Associated production of a top-quark pair with vector bosons at NLO in QCD: impact on \( \mathrm{t}\overline{\mathrm{t}}\mathrm{H} \) searches at the LHC

Journal of High Energy Physics, Feb 2016

We study the production of a top-quark pair in association with one and two vector bosons, \( t\overline{t}V \) and \( t\overline{t}V\kern0.1em V \) with V = γ, Z, W ±, at the LHC. We provide predictions at next-to-leading order in QCD for total cross sections and top-quark charge asymmetries as well as for differential distributions. A thorough discussion of the residual theoretical uncertainties related to missing higher orders and to parton distribution functions is presented. As an application, we calculate the total cross sections for this class of processes (together with \( t\overline{t}H \) and \( t\overline{t}t\overline{t} \) production) at hadron colliders for energies up to 100 TeV. In addition, by matching the NLO calculation to a parton shower, we determine the contribution of \( t\overline{t}V \) and \( t\overline{t}V\kern0.1em V \) to final state signatures (two-photon and two-same-sign-, three-and four-lepton) relevant for \( t\overline{t}H \) analyses at the Run II of the LHC.

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Associated production of a top-quark pair with vector bosons at NLO in QCD: impact on \( \mathrm{t}\overline{\mathrm{t}}\mathrm{H} \) searches at the LHC

JHE Associated production of a top-quark pair with vector Fabio Maltoni 0 1 2 3 Davide Pagani 0 1 2 3 Ioannis Tsinikos 0 1 2 3 0 Chemin du Cyclotron , 2, Louvain-la-Neuve, B-1348 Belgium 1 CP3 Universite catholique de Louvain 2 Centre for Cosmology , Particle Physics and Phenomenology 3 in MadGraph5 We study the production of a top-quark pair in association with one and two vector bosons, ttV and ttV V with V = ; Z; W , at the LHC. We provide predictions at next-to-leading order in QCD for total cross sections and top-quark charge asymmetries as well as for di erential distributions. A thorough discussion of the residual theoretical uncertainties related to missing higher orders and to parton distribution functions is presented. As an application, we calculate the total cross sections for this class of processes (together with ttH and tttt production) at hadron colliders for energies up to 100 TeV. In addition, by matching the NLO calculation to a parton shower, we determine the contri- QCD Phenomenology; NLO Computations - HJEP02(16)3 bution of ttV and ttV V to nal state signatures (two-photon and two-same-sign-, threeand four-lepton) relevant for ttH analyses at the Run II of the LHC. 1 Introduction 2 Fixed-order corrections at the production level 3 4 1 2.1 ttV processes and ttH production 2.2 ttV V processes 2.3 tttt production 2.4 Total cross sections from 8 to 100 TeV Analyses of ttH signatures 3.1 3.2 Signature with two photons Signatures with leptons Conclusions Introduction With the second run of the LHC at 13 TeV of centre of mass energy, the Standard Model (SM) is being probed at the highest energy scale ever reached in collider experiments. At these energies, heavy particles and high-multiplicity nal states are abundantly produced, o ering the opportunity to scrutinise the dynamics and the strength of the interactions among the heaviest particles discovered so far: the W and Z bosons, the top quark and the recently observed scalar boson [1, 2]. The possibility of measuring the couplings of the top quark with the W and Z bosons and the triple (quadruple) gauge-boson couplings will further test the consistency of the SM and in case quantify possible deviations. In addition, the couplings of the Higgs with the W and Z bosons and the top quark, which are also crucial to fully characterise the scalar sector of the SM, could possibly open a window on Beyond-the-Standard-Model (BSM) interactions. Besides the study of their interactions, nal states involving the heaviest states of the SM are an important part of the LHC program, because they naturally lead to highmultiplicity nal states (with or without missing transverse momentum). This kind of signatures are typical in BSM scenarios featuring new heavy states that decay via long chains involving, e.g., dark matter candidates. Thus, either as signal or as background processes, predictions for this class of SM processes need to be known at the best possible accuracy and precision to maximise the sensitivity to deviations from the SM. In other words, the size of higher-order corrections and the total theoretical uncertainties have to energies and luminosities, the phenomenological relevance of this kind of processes and the impact of higher-order corrections on the corresponding theoretical predictions are expected to become even more relevant [3]. In this work we focus on a speci c class of high-multiplicity production process in the SM, i.e., the associated production of a top-quark pair with either one (ttV ) or two gauge vector bosons (ttV V ). The former includes the processes ttW tt , while the latter counts six di erent nal states, i.e., ttW +W , ttZZ, tt (ttW + + ttW ), ttZ and , ttW ttW Z and ttZ . In addition, we consider also the associated production of two top-quark pairs (tttt), since it will be relevant for the phenomenological analyses that are presented in this work. The aim of our work is twofold. Firstly, we perform a detailed study of the predictions at xed NLO QCD accuracy for all the ttV and ttV V processes, together with ttH and tttt production, within the same calculation framework and using the same input parameters. This approach allows to investigate, for the rst time, whether either common features or substantial di erences exist among the theoretical predictions for di erent nal states. More speci cally, we investigate the impact of NLO QCD corrections on total cross sections and di erential distributions. We systematically study the residual theoretical uncertainties due to missing higher orders by considering the dependence of key observables on di erent de nitions of central renormalisation and factorisation scales and on their variations. NLO QCD corrections are known for ttH in [4{7], for tt in [8, 9], for ttZ in [9{13], for ttW in [9, 13{15] and for tttt in [16, 17]. NLO electroweak and QCD corrections have also already been calculated for ttH in [18{20] and for ttW and ttZ in [20]. Moreover, in the case of ttH, NLO QCD corrections have been matched to parton showers [21, 22] and calculated for o -shell top (anti)quarks with leptonic decays in [23]. In the case of tt , NLO QCD corrections have been matched to parton showers in [24]. For the ttV V processes a detailed study of NLO QCD corrections has been performed only for tt [25, 26]. So far, only representative results at the level of total cross sections have been presented for the remaining ttV V processes [3, 17]. When possible, i.e. for ttV , ttH and tt , our results have been checked against those available in the literature in previous works [9, 13, 14, 17, 20{22, 24, 25], and we have found perfect agreement with them. This cross-check can also be interpreted as a further veri cation of the correctness of both the results in the literature and of the automation of the calculation of NLO QCD corrections Secondly, we perform a complete analysis, at NLO QCD accuracy including the matching to parton shower and decays, in a realistic experimental setup, for both signal and background processes involved in the searches for ttH at the LHC. Speci cally, we consider the cases where the Higgs boson decays either into two photons (H ! ), or into leptons (via H ! W W , H ! ZZ , H ! the CMS and ATLAS collaborations at the LHC with 7 and 8 TeV [27{29]. In the rst case, the process tt ttW +W , ttZZ, ttW is the main irreducible background. In the second case, the processes Z are part of the background, although their rates are very small, as we will see. However, ttW +W production, e.g, has already been taken into account at LO in the analyses of the CMS collaboration