthermore compared all parts of the NLO-QCD calculation to the respective results generated with the code of Ref. [11]. We found full agreement for integrated cross sections and differential distributions at LO and at NLO-QCD, both within inclusive cuts and after imposing VBF-specific selection criteria. Finally, we remark that in order to produce the plots presented in this work, we have used a new version of the POWHEG BOX files that were kindly provided to us by Paolo Nason and that will soon be released as part of the Version 2 of the POWHEG BOX. In particular these files allow to compute the integration grids in parallel and have a more efficient calculation of the upper bounds. 3. Phenomenological results Ourimplementation of VBF W+W−jj productionin thePOWHEG BOXis publiclyavailable. InstructionsfordownloadingthecodeareavailablefromthethewebsiteofthePOWHEG BOX project, http://powhegbox.mib.infn.it. Technical parameters of the code and recom- mendations for its use can be found in a documentation that is provided together with the code. In this article, we present results obtained with our POWHEG BOX implementation – 6 – for some representative setups. The user of the POWHEG BOX is of course free to perform studies with settings of her own choice. 3.1 Results at 8 TeV Weconsiderproton-protoncollisionsatacenter-of massenergyof√s= 8TeV.Forthepar- tondistributionfunctionsoftheprotonweusetheNLOsetoftheMSTW2008parametriza- tion [36], as implemented in the LHAPDF library [37]. Jets are defined according to the anti- k algorithm [31,32] withR = 0.4, makinguseoftheFASTJETpackage [38]. Aselectroweak T (EW) input parameters we use the mass of the Z boson, m = 91.188 GeV, the mass of Z the W boson, m = 80.419 GeV, and the Fermi constant, G = 1.16639 10−5 GeV−1. W F × Other EW parameters are obtain from these via tree-level electroweak relations. For the widths of the weak bosons we use Γ = 2.51 GeV, Γ = 2.099 GeV. In case semi-leptonic Z W decay modes areconsidered, thehadronicwidth is corrected with a factor [1+α (m )/π]. s W The factorization and renormalization scales are set to µ = µ = m throughout. F R W 3.1.1 Fully leptonic decay mode VBF W+W−jj production with fully leptonic decays of the W bosons is an important channel in the Higgs search over a wide mass range. Here, we present numerical results for electroweak e+ν µ−ν¯ jj production at the LHC within the setup outlined above. The e µ mass of the Higgs boson is set to m = 125 GeV, the region where the ATLAS and CMS H collaborations observe a new resonance compatible with the Higgs boson predicted by the Standard Model [1,2]. The width of the Higgs boson is set to Γ = 0.00498 GeV. Our H phenomenological study is inspired by the analysis strategy of Ref. [39]. We require the presence of two jets with p > 25 GeV, y < 4.5. (3.1) T,j j The two hardest jets inside the considered rapidity range are referred to as “tagging jets”. These two tagging jets are furthermore required to be well-separated from each other, y y < 3.8, y y < 0, m > 500 GeV. (3.2) j1 j2 j1 j2 j1j2 | − | × We require missing energy and two hard charged leptons in the central rapidity region, y < 2.5, p > 25 GeV, p > 15 GeV, pmiss > 25 GeV, (3.3) ℓ T,ℓ1 T,ℓ2 T which are well-separated from each other and from the jets, R > 0.3, R > 0.3, (3.4) ℓℓ jℓ but close in azimuthal angle, φ φ < 1.8, (3.5) | ℓ1 − ℓ2| and located in the rapidity region between the two tagging jets, min y ,y <y < max y ,y . (3.6) j1 j2 ℓ j1 j2 { } { } – 7 – 10-2 10-2 V] WW continuum V] POWHEG+PYTHIA e e G Higgs resonance G NLO [fb/W10-3 Sum [fb/W10-3 W W T, T, M M d 10-4 d 10-4 σ/ σ/ d d 10-5 10-5 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 M [GeV] M [GeV] T, WW T, WW Figure 3: Transverse mass distribution of the four-lepton system, as defined in Eq. (3.7), for pp e+ν µ−ν¯ jj at the LHC with √s = 8 TeV within the VBF cuts of Eqs. (3.1)–(3.6). Left e µ → panel: results at NLO-QCDaccuracyfor the Higgs resonance(blue line), the WW continuum(red line), and their sum (black line). Right panel: Sum of the two contributions at NLO-QCD (blue solid lines) and with POWHEG+PYTHIA(red dashed lines). When thesecuts areapplied,theinclusivecross section contributions forVBFe+ν µ−ν¯ jj e µ production given in Sec. 2 are given by σVBF = (0.202 0.002) fb and σVBF = (0.268 WW ± Higgs ± 0.003) fb at NLO-QCD, amounting to a total of σVBF = (0.470 0.003) fb. Because of ± our selection cuts, in particular the cut on the azimuthal angle separation of the charged leptons, Eq.