Complete off-shell effects for top-antitop + jet production with leptonic decays at the LHC
CComplete off-shell effects for top-antitop + jetproduction with leptonic decays at the LHC
Giuseppe Bevilacqua ∗ University of Debrecen and MTA-DE Particle Physics Research Group, H-4002 Debrecen, POBox 400, HungaryE-mail: [email protected]
A brief summary of the calculation of the NLO QCD corrections to the process pp → e + ν e µ − ¯ ν µ b ¯ b j + X is reported. This provides a complete description of the process of t ¯ t + jet pro-duction with leptonic decays beyond the narrow-width approximation. Off-shell effects for topquarks and W boson decays are fully taken into account, namely all resonant and non-resonantcontributions at the order O ( α S α ) are included in the calculation. Selected results for total anddifferential cross sections are shown for the case of the LHC Run I at the energy of 8 TeV. XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects11-15 April, 2016DESY Hamburg, Germany ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ h e p - ph ] J un omplete off-shell effects for t ¯ t j production with leptonic decays at the LHC Giuseppe Bevilacqua
1. Introduction
With the start of Run II in 2015, the LHC entered a new stage of operation. Proton collisionsare now delivered at the record energy of 13 TeV, compared with the maximum of 8 TeV reachedduring the previous stage. The first analyses have already started to complement the results of RunI, among which the discovery and characterization of a narrow light Higgs boson was one of thegreatest outcomes. The production of top quark pairs in association with a hard jet ( t ¯ t j ) is of par-ticular interest in this context. Besides representing a background for Higgs boson searches in theVector Boson Fusion and t ¯ tH channels, it plays an important role in searches of physics beyondthe Standard Model (SM). For example, typical signatures of supersymmetric particle decays in-volve hadronic jets, charged leptons and missing p T , resembling in this way t ¯ t + jets final states.But the t ¯ t j process is also an interesting signal on its own. Given that a significant fraction of theinclusive t ¯ t sample appears in association with hard jets, the accurate description of this processcontributes to a more precise understanding of the dominant mechanism of top quark production atthe LHC [1–3]. Last but not least, t ¯ t j has proven to provide a competitive method for the measure-ment of the top quark mass based on the analysis of its invariant mass distribution [4, 5].The lifetime of the top quark is extremely short: any realistic simulation of processes involvingtop production shall treat tops as intermediate, finite-width states. Since top quarks decay almostexclusively to a W boson and a b quark in the SM, one of the conceptually simplest final statesthat provides a complete description of t ¯ t j hadroproduction is pp → e + ν e µ − ¯ ν µ b ¯ b j . By gaugeinvariance, one must incorporate different kinds of contributions to the amplitude for such finalstate in addition to the double-resonant, genuine t ¯ t j diagrams (see Figure 1). It is only in thenarrow-width limit ( Γ t / m t →
0) that the additional contributions, part of the so-called off-shelleffects , are fully suppressed and let the cross section factorize into on-shell t ¯ t j production anddecay.Despite technical advances, calculations involving multi-particle final states remain challeng-ing. All previous studies of t ¯ t j production at the next-to-leading order (NLO) have resorted tothe approximation of on-shell top quarks. This allowed significant progress in the state-of-the-artdescription, while being adequate for many applications. There are however issues that cannot beaddressed without a complete calculation, like the impact of the non-resonant irreducible back-grounds and the relevance of the off-shellness of top quark and gauge boson decays. If, on theone hand, such effects are expected to be suppressed by powers of Γ t / m t for inclusive observ-ables [34–38], they are known to play a more relevant role in specific regions of the phase space.The first QCD corrections to t ¯ t + jet hadroproduction have been computed in the picture ofstable top quarks [6, 7]. Afterwards, effects of top quark decays have been included, first at LO[8] and then at NLO accuracy [9]. On-shell t ¯ t j production has been also matched with partonshowers at NLO [10–12]. It is only quite recently that the QCD corrections to the full process, pp → e + ν e µ − ¯ ν µ b ¯ b j + X , have started to appear. We report on the first calculation of this kind, aspresented in [13].