at 7 and 8 TeV, see for instance [27]. A contribution of similar size can originate also from tttt production [30], which consequently + ), which have already been analysed by { 2 { has to be included for a correct estimation of the background.1 Furthermore, depending on the exact nal state signature, the ttV processes can give the dominant contribution, which is typically one order of magnitude larger than in ttV V and tttt production. In this work, the calculation of the NLO QCD corrections and the corresponding event generation has been performed in the MadGraph5 aMC@NLO framework [17]. This code allows the automatic calculation of tree-level amplitudes, subtraction terms and their integration over phase space [31] as well as of loop-amplitudes [9, 32, 33] once the relevant Feynman rules and UV/R2 counterterms for a given theory are provided [34{36]. Event generation is obtained by matching short-distance events to the shower employing the MC@NLO method [37], which is implemented for Pythia6 [38], Pythia8 [39], HERWIG6 [40] and HERWIG++ [41]. The reader can nd in the text all the inputs and set of instructions that are necessary to obtain the results presented here. The paper is organised as follows. In section 2 we present a detailed study of the predictions at NLO QCD accuracy for the total cross sections of ttV , ttV V and tttt production. We study their dependences on the variation of the factorisation and renormalisation scales. Furthermore, we investigate the di erences among the use of a xed scale and two possible de nitions of dynamical scales. Inclusive and di erential K-factors are also shown. As already mentioned above, these processes are backgrounds to the ttH production with the Higgs boson decaying into leptons, which is also considered in this work. To this purpose, we show also the same kind of results for ttH production. In addition, in the case of ttV and ttH, we provide predictions at NLO in QCD for the corresponding top-charge asymmetries and in order to investigate the behaviour of the perturbative expansion for some key observables, we also compute ttV j and ttHj cross sections at NLO in QCD. Such results appear here for the rst time. In section 2 we also study the dependence of the total cross sections and of global K-factors for ttV V and ttV processes as well as for ttH and tttt production on the total energy of the proton-proton system, providing predictions in the range from 8 to 100 TeV. In section 3 we present results at NLO accuracy for the background and signal relevant for ttH production. In subsection 3.1 we consider the signature where the Higgs decays into photons. In our analysis we implement a selection and a de nition of the signal region that are very similar to those of the corresponding CMS study [27]. For the signal and background processes tt , we compare LO, NLO results and LO predictions rescaled by a global at K-factor for production only, as obtained in section 2. We discuss the range of validity and the limitations of the last approximation, which is typically employed in the experimental analyses. In subsection 3.2 we present an analysis at NLO in QCD accuracy for the searches of ttH production with the Higgs boson subsequently decaying into leptons (via vector bosons), on the same lines of subsection 3.1. In this case, we consider di erent signal regions and exclusive nal states, which can receive contributions from tttt production and from all the ttV and ttV V processes involving at least a heavy vector boson. Also here, we compare LO, NLO results and LO predictions rescaled by a 1Triple top-quark production, tttW and tttj, a process mediated by a weak current, is characterised by Fixed-order corrections at the production level In this section we describe the e ects of xed-order NLO QCD corrections at the production level for ttV processes and ttH production (subsection 2.1), for ttV V processes (subsection 2.2) and then for tttt production (subsection 2.3). All the results are shown for 13 TeV collisions at the LHC. In subsection 2.4 we provide total cross sections and global K-factors for proton-proton collision energies from 8 to 100 TeV. With the exception of tt , detailed studies at NLO for ttV V processes are presented here for the rst time. The other processes have already been investigated in previous works, whose references have been listed in introduction. Here, we (re-)perform all such calculations within the same framework, MadGraph5 aMC@NLO, using a consistent set of input parameters and paying special attention to features that are either universally shared or di er among the various processes. Moreover, we investigate aspects that have been only partially studied in previous works, such as the dependence on (the de nition of) the factorisation and renormalisation scales, both at integrated and di erential level. To this aim we de ne the variables that will be used as renormalisation and factorisation scales. Besides a xed scale, we will in general explore the e ect of dynamical scales that depend on the transverse masses (mT;i) of the nal-state particles. Speci cally, we will employ the arithmetic mean of the mT;i of the nal-state particles ( a) and the geometric mean ( g), which are de ned as a = 0 HT := N 1 N Y i=1;N X i=1;N(+1) 11=N mT;iA : mT;i ; (2.1) (2.2) HJEP02(16)3 In these two de nitions N is the number of nal-state particles at LO and with N (+1) in eq. (2.1) we understand that, for the real-emission events contributing at NLO, we take into account the transverse mass of the emitted parton.2 There are two key aspects in the de nition of a dynamical scale: the normalisation and the functional form. We have chosen a \natural" average normalisation in both cases leading to a value close to mt when the transverse momenta in the Born con guration can be neglected. This is somewhat conventional in our approach as the information on what could be considered a good choice (barring the limited evidence that a NLO calculation can give for that in rst place) can be only gathered a posteriori by explicitly evaluating the scale dependence 2This cannot be done for g; soft real emission would lead to g 0. Conversely, a can also be de ned of the results. For this reason, in our studies of the total cross section predictions, we vary scales over a quite extended range, c=8 < < 8 c. More elaborate choices of evenby-event scales, such as a CKKW-like one [42] where factorisation and renormalisation scales are \local" and evaluated by assigning a parton-shower like history to the nal state con guration, could be also considered. Being ours the rst comprehensive study for this class of processes and our aim that of gaining a basic understanding of the dynamical features of these processes, we focus on the simpler de nitions above and leave possible re nements to speci c applications. All the NLO and LO results have been produced with the MSTW2008 (68% c.l.) PDFs [43] respectively at NLO or LO accuracy, in the ve- avour-scheme (5FS) and with the associated values of s . ttW +W production, however, has been calculated in the four- avour-scheme (4FS) with 4FS PDFs, since the 5FS introduces intermediate top-quark resonances that need to be subtracted and thus unnecessary technical complications. The mass of the top quark has been set to mt = 173 GeV and the mass of the Higgs are performed by leaving the top quark and the vector bosons stable. In simulations at NLO+PS accuracy, they are decayed by employing MadSpin [44, 45] or by Pythia8. If not stated otherwise photons are required to have a transverse momentum larger than 20 GeV (pT ( ) > 20 GeV) and Frixione isolation [46] is imposed for jets and additional photons, with the technical cut R0 = 0:4. The ne structure constant is set equal to its corresponding value in the G -scheme for all the processes.3 2.1 ttV processes and ttH production lines) and and (2.2). As rst step, we show for ttH production and all the ttV processes the dependence of the NLO total cross sections, at 