(3.5), theHiggs contribution isslightly preferredcomparedtotheWW contin- uum. The VBF cross section at NLO QCD changes by less than 2% whenthe factorization and renormalization scales are varied simultaneously in the range µ = µ = m /2 to F R W 2M . Slightly larger scale uncertainties are found for distributions related to jets that are W emittedinadditiontothetwotaggingjets. Assuchjetscanfirstoccurviathereal-emission contributions of the NLO calculation, their kinematic properties are effectively described at LO only, and thus plagued by larger scale uncertainties than true NLO observables. While our calculation has been performed for a fixed choice of scale that should facilitate comparison to future calculations, we mention that more sophisticated choices are possible with our code, for instance like those suggested in the context of the MINLO method [40]. Since the invariant mass of the e+ν µ−ν¯ system cannot be fully reconstructed, it is e µ common to consider the transverse mass instead, which is defined as m = (Eℓℓ+Emiss)2 p~ℓℓ+~pmiss 2, with Eℓℓ = p~ℓℓ 2+m2 . (3.7) T,WW T T −| T T | T | T | ℓℓ q q Figure 3 (a) shows the respective contributions to dσVBF/dm of the Higgs resonance T,WW and of the WW continuum, as defined in Sec. 2, as well as their sum. The Higgs contri- bution is peaked at m m , while the WW continuum is largest in the kinematic T,WW H ∼ range where two weak bosons can be produced on-shell. In Fig. 3 (b), we show the transverse mass distribution at pure NLO QCD, as well as at NLO matched with a parton-shower program via POWHEG (NLO+PS). For the parton shower,hereandinthefollowingweareusingPYTHIA6.4.25[19]withthePerugia0tunefor the shower, including hadronization corrections, multi-parton interactions and underlying event. WedonottakeQEDradiationeffectsintoaccount. Theshapeofthetransversemass – 8 – -1 10 POWHEG+PYTHIA ] V e NLO G 10-2 / b f [ 3 pt, j 10-3 d / σ d -4 10 -5 10 0 10 20 30 40 50 60 70 80 90 100 p [GeV] t, j3 Figure 4: Transverse momentum distribution of the third jet in pp e+ν µ−ν¯ jj at e µ → the LHC within the VBF cuts of Eqs. (3.1)–(3.6) at NLO-QCD (blue solid lines) and with POWHEG+PYTHIA(red dashed lines). distribution is only barely affected by parton-shower effects. Similarly small distortions of shapesareobserved forthetransversemomentum andrapidity distributionsof theleptons, as well as for their azimuthal angle separation. The overall normalization of the VBF cross sections decreases by about 2% when the NLO calculation is combined with PYTHIA. The parton shower mostly gives rise to the emission of soft or collinear radiation, while the probability for the emission of hard extra jets does not increase because of parton-shower effects. Indeed, the productionrate of a third hardjet decreases when the NLO calculation is merged with PYTHIA, as illustrated in Fig. 4, which shows the transverse momentum distribution of the third jet in pp e+ν µ−ν¯ jj at NLO QCD and for POWHEG+PYTHIA. e µ → At NLO, only the real-emission contributions can give rise to a third jet. Distributions related to this jet are thus effectively described only at the lowest non-vanishing order in the fixed-order predictions, while in the POWHEG+PYTHIA results soft-collinear radiation is resummed at leading-logarithmic accuracy via the Sudakov factor, resulting in a damping of contributions with very small p . T,j3 Aquantitativeunderstandingofcentraljetsthatarelocatedinbetweenthetwotagging jets is ofcrucialimportanceforthediscriminationof VBFevents fromhardQCDprocesses as well as from underlying event and pile-up effects at the LHC. These backgrounds are characterized by a considerable amount of jet activity in the central-rapidity region of the detector, whereas the emission of hard jets at central rapidities is strongly suppressed in VBF processes. Figure 5 shows the rapidity distribution of the third jet in VBF-induced e+ν µ−ν¯ jj production at the LHC. Obviously, the shape of the NLO-QCD distributions e µ is not particularly sensitive to the transverse momentum cut imposed on the third jet. However, when the NLO calculation is merged with PYTHIA, the central-rapidity region is considerably filled by extra jets, as illustrated in the left panel of Fig. 5, where in addition – 9 –