2. Technical aspects of the calculation
According to
QGRAF [14] there are about 39000 one-loop diagrams contributing to the am-1 omplete off-shell effects for t ¯ t j production with leptonic decays at the LHC Giuseppe Bevilacqua(a) (b) (c) (d)
Figure 1: Representative tree-level contributions to gg → e + ν e µ − ¯ ν µ b ¯ bg at the order O ( α S α ) : double-resonant (a), single-resonant (b) and non-resonant (c,d). Diagrams (b,c,d) are examples ofnon-factorizable contributions to t ¯ t + jet production. (a) (b) (c) (d) Figure 2: Representative one-loop contributions to gg → e + ν e µ − ¯ ν µ b ¯ bg at the order O ( α S α ) .Diagrams (a,b,c) are examples of non-factorizable contributions to t ¯ t + jet production.plitude of the most challenging partonic subprocess, gg → e + ν e µ − ¯ ν µ b ¯ bg , at the order O ( α S α ) .The most complicated ones are the 120 heptagons and 1155 hexagons, with tensor integrals upto rank six (see Figure 2). We report these numbers as they customarily measure the complexityof NLO calculations, albeit we do not evaluate individual Feynman diagrams in our approach butrather employ more efficient Dyson-Schwinger recursion in association with the OPP reductionmethod [15–17]. The virtual corrections are computed by use of the packages HELAC-1LOOP [18],
CutTools [19] and
OneLOop [20], which are part of the
HELAC-NLO framework [21].Inheriting the structures of the
HELAC-PHEGAS
Monte Carlo [22–24], the framework providesall the elements required to compute NLO QCD corrections to arbitrary processes in the SM. Newfunctionalities have been introduced to cope with the complexity of the current project, amongwhich the optimization of the algorithms for selecting loop topologies and the automated selectionof contributions of different perturbative orders in α S and α . Numerical stability is monitored bychecking Ward identities at every phase space point, using higher precision to recompute eventswhich fail the gauge-invariance check. To regularize resonances of unstable particles, the com-plex mass scheme [25] is employed. This requires the evaluation of scalar integrals with complexmasses, which is supported by the OneLOop library. The infrared divergencies arising from thereal corrections are isolated by use of subtraction methods. Specifically, we adopt two independentschemes in our calculation: the standard Catani-Seymour subtraction [26, 27] and the alternativeNagy-Soper scheme [28], both implemented in
HELAC-DIPOLES [29]. Phase space integrationsare performed with the multichannel generator
KALEU [30]. We cross check the stability of the real2 omplete off-shell effects for t ¯ t j production with leptonic decays at the LHC Giuseppe Bevilacqua corrections by systematic comparisons of the results obtained with the two subtraction schemes.
3. Phenomenological results
We present here selected results of interest for the LHC Run I at the energy of 8 TeV. The SMparameters are set as follows, G F = . · − GeV , m t = . , m W = .
399 GeV , Γ W = . , m Z = . , Γ Z = . , Γ LO t = . , Γ NLO t = . . We consistently evaluate the top quark width at LO and NLO [31]. Since leptonic decays do notreceive QCD corrections, the widths of W and Z bosons are the same everywhere in our calcula-tion. All leptons and quarks, except the top, are considered massless. We adopt the MSTW2008parton distribution functions [32], specifically MSTW2008lo68cl with 1-loop running α s at LOand MSTW2008nlo68cl with 2-loop running α s at NLO. Due to their small size (0.8% of the totalLO cross section), contributions from initial-state b quarks are neglected. Jets are defined out ofpartons with pseudorapidity | η | < anti - k T clustering algorithm [33] with resolution pa-rameter R = .