13 TeV, on the variation of the renormalisation and factorisation scales r and f . This dependence is shown in gure 1 by keeping varying it by a factor eight around the central value = = mt (dotted lines). The scales a and g are respectively de ned in eqs. (2.1) As typically a is larger than g and mt, the bulk of the cross sections originates from phase-space regions where s( a) < s( g); s(mt). Consequently, such choice gives systematically smaller cross sections. On the other hand, the dynamical scale choice g leads to results very close in shape and normalisation to a xed scale of order mt. Driven by the necessity of making a choice, in the following of this section and in the analyses of section 3 we will use g as reference scale. Also, we will independently vary f and r by a factor of two around the central value g, g=2 < f ; r < 2 g, in order to estimate the uncertainty of missing higher orders. This generally includes, e.g., almost the same range of values spanned by varying = r = f by a factor of four around the central value = a, a=4 < < 4 a (cf. gure 1) and thus it can be seen as a conservative choice. In any case, while certainly justi ed a priori as well as a posteriori, we stress that 3This scheme choice for is particularly suitable for processes involving W bosons [47]. Anyway, in our can be obtained by simply rescaling the numbers listed in this paper. ttZ 1.23 ]bp1.4 LHCμc1=3μTgeV [ ttH O L N M a _ 5 M 2 4 8 ttH < 8 c for the three di erent choices of the central value c : g, a, mt. The upper plot refers to tt production, the lower plot to ttW , ttZ and ttH production. The rst uncertainty is given by the scale variation within g=2 < f ; r < 2 g, the second one by PDFs. The relative statistical integration error is equal or smaller than one permille. the = g choice is an operational one, i.e. we do not consider it as our \best guess" but just use it as reference for making meaningful comparisons with other possible scale de nitions and among di erent processes. Using the procedure described before, in table 1 we list, for all the processes, LO and NLO cross sections together with PDF and scale uncertainties, and K-factors for the central values. The dependence of the LO and NLO cross sections on = r = f is also shown in gure 2 in the range g=8 < < 8 g. As expected, for all the processes, the scale dependence is strongly reduced from LO to NLO predictions both in the standard interval g=2 < < 2 g as well as in the full range g=8 < < 8 g. For tt process (upper plots in gures 1 and 2), we nd that in general the dependence of the cross-section scale variation is not strongly a ected by the minimum pT of the photon, giving similar results for pT ( ) > 20 GeV and pT ( ) > 50 GeV. As already stated in section 1, with ttW we refer to the sum of the ttW + and ttW contributions. We now show the impact of NLO QCD corrections on important distributions and we all the processes we analysed the distribution of the invariant mass of the top-quark pair 1/8 with c = production. LO | 1/4 1/2 1 ttγ M 0.8 0.6 0.4 0.2 0 1/8 | 1/4 1/2 1 LO ttZ ttW± ttH O L N M a _ 5 h p a r M 2 4 8 g. The upper plot refers to tt production, the lower plot to ttW , ttZ and ttH scalar boson. Given the large amount of distributions, we show only representative results. All the distributions considered and additional ones can be produced via the public code For each gure, we display together the same type of distributions for the four di erent processes: tt , ttH, ttW and ttZ. Most of the plots for each individual process will be displayed in the format described in the following. In each plot, the main panel shows the speci c distribution at LO (blue) and NLO QCD (red) accuracy, with = f = r equal to the reference scale g. In the rst inset we display scale and PDF uncertainties normalised to the blue curve, i.e., the LO with = g. The mouse-grey band indicates the scale variation at LO in the standard range g=2 < f ; r < 2 g, while the dark-grey band shows the PDF uncertainty. The black dashed line is the central value of the grey band, thus it is by de nition equal to one. The solid black line is the NLO QCD di erential K-factor at the scale = g, the red band around it indicates the scale variation in the standard range g=2 < f ; r < 2 g. The additional blue borders show the PDF uncertainty. We stress that in the plots, as well as in the tables, scale uncertainties are always obtained by the independent variation of the factorisation and renormalisation scales, via the reweighting technique introduced in [48]. The second and third insets show the same content of the rst inset, but with di erent scales. In the second panel both LO and NLO have been evaluated with = a, in the third panel with The fourth and the fth panels show a direct comparison of NLO QCD predictions using the scale g and, respectively, a and mt. All curves are normalised to the red curve in the main panel, i.e., the NLO with = g. The mouse-grey band now indicates the scale variation dependence of NLO QCD with = g. Again the dashed black line, the central value, is by de nition equal to one and the dark-grey borders represent the PDF uncertainties. The black solid line in the fourth panel is the ratio of the NLO QCD predictions at the scale a and g. The red band shows the scale dependence of NLO QCD predictions at the scale a, again normalised to the central value of NLO QCD at the scale { 7 { b b m m NLO LO O LN pahrGd MadGra )g1.4 LO unc. NLO unc. the plots is described in detail in the text. g, denoted as R( a). Blue bands indicate the PDF uncertainties. The fth panel, R(mt), is completely analogous to the fourth panel, but it compares NLO QCD predictions with g and mt as central scales. We start with gure 3, which shows the distributions for the invariant mass of the topquark pair (m(tt)) for the four production processes. From this distribution it is possible to note some features that are in general true for most of the distributions. As can be seen in the fourth insets, the use of = a leads to NLO values compatible with, but systematically { 8 { LO NLO Mad 5h_p Gra ad M smaller than, those obtained with = g. Conversely, the using = mt leads to scale uncertainties bands that overlap with those obtained with = g. By comparing the rst three insets for the di erent processes, it can be noted that the reduction of the scale dependence from LO to NLO results is stronger in ttH production than for the ttV processes. As we said, all these features are not peculiar for the m(tt) distribution, and are consistent with the total cross section analysis presented before, see gure 1 and table 1. From gure 3 one can see that the two dynamical scales g and a yield atter K-factors than those from the xed scale mt, supporting a posteriori such a reference scale. While this feature is general, there are important exceptions. This is particular evident for the distributions of the pT of the top-quark pair (pT (tt)) in gure 4, where the di erential K-factors strongly depend on the value of pT (tt) for both dynamical and xed scales. The relative size of QCD corrections grows with the values of pT (tt) and this e ect is especially large in ttW K-factors. and tt production. In the following we investigate the origin of these large Top-quark pairs with a large pT originate at LO from the recoil against a hard vector or scalar boson. Conversely, at NLO, the largest contribution to this kinetic con guration emerges from the recoil of the top-quark pair against a hard jet and a soft scalar or vector boson (see the sketches in gure 5). In particular, the cross section for a top-quark pair with a large pT receives large corrections from (anti)quark-gluon initial state, which appears for the rst time in the NLO QCD corrections. This e ect is further enhanced in ttW production for two di erent reasons. First, at LO ttW production does not originate, unlike the other production processes, form the gluon-gluon initial state, which has the largest partonic luminosity. Thus, the relative corrections induced by (anti)quark-gluon initial states have a larger impact. Second, the emission of a W collinear to the nal-state (anti)quark in qg ! ttW q0 can be approximated as the qg ! ttq process times a q ! q0W splitting. For the W momentum, the splitting involves a soft and collinear singularity which is regulated by the W mass. Thus, once the W momentum is integrated, the qg ! ttW q0 process yields contributions to the pT (tt) distributions that are proportional to s log2 [pT (tt)=mW ].4 The same e ect has been already observed for the pT distribution of one vector boson in NLO QCD and EW corrections to W W ; W Z and ZZ bosons hadroproduction [49{51]. The argument above clari es the origin of the enhancement at high pT of the tt pair, yet it raises the question of the reliability of the NLO predictions for ttV in this region of the phase space. In particular the giant K-factors and the large scale dependence call for better predictions. At rst, one could argue that only a complete NNLO calculation for ttV would settle this issue. However, since the dominant kinematic con gurations (see the sketch on the right in gure 5) feature a hard jet, it is possible to start from the ttV j nal state and reduce the problem to the computation of NLO corrections to ttV j. Such predictions can be automatically obtained within MadGraph5 aMC@NLO. We have therefore computed results for di erent minimum pT for the extra jet both at NLO and LO accuracy. In gure 6 we summarise the most important features of the ttW (j) cross 4In ttZ the same argument holds for the q ! qZ splitting in qg ! ttZq. However, the larger mass of [pT 0.01 0.0001 )g9 μ ( 5 Κ n i LO MCa 0.1 0.0001 n i b / d / LO MCa 5_ aph r MadG described in detail in the text. section as a function of the pT (tt) as obtained from di erent calculations and orders. Similar results, even though less extreme, hold for ttZ and ttH nal states and therefore we do not show them for sake of brevity. In gure 6, the solid blue and red curves correspond to the predictions of pT (tt) as obtained from ttW calculation at LO and NLO, respectively. The dashed light blue, purple and mouse-grey curves are obtained by calculating ttW j at LO (yet with NLO PDFs and s and same scale choice in order to consistently compare them with NLO ttW results) with a minimum pT cut for the jets of 50, 100, 150 GeV, respectively. The three curves, while having a di erent threshold behaviour, all HJEP02(16)3 jet takes most of the recoil and the W boson is soft. n i p [ T /dσ 0.001 0.0001 )g2 μ (Κ1 LHC13 ­ ± (μg) ttW ­ ttW±j (μg) NLO LO NLO pT(j) > 100 GeV LO pT(j) > 50 GeV LO pT(j) > 100 GeV LO pT(j) > 150 GeV O L N r G d a M t­tW±j pT(j) > 100 GeV (green), for di erent minimum cuts (50, 100, 150 GeV) on the jet pT . The lower inset shows the di erential K-factor as well as the residual uncertainties as given by the ttW j calculation. tend smoothly to the ttW prediction at NLO at high pT (tt), clearly illustrating the fact that the dominant contributions come from kinematic con gurations featuring a hard jet, such as those depicted on the right of gure 5. Finally, the dashed green line is the pT (tt) as obtained from ttW j at NLO in QCD with a minimum pT cut of the jet of 100 GeV. This prediction for pT (tt) at high pT is stable and reliable, and in particular does not feature any large K-factor, as can be seen in the lower inset which displays the di erential K-factor for ttW j production with pT cut of the jet of 100 GeV. For large pT (tt), NLO corrections to ttW j reduce the scale dependence of LO predictions, but do not increase their central NLO LO g of ttV . The (N)LO cross sections are calculated with (N)LO PDFs, the relative statistical integration error is equal or smaller than one permil. value. Consequently, as we do not expect large e ects from NNLO corrections in ttW production at large pT (tt), a simulation of NLO ttV +jets merged sample a la FxFx [52] should be su cient to provide reliable predictions over the full phase space. For completeness, we provide in table 2 the total cross sections at LO and NLO accuracy for ttW j, as well as ttZj and ttHj production, with a cut pT (j) > 100 GeV. At variance with what has been done in gure 6, LO cross sections are calculated with LO PDFs and the corresponding s, as done in the rest of the article. The mechanism discussed in detail in previous paragraphs is also the source of the giant K-factors for large pT (tt) in tt production, see gure 4. This process can originate from the gluon-gluon initial state at LO, however, the emission of a photon involves soft and collinear singularities, which are not regulated by physical masses. When the photon is collinear to the nal-state (anti)quark, the qg ! tt q process can be approximated as the qg ! ttq process times a q ! q splitting. Here, soft and collinear divergencies are regulated by both the cut on the pT of the photon (pcTut) and the Frixione isolation parameter R0. We checked that, increasing the values of pcTut and/or R0, the size of the K-factors is reduced. It is interesting to note also that corrections in the tail are much larger for = g than = a. This is due to the fact that the softest photons, which give the largest contributions, sizeably reduce the value of g, whereas a is by construction larger than 2pT (tt). This also suggests that g might be an appropriate scale choice for this process only when the minimum pT cut and the isolation on the photon are harder.5 In gures 7 and 8 we show the pT distributions for the top quark and the vector or scalar boson, pT (t) and pT (V ), respectively. For these two observables, we nd the general features which have already been addressed for the m(tt) distributions in gure 3. In gure 9 we display the distributions for the rapidity of the vector or scalar boson, y(V ). In the four processes considered here, the vector or scalar boson is radiated in di erent ways at LO. In ttH production, the Higgs boson is never radiated from the initial state. In ttZ and tt production, in the quark-antiquark channel the vector boson can be emitted from the initial and nal states, but in the gluon-gluon channel it can be radiated only from the nal state. In ttW production, the W is always emitted from 5Assuming mT (t) mT (t) and mT ( ) = pcut, the the ratio a= g increases by increasing pT (t) and, T when mT (t) > pcTut, decreases by increasing pcTut. Moreover, under the same assumption, a = g at 50 100 150 pT(t) [GeV]250 300 350 400 200 0 LO Mad Gdra n i b / d / pT0.01 n i b / p [ )t 1.4 (m 1 Κ0.6 ) 1.2 NLO LO OL MadG arph MadG LO unc. 0.01 )g1.4 n i b / μ (Κ0.6 )a1.4 described in detail in the text. the initial state. The initial-state radiation of a vector boson is enhanced in the forward and backward direction, i.e., when it is collinear to the beam-pipe axis. Consequently, the vector boson is more peripherally distributed in ttW production, which involves only initial state radiation, than in tt and especially ttZ production. In ttH production, large values of jy(V )j are not related to any enhancement and indeed the y(V ) distribution is much more central than in ttV processes. These features can be quanti ed by looking, e.g., at the ratio r(V ) := ddy (jyj = 0)= ddy (jyj = 3). At LO we nd, r(W ) r(Z) 17:5 and r(H) 40. As can be seen in the rst three insets of the plots of gure 9, 5, r( ) 8:5, n i b / d / σ p [pT 0.01 0.001 1 )g1.4 LO unc. NLO unc. NLO Κ0.6 )t 1.2 (m 1 n i b / T R 0.8 0.1 t­tH (μg), LHC13 50 100 150 the plots is described in detail in the text. NLO QCD corrections decrease the values of r(V ) for ttW and tt production, i.e. the vector bosons are even more peripherally distributed (r(W ) 3:5, r( ) 5:5). A similar but milder e ect is observed also in ttZ production (r(Z) 16). On the contrary, NLO QCD corrections make the distribution of the rapidity of the Higgs boson even more central (r(H) 53). In gure 9 one can also notice how the reduction of the scale dependence from LO to NLO results is much