5. Our analysis requires exactly two b -jets, at least one light-jet, two charged leptonsand missing p T . The following phase space cuts are applied, p T (cid:96) >
30 GeV , p T j >
40 GeV , p T miss >
40 GeV , ∆ R j j > . , ∆ R (cid:96)(cid:96) > . , ∆ R (cid:96) j > . , | y (cid:96) | < . , | y j | < . , where (cid:96) denotes charged leptons while j stands for either light-jets or b -jets. For the renormaliza-tion and factorization scales we choose µ R = µ F = µ = m t and estimate scale uncertainties by afactor-2 variation around the central value µ .For the case of the LHC with √ s = σ LO = . + . − . fb , σ NLO = . − . − . fb , (3.1)where the error bands denote scale uncertainties. We observe moderate, negative NLO QCD cor-rections of -13% at the central scale choice µ = m t . Also, the scale uncertainty of the total crosssection is significantly reduced going from LO to NLO, from about 60% down to 20%. It isinteresting to note that the higher-order corrections have a different impact on different observ-ables. Figure 3 shows distributions of transverse momentum and rapidity for the hardest light-jetand b -jet respectively. The upper panels contain the distributions themselves with the associatedscale-dependence bands, the lower panels display the differential K factor. While corrections lookrelatively stable for the case of rapidities, shape distortions up to 50% affect the p T distributions.Clearly, rescaling LO differential cross sections with a suitably chosen global K factor is not a fairapproximation of the full NLO result in this case. Further insight into judicious dynamical scaleswhich could help to obtain more stable differential K factors is required.3 omplete off-shell effects for t ¯ t j production with leptonic decays at the LHC Giuseppe Bevilacqua
To get an estimate of the numerical relevance of the non-factorizable corrections, we have alsocompared the results of the full calculation with its narrow-width limit. The latter is obtained byrescaling consistently the tbW coupling and the top quark width by a small factor in order to mimicthe limit Γ t →
0. Based on this procedure, we estimate the impact of the off-shell effects at thelevel of 1% ( ) of the total LO (NLO) cross section, fairly consistent with the value of the ratio Γ t / m t which characterizes the expected order of magnitude of such contributions at the inclusivelevel. It should be noticed, however, that the impact of the off-shell effects can be much largeron a more exclusive ground. Previous studies on t ¯ t production have shown that such effects reachseveral tens of percent in observables such as the cross section in exclusive b -jet bins [36], or theminimum invariant mass of the positron and b -jet (hereafter denoted M be + ) [37, 38]. The latter isof particular interest, related as it is to one of the currently used methods for extracting the topquark mass [39–41]. The M be + distribution for our t ¯ t j process is shown in Figure 4, together withthe invariant mass of the top quark reconstructed from its decay products. Once more, the higher-order corrections are important to describe properly the whole range of these observables. The M be + distribution displays the signature of a kinematical endpoint around the value M be + = (cid:113) m t − m W ≈ . W bosons. Additional jet radiation and off-shell effects smear this endpoint and generate a tailat large values of invariant mass, which is highly sensitive to QCD corrections.
4. Conclusions
We have computed NLO QCD corrections to the process pp → e + ν e µ − ¯ ν µ b ¯ b j + X , includingfor the first time complete off-shell effects for top and W boson decays. The QCD corrections lookglobally moderate (-13% of the total cross section) but display a larger impact at the differentiallevel. A thorough investigation of dynamical scales is desirable in order to improve the convergenceof the perturbative expansion in several distributions of interest. We have estimated the size of thetop quark off-shell effects at the level of 2% of the total NLO cross section, in fair agreement withexpectations dictated by the ratio Γ t / m t . The results presented in this work are the starting point ofa wider analysis aimed at providing more accurate NLO predictions for t ¯ t + jet production in theleptonic decay channel, without resorting to any on-shell approximation. Our results can help toimprove the description of the t ¯ t + jet SM background for analyses of Higgs production via VectorBoson Fusion, t ¯ tH production or searches of signals beyond the SM. They have also applications toalternative methods for the determination of the top quark mass [4,5], where a full simulation of the t ¯ t j final state beyond the narrow-width approximation is desirable for a more precise assessmentof the theoretical uncertainties. References [1] M. Czakon, P. Fiedler and A. Mitov, Phys. Rev. Lett. (2013) 252004 [arXiv:1303.6254 [hep-ph]].[2] M. Czakon, D. Heymes and A. Mitov, Phys. Rev. Lett. (2016) no.8, 082003 [arXiv:1511.00549[hep-ph]].[3] M. Czakon, D. Heymes and A. Mitov, arXiv:1606.03350 [hep-ph]. omplete off-shell effects for t ¯ t j production with leptonic decays at the LHC Giuseppe Bevilacqua − − d σ dp T j [f b / G e V ] N L O L O p T j [GeV]LONLO 10 − − d σ dp T b [f b / G e v ] N L O L O p Tb [GeV]LONLO d σ d y j [f b ] -2 -1 0 1 2 N L O L O y j LONLO 10 d σ d y b [f b ] -2 -1 0 1 2 N L O L O y b LONLO
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Upper plots : transverse momentum of the hardest light-jet (left) and of b -jet(right). Lower plots ; rapidity of the hardest light-jet (left) and b -jet (right). Results for pp → e + ν e µ − ¯ ν µ b ¯ b j + X at the LHC with √ s = − − d σ d M b e + [f b / G e v ] N L O L O M be + [GeV]LONLO − d σ d M t [f b / G e v ]
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