higher in ttH production than in ttV type processes. Furthermore, for this observable, K-factors are in general not at also with the use of LO O apr adMG LO unc. NLO unc. LO hpar adMG LO aph r aMdG LO unc. n i b / d / n i b / b NLO LO LNO raph dGa M OLN 0.001 )g1.14 μ (Κ0.6 ) 1.4 n i y d / ( R 0.8 of the plots is described in detail in the text. dynamical scales. From a phenomenological point of view, this is particularly important for ttW and tt , since the cross section originating from the peripheral region is not extremely suppressed, as can be seen from the aforementioned values of r(W ) and r( ). In gure 10 we show distributions for the rapidities of the top quark and antiquark, y(t) and y(t). In this case we use a slightly di erent format for the plots. In the main panel, as in the format of the previous plots, we show LO results in blue and NLO results in red. Solid lines correspond to y(t), while dashed lines refer to y(t). In the rst and second inset C r G G d d a a M M HJEP02(16)3 −3 −2 −1 1 2 3 −3 −2 −1 1 2 3 y(t), y(t) ­ 0 y(t), y(t) ­ NLO t LO t NLO t LO t ­ ­ NLO t LO t NLO t LO t ­ ­ d / n i b / 0.001 1.2 LO 1 N0.8 n i b / b d / [yp0.01 we plot the ratio of the y(t) and y(t) distributions respectively at NLO and LO accuracy. This ratio is helpful to easily identify which distribution is more central(peripheral) and if there is a central asymmetry for the top-quark pair. Also here, although it is not shown in the plots, K-factors are not in general at. In the case of tt production the central asymmetry, or the forward-backward asymmetry in proton-antiproton collisions, originates from QCD and EW corrections. At NLO, the asymmetry arises from the interference of initial- and nal-state radiation of neutral vector bosons (gluon in QCD corrections, and photons or Z bosons in EW corrections) [53{58]. Thus, the real radiation contributions involve, at LO, the processes pp ! ttZ and pp ! tt , which are studied here both at LO and at NLO accuracy. As can be seen from gure 10, tt production yields an asymmetry already at LO, a feature studied in [ 59 ]. The ttZ production central asymmetry is also expected to be non vanishing at LO, but the results plotted in gure 10 tell us that the actual value is very small. The asymmetry is instead analytically zero in ttW (ttH) production, where the interference of initial- and nalstate W (Higgs) bosons is not possible.6 6In principle, when the couplings of light- avour quarks are considered non-vanishing, initial-state radiation of a Higgs boson is possible and also a very small asymmetry is generated. However, this possibility is ignored here. LO NLO LO NLO = g. The rst uncertainty is given by the scale variation within second one by PDFs. The assigned error is the absolute statistical integration error. At NLO, all the ttV processes and the ttH production have an asymmetry, as can be seen in gure 10 from the ratios of the y(t) and y(t) distributions at NLO. In the case of ttW production the asymmetry, which is generated by NLO QCD corrections, has already been studied in detail in [15]. In all the other cases it is analysed for the rst time here. NLO and LO results at 13 TeV for Ac de ned as Ac = (jytj > jytj) (jytj < jytj) (jytj > jytj) + (jytj < jytj) (2.3) are listed in table 3, which clearly demonstrates that NLO QCD e ects cannot be neglected, once again, in the predictions of the asymmetries. For ttW and ttH production, an asymmetry is actually generated only at NLO. Furthermore, NLO QCD corrections change sign and increase by a factor 7 the asymmetry in ttZ production and they decrease it by a factor larger than two in tt production. Thus, NLO results point to the necessity of reassessing the phenomenological impact of the tt signature, which is based on a LO calculation [ 59 ]. Moreover, we have also checked that for pT ( ) > 50 GeV both the LO and NLO central values of the asymmetry are very similar (within 5 per cent) to the results in table 3, where pT ( ) > 20 GeV. 2.2 ttV V processes We start showing for all the ttV V processes the dependence of the NLO total cross sections, at 13 TeV, on the variation of the renormalisation and factorisation scales r and f . This dependence is shown in gure 11 and it is obtained by varying = r = f by a factor eight around the central value = = a (dashed lines) and = mt (dotted lines). Again, for all the processes and especially for those with a photon in the nal state, we nd that a typically leads to larger cross sections than g and mt. For this class of processes we also investigated the e ect of the independent variation of factorisation and renormalisation scales. We found that the condition r = f captures the full dependence in the ( r; f ) plane in the range a=2 < f ; r < 2 a. On the other hand, in the full a=8 < f ; r < 8 a region o -diagonal values might di er from the values spanned at f = r. ttZZ ttZZ ttW+W­[4f] ttγγ 5 h p a r G d a M O L N 5 h p a r G d a M | 1/4 1/2 1 2 4 8 r μ = μ [μc] HJEP02(16)3 < 8 c for the three di erent choices of the central value c : g, a, mt. | 1/4 1/2 1 2 4 8 r μ = μ [μc] with c = g for the ttV V processes. In table 4 we list, for all the processes, LO and NLO cross sections together with PDF and scale uncertainties, and K-factors for the central values. Again scale uncertainties are evaluated by varying independently the factorisation and the renormalisation scales in the interval g=2 < f ; r < 2 g. The dependence of the LO and NLO cross sections on = r = f is shown in gure 12 in the range g=8 < < 8 g. As expected, for all the processes, the scale dependence is strongly reduced from LO to NLO predictions both in the standard interval g=2 < < 2 g as well as in the full range g=8 < < 8 g. For the central scale = g, K-factors are very close to unity. It is interesting to note that NLO curves display a plateau around g=2 or g=4, corresponding to HT =8 and HT =16, respectively. We show now the impact of NLO QCD corrections for relevant distributions and we discuss their dependence on scale choice and its variation. For all the processes we have ttW +W [4f] 11:84+81:13:2%% +2:3% 2:4% ttZZ NLO LO is given by the scale variation within g=2 < f ; r < 2 g, the second one by PDFs. The relative statistical integration error is equal or smaller than one permille. considered the distribution of the invariant mass of the top-quark pair and the pT and the rapidity of the (anti)top quark, of the top-quark pair and of the vector bosons. Again, given the large amount of distributions that is possible to consider for such a nal state, we show only representative results. We remind the interested reader that additional distributions can be easily produced via the public code MadGraph5 aMC@NLO. For each gure, we display together the same type of distributions for the six di erent processes: tt , ttZZ, ttW +W , ttW Z, ttW and ttZ . We start with gure 13, which shows the m(tt) distributions. The format of the plot is the same used for most of the distribution plots in subsection 2.1, where it is also described in detail. For m(tt) distributions, we notice features that are in general common to all the distributions and have already been addressed for ttV processes in subsection 2.1. For instance, the use of = a leads to NLO values compatible with, but systematically smaller than, those obtained with = g. Conversely, the choice = mt leads to scale uncertainties bands that overlaps with those obtained with = g. The NLO corrections in ttZZ production are very close to zero, for = g, and very stable under scale variation (see also table 4). For all the processes, the two dynamical scales g and a yield atter K-factors than those from the xed scale mt. In gure 14 we show the distributions for pT (tt). As for ttV processes (see gure 4), these distributions receive large corrections in the tails. This e ect is especially strong for the processes involving a photon in the nal state, namely, tt , ttZ for all the three choices of employed here, K-factors are not at. Surprisingly, the Kfactors for ttZZ, ttW of pT (tt) when Z and ttW +W production show a larger dependence on the value is a dynamical quantity, as can be seen from a comparison of the rst ( = g) and second ( = a) insets with the third insets ( = mt). From the fourth insets of all the six plots, it is possible to notice how the scale dependence at NLO for = g it is much larger than for = a. Exactly as we argued for ttV processes, NLO ttV V +jets merged sample a la FxFx should be used for an accurate prediction of these tails. In gure 15 we show the distributions for pT (t). Most of the features discussed for m(tt) in gure 13 appear also for these distributions. The same applies to the distributions of the pT of the two vector bosons, which are displayed in gure 16. In the plots of gure 16 and in all the remaining gures of this section we use the same format used in subsection 2.1 for gure 10. Thus, di erential K-factors will not be explicitly shown. In the rst and second inset we show the ratio of the distributions of the pT of the two vector bosons, respectively at NLO and LO accuracies. In the case of tt production, 1 is the hardest photon, while 2 is the softest one. Similarly, in ttZZ production, Z1 is the hardest Z boson, while Z2 is the softest one. As can be noticed, for each process this ratio is the same at LO and NLO accuracy and thus it is not sensitive to NLO QCD corrections. In gure 17 we show the distributions for y(t) and y(t). The ttV V processes, with the exception of ttW +W ,7 at LO exhibit a central asymmetry for top (anti-)quarks. Top quarks are more centrally distributed than top antiquarks in tt , ttW productions, while they are more peripherally distributed in ttZZ and ttW Z production. In all the ttV V processes, NLO QCD corrections lead to a relatively more peripheral distribution of top quarks than antiquarks. This e ects yield to a non-vanishing central asymmetry for ttW +W production and almost cancel the LO central asymmetry of ttZ production. Here, we refrain to present results for the central asymmetries of ttV V processes, since it is extremely unlikely that at the LHC it will be possible to accumulate enough statistics to perform these measurements. In gure 18 we show the distributions for y(V1) and y(V2). Comparing the rst and second insets, only small di erences can be seen for the ratios of the distributions at LO and NLO. Thus, unlike for the top quark and antiquark, the rapidity of the rst and the second vector boson receive NLO relative di erential corrections that are very similar in size. Both in the distributions of the rapidities of the top (anti)quark and of the vector bosons, NLO QCD corrections in general induce non- at K-factors, also with the use of dynamical scales.8 2.3 tttt production In this section we present results for tttt production. We start by showing in gure 19 the scale dependence of the LO (blue lines) and NLO (red lines) total cross section at 13 TeV. As for the previous cases, we vary = r = f by a factor eight around the central value = g (solid lines), a (dashes lines) and, due to the much heavier nal state, = 2mt (dotted lines). In this case we also show with a dot-dashed line the dependence of the NLO cross section on an alternative de nition of average scale where possible additional partons appearing in the nal state do not contribute. LO = N1 Pi=1;N mT;i, a 7Analytically, this process is supposed to give an asymmetry. Numerically, it turns out that it can be safely considered as zero. 8We explicitly veri ed it and it can be easily reproduced via the public version of MadGraph5 aMC@NLO, which has also been used for the phenomenological study presented here. 15 μc = 2mt 0 1/8 | 1/4 1/2 1 tttt (NLO) tttt (LO) 5 h p a r dependence in the interval c=8 < < 8 c for the four di erent choices of the central value c As expected, predictions relative to g and LO are very close. Conversely, a and a LO show a non-negligible di erence. Note that the value of a and a LO is the same for a Born and and virtual contributions for any kinematic con guration. Thus, the di erence between dashed and dot-dashed lines is formally an NNLO e ect that arise from di erences in the scale renormalisation for real radiation events only. To investigate the origin of this e ect, we have explicitly checked that the di erence is mainly induced by the corresponding change in the renormalisation scale and not of the factorisation scale. Similar behaviour is also found in ttV and ttV V processes, yet since the masses of the nal-state particles are di erent and the s coupling order lower, g and LO lines are more distant than in tttt a Since the LO cross section is of O( s4), it strongly depends on the value of the renormalisation scale, as can be seen in gure 19. This dependence is considerably reduced at NLO QCD accuracy in the standard interval g=2 < < 2 g. Conversely, for the value of the cross section falls down rapidly, reaching zero for g=8. This is a signal that in this region the dependence of the cross section on is not under control. Qualitatively similar considerations apply also for the di erent choices of scales, as can be seen in gure 19. In eqs. (2.4) and (2.5), we list the NLO and LO cross sections evaluated at the scale = g together with scale and PDF uncertainties. As done in previous subsections, scale uncertainties are evaluated by varying the factorisation and renormalisation scales in the standard interval g=2 < f ; r < 2 g. As a result the total cross section at LHC 13 TeV for the = g central scale choice reads NLO = 13:31+2255::83%% +56::86%% fb ; LO = 10:94+8411::16%% +44::87%% fb ; K factor = 1:22 : (2.4) (2.5) (2.6) HJEP02(16)3 Di erent choices for the central value and functional form of the scales, as well as the interval of variation, lead to predictions that are compatible with the result above, see also e.g. [16]. We now discuss the e ect of NLO QCD corrections on di erential distributions. We analysed the distribution of the invariant mass, the pT and the rapidity of top (anti-)quark and the possible top-quark pairs. Again, given the large amount of distributions, we show only representative results. All the distributions considered and additional ones can be produced via the public code MadGraph5 aMC@NLO. For this process the scale dependence of many distributions has been studied also in [16] and our results are in agreement with those therein. In gure 20 we show plots with the same formats as those used and described in the previous sections. Speci cally, we display the distributions for the total pT of the two hardest top quark and antiquark (pT (t1t1)), their invariant mass (m(t1t1)), the rapidity of the hardest top quark y(t1) and the invariant mass of the tttt system (m(tttt)). Also, in the last plot of gure 20, we show the pT distributions of the hardest together with the softest top quarks, pT (t1) and pT (t2), and their ratios at NLO and LO. We avoid repeating once again the general features that have already been pointed out several times in the previous two sections; they are still valid for tttt production. Here, we have found, interestingly, that NLO corrections give a sizeable enhancement in the threshold region for m(t1t1). It is worth to notice that also for this process NLO QCD corrections are very large in the tail of the pT (t1t1) distribution, especially with the use of dynamical scales. We have veri ed that in these regions of phase space the qg ! ttttq contributions are important. Finally, as can be seen in the last plot, we nd that the ratios of pT (t1) and pT (t2) distributions are not sensitive to NLO QCD corrections. Total cross sections from 8 to 100 TeV In addition to the studies performed for the LHC at 13 TeV, in this subsection we discuss and show results for the dependence of the total cross section on the energy of the protonproton collision. In gure 21 NLO QCD total cross sections are plotted from 8 to 100 TeV, as bands including scale and PDF uncertainties. The corresponding numerical values are listed in table 5. As usual, central values refers to g, and scale uncertainties are obtained by varying independently r and f in the standard interval g=2 < f ; r < 2 g. In the upper plot of gure 21 we show the results for ttH production and ttV processes, whereas tttt production and ttV V processes results are displayed in the lower plot. In both plots we show the dependence of the K-factors at = g on the energy (the rst and the second inset). The rst insets refer to processes with zero-total-charge nal states, whereas the second insets refer to processes with charged nal states. The very di erent qualitative behaviours between the two classes of processes is due to the fact that the former include already at LO an initial state with gluons, whereas the latter do not. The gluon appears in the partonic initial states of charged processes only at NLO via the (anti)quark-gluon channel. At small Bjorken-x's, the gluon PDF grows much faster than the (anti)quark PDF. Thus, increasing the energy of the collider, the relative corrections induced by the (anti)quark-gluon initial states leads to the growth of the K-factors and dominates in their tt ttW Z ttZ ttW tttt ttZ ttW tt ttH 0:502+2:9% +2:7% 8:6% 2:2% 2:12+3:8% +1:9% 8:6% 1:8% 2:59+4:3% +1:8% 8:7% 1:8% 11:1+6:9% +1:2% 9:1% 1:4% 21:1+8:1% +1:1% 9:4% 1:3% 51:6+9:9% +0:9% 9:8% 1:1% 204+11:3% +0:8% 9:9% 1:0% 11:1% +2:9% 2:7% 11:8+8:3% 11:2% +2:3% 2:4% 14:4+12:2% +2:6% 12:8% 2:9% 66:6+9:5% 10:8% +1:6% 2:0% 130+10:2% +1:5% 10:8% 1:8% HJEP02(16)3 327+10:9% +1:3% 10:6% 1:6% 1336+10:3% +1:0% 9:9% 1:3% 2:77+6:4% 10:5% +1:9% 1:5% 10:3+13:9% +1:3% 13:3% 1:3% 12+12:5% +1:2% 12:6% 1:2% 44:8+15:7% +0:9% 13:5% 0:9% 78:2+16:4% +0:8% 13:6% 0:9% 184+19:2% +0:8% 14:7% 0:9% 624+15:5% +0:7% 13:4% 1:0% 1:13+5:8% +3:1% 9:8% 2:1% 4:16+9:8% 10:7% +2:2% 1:6% 4:96+10:4% +2:1% 10:8% 1:6% 17:8+15:1% +1:5% 12:6% 1:1% 30:2+18:3% +1:2% 14:1% 0:9% 66+18:9% +1:1% 14:3% 0:8% 210+21:6% +1:0% 15:8% 0:8% 1:39+6:9% 11:2% +2:5% 2:2% 5:77+10:5% +1:8% 12:1% 1:9% 6:95+10:7% +1:8% 12:1% 1:9% 29:9+12:9% +1:3% 12:4% 1:5% 56:5+13:2% +1:2% 12:2% 1:4% 138+13:7% +1:0% 12:0% 1:1% 533+13:3% +0:8% 11:1% 1:0% 2:01+7:9% 10:5% +2:6% 1:8% 6:73+12:0% +1:8% 11:6% 1:4% 7:99+12:8% +1:7% 11:9% 1:3% 27:6+18:7% +1:2% 14:4% 0:9% 46:3+20:2% +1:1% 15:1% 0:8% 98:4+21:9% +1:0% 15:9% 0:7% 318+22:5% +1:0% 17:7% 0:7% 1:71+24:9% +7:9% 26:2% 8:4% 13:3+25:8% +5:8% 25:3% 6:6% 17:8+26:6% +5:5% 25:4% 6:4% 130+26:7% +3:8% 24:3% 4:6% 297+25:5% +3:1% 23:3% 3:9% 929+24:9% +2:4% 22:4% 3:0% 4934+25:0% +1:7% 21:3% 2:1% 0:226+9:0% 11:9% are calculated with percent accuracy, whereas for the processes with three nal-state particles with per mill. | | | | | | 13 14 ttZ ttW± 25 33 50 ttH O L a _ a r G d a M 100 | | | | | | 13 14 ttZZ 25 33 | | | 50 tttt ttW±Z ttZγ ttW±γ O L N C M a _ 5 h a r G d a M 100 [p1O02 L N σ 10 1 10­1 rso 2 t fca1.5 ­ K 1 8 1 a Kf­ 1 rso 2 t fca1.5 ­ K 1 8 ttV, ttH production at pp colliders at NLO in QCD central μf = μr = μg , MSTW2008 NLO PDFs (68% cl) uncertainties (added linearly). The upper plot refers to ttV processes and ttH production, the lower plot to ttV V processes and tttt production. For nal states with photons the pT ( ) > 20 GeV cut is applied. ttW available. energy dependence. Also, as can be seen in gure 21 and table 5, these processes present a larger dependence on the scale variation than the uncharged processes. The di erences in the slopes of the curves in the main panels of the plots are also mostly due to the gluon PDF. Charged processes do not originate from the gluon-gluon initial state neither at LO nor at NLO. For this reason, their growth with the increasing of the energy is smaller than for the uncharged processes. All these arguments point to the fact that, at 100 TeV collider, it will be crucial to have NNLO QCD corrections for ttW , and ttW Z processes, if precise measurements to be compared with theory will be whereas ttV V processes are of O( s2 2). The fact that tttt production is the process with the rapidest growth is again due to percentage content of gluon-gluon-initiated channels, which is higher than for all the other processes, see gure 22. From the left plot of gure 21, it is easy also to note that the scale uncertainty of tttt production is larger than for the ttV V processes. In this case, the di erence originates from the di erent powers of s at LO; tttt production is of O( s4) 3 Analyses of ttH signatures In this section we provide numerical results for the contributions of signal and irreducible background processes to two di erent classes of ttH signatures at the LHC. In subsection 3.1 we consider a signature involving two isolated photons emerging from the decay of the Higgs boson into photons, H ! H ! W W and H ! involving two or more leptons, where ttH production can contribute via the H ! ZZ , decays. We perform both the analyses at 13 TeV and we adopt . In subsection 3.2 we analyse three di erent signatures ttV, ttH production at pp colliders at LO μf = μr = μg , MSTW2008 LO PDFs L L ttVV, tttt production at pp colliders at LO μf = μr = μg , MSTW2008 LO PDFs ttZ 50 ttH 100 O L N a 5 h a r G d a M ttZZ tttt 100 O L N a r HJEP02(16)3 | | 13 14 25 33 | | 13 14 | 25 33 Relative contribution of the gg channel to the total cross section at LO for ttV; ttH; ttV V and tttt processes for pp collisions from 8 to 100 TeV centre-of-mass energy. For nal states with photons the pT ( ) > 20 GeV cut is applied. the cuts of [27].9 The preselection cuts, which are common for both the analyses, are: pT (e) > 7 GeV ; j ( )j < 2:5 ; j (e) < 2:5j ; pT (j) > 25 GeV ; pT ( ) > 5 GeV ; j (j)j < 2:4 ; j ( )j < 2:4 ; (3.1) where jets are clustered via anti-kT algorithm [60] with the distance parameter R = 0:5. Event by event, only particles satisfying the preselection cuts in eq. (3.1) are considered and, for each jet j and lepton `, if R(j; `) < 0:5 the lepton ` is clustered into the jet j. With the symbol `, unless otherwise speci ed, we always refer to electrons(positrons) and (anti)muons, not to (anti)leptons. All the simulations for the signal and the background processes have been performed at NLO QCD accuracy matched with parton shower e ects (NLO + PS). Events are generated via MadGraph5 aMC@NLO, parton shower and hadronization e ects are realised in Pythia8 [39], and jets are clustered via FastJet [61].10 Unless di erently speci ed, decays of the heavy states, including leptons, are performed in Pythia8. In the showering, only QCD e ects have been included; QED and purely weak e ects are not included. Furthermore, multi-parton interaction and underlying event e ects are not taken into account. In order to discuss NLO e ects at the analysis level, in the following we will also report results for events generated at LO accuracy including shower and hadronization e ects (LO + PS). As done for the xed-order studies in section 2, LO + PS and NLO + PS central values are evaluated at f = r = g and scale uncertainties are obtained by varying independently the factorisation and the renormalisation scale in the interval g=2 < f ; r < 2 g. 3.1 Signature with two photons The present analysis focuses on the Higgs boson decaying into two photons in ttH production, which presents as irreducible background the tt production. In our simulation, top 9In our simulation we do not take into account particle identi cation e ciencies and possible misiden 10In our simulation, b-tagging is performed by looking directly at B hadrons, which we keep stable. 1.09 LO K 1:466+81:17:0%% processes at 13 TeV. The rst uncertainty is given by scale variation, the second by PDFs. The assigned error is the statistical Monte Carlo uncertainty. quark pairs are decayed via Madspin for both the signal and the background, whereas the HJEP02(16)3 loop-induced H ! branching ratio BR(H ! addition, the following cuts are applied: decay is forced in Pythia8 and event weights are rescaled by the ) = 2:28 10 3, which is taken from [62]. In this analysis, at least two jets are required and one of them has to be b-tagged. In 100 GeV < m( 1 2) < 180 GeV ; pT ( 1) > 2 m( 1 2) ; pT ( 2) > 25 GeV ; R( 1; 2); R( 1;2; j) > 0:4 ; R( 1;2; `) > 0:4 ; pT (`1) > 20 GeV ; and an additional cut R(`i; `j ) > 0:4 is applied if leptons are more than one. With 1 and 2 we respectively denote the hard and the soft photon, analogously `1 indicates the hardest lepton. Cuts on lepton(s) imply that the fully and semileptonic decays of the top-quark pair are selected. Results at LO + PS and NLO + PS accuracy are listed in table 6 for the signal and the tt background. Also, we display xed order results (LO, NLO) at production level only, without including top decays, shower and hadronization e ects. In order to be as close as possible to the analyses level, we apply the cuts in eqs. (3.1) and (3.2) that involve only photons. Thus, the di erence between LO and NLO results of tt in tables 4 and 6 are solely due to these cuts. In table 6, we show global K-factors both at xed order (K := NLO=LO) and including decays, shower and hadronization e ects, and all the cuts employed in the analysis (KPS := NLO + PS=LO + PS). Comparing KPS and K it is possible to directly quantify the di erence between a complete NLO simulation (KPS) and the simulation typically performed at experimental level, i.e., a LO + PS simulation rescaled by a K-factor from production only (K). As shown in table 6, e.g., the second approach would underestimate the prediction for tt production w.r.t. a complete NLO + PS simulation. This di erence is not of particular relevance at the level of discovery, which mostly relies on an identi cation of a peak in the m( 1 2) (see also gure 23), but could be important in the determination of signal rates and in the extraction of Higgs couplings. Conversely, the di erence between K and KPS is much smaller for the signal. (3.2) (3.3) PS­ ttH1.5 Κ0.5 PS­ ttγγ 1.5 1 1 Κ0.5 10−4 10−6 1.5 PS­ ttH Κ0.5 PS­ ttγγ 1.5 1 1 Κ0.5 NLO+PS (μg), LHC13 NLO+PS (μg), LHC13 4e−05 ] d / σ /bb 3e−05 RΔ2e−05 d 1e−05 PS­ ttH1.5 Κ0.5 PS­ ttγγ 1.5 1 1 Κ0.5 10−4 n i T p d / dσ10−6 10−7 1 Κ0.5 ­ ttγγ LO unc. NLO unc. ­ t­tH(γγ) O L L N N a a 5 5 h h p p a a r r G LO unc. NLO unc. 100 110 120 130 140 150 160 170 180 0 5 5 h h p p a a r r LO unc. NLO unc. 0 200 250 300 350 0 20 40 60 80 100 120 140 160 180 pT(γ1) [GeV] pT(γ2) [GeV] In gure 23 we show representative di erential distributions at NLO + PS accuracy for the signal (red) and background (black) processes. In the two insets we display the di erential K-factor for the signal (KtPtHS ) and the background (KtPtS ) using the same layout and conventions adopted in the plots of section 2. In particular, we plot the invariant mass of the two photons (m( 1 2)) their distance ( R( 1; 2)) and the transverse mo mentum of the hard (pT ( 1)) and the soft (pT ( 2)) photon. We note that predictions for key discriminating observables, such as the R( 1; 2) and pT ( 2) are in good theoretical control. 3.2 Signatures with leptons H and H ! This analysis involves three di erent signatures and signal regions that includes two or more leptons and it is speci cally designed for ttH production with subsequent H ! ZZ , decays. In the simulation, all the decays of the massive particles are performed in Pythia8. In the case of the signal processes, the Higgs boson is forced to decay to the speci c nal state (H ! ZZ , H ! or H ! + ) and event weights are rescaled by the corresponding branching ratios, which are taken W W ) = 2:15 10 1, BR(H ! ZZ ) = 2:64 10 2, BR(H ! ) = 6:32 10 2. The isolation of leptons from the hadronic activity is performed by directly selecting only prompt leptons in the analyses, i.e., only leptons emerging from Z, W or from leptons which emerge from Z, W or Higgs bosons.11 We consider as irreducible background the contribution from ttW , ttZ= , ttW +W , ttZZ, ttW Z and tttt production.12 Precisely, with the notation ttZ= we mean the full process tt`+` (` = e; ; ), where Z and photon propagators, from which the `+` pair emerges, can both go o -shell and interfere.13 All the processes, with the exception of ttZ= , have been also studied at xed-order accuracy in section 2. In the analyses the following common cuts are applied in order to select at least two (3.4) Then, the three signatures and the corresponding signal regions are de ned as described Signal region one (SR1): two same-sign leptons Exactly two same-sign leptons with pT (`) > 20 GeV are requested. The event is selected if it includes at least four jets with one or more of them that are b-tagged. Furthermore it is required that pT (`1) + pT (`2) + Emiss > 100 GeV and, for the T dielectron events, jm(e e ) mZ j > 10 GeV and Emiss > 30 GeV, in order to suppress T background from electron sign misidenti cation in Z boson decays. Signal region two (SR2): three leptons Exactly three leptons with pT (`1) > 20 GeV, pT (`2) > 10 GeV, pT (`3 = e( )) > 7(5) GeV are requested. The event is selected if it includes at least two jets with one or more of them that are b-tagged. For a Z boson background suppression, events with an opposite-sign same- avour lepton pair are required to have jm(`+` ) mZ j > 10 GeV. Also, for this kind of events if the number of jets is equal or less than three, the cut Emiss > 80 GeV is applied. Signal region three (SR3): four leptons analyses of [27]. ) contributions. Exactly four leptons with pT (`1) > 20 GeV, pT (`2) > 10 GeV, pT (`3;4 = e( )) > 7(5) GeV are requested. The event is selected if it includes at least two jets with one or more of them that are b-tagged. Also here, for a Z boson background suppression, events with an opposite-sign same- avor lepton pair are required to have jm(`+` ) mZ j > 10 GeV. 11We observed that applying hadronic isolation cuts as done in [27] we obtain results with at most 10% di erence with those presented here by selecting prompt leptons. K-factors are independent of the application of hadronic isolation cuts. 12In principle also ttW and ttZ production can contribute to the signatures speci ed in the following. However, they are a small fraction of ttW and ttZ production and indeed are not taken into account in the 13To this purpose, we excluded Higgs boson propagators in order to avoid a double count of the ttH(H ! For both signal and background processes, results at LO + PS and NLO + PS accuracy as well as KPS-factors are listed in table 7 for the three signal regions. Also, for each process we display the value of the global K-factor (listed also in section 2), which does not take into account shower e ects, cuts and decays. A posteriori, we observe that in these analyses the K-factors are almost insensitive of shower e ects and the applied cuts. This is evident from a comparison of the values of K and KPS in table 7, where the largest discrepancy stems from the ttZ= process in SR1. We also veri ed, with the help of Madspin, that results in the SR3 (SR2 for ttW ) do not change when spin-correlation e ects are taken into account in the decays.14 It is important to note that, a priori, with di erent cuts and/or at di erent energies, K and KPS could be in principle di erent and spin correlation e ects may be not negligible. Thus, a genuine NLO+PS simulation is always preferable. 4 In this paper we have presented a thorough study at NLO QCD accuracy for ttV and ttV V processes as well as for ttH and tttt production within the same computational framework and using the same input parameters. In the case of ttV V processes, with the exception of tt production, NLO cross sections have been studied for the rst time here. Moreover, we have performed a complete analysis with realistic selection cuts on nal states at NLO QCD accuracy including the matching to parton shower and decays, for both signal and background processes relevant for searches at the LHC for the ttH production. Speci cally, we have considered the cases where the Higgs boson decays either into leptons, where ttV and ttV V processes and tttt production provide backgrounds, or into two photons giving the same signature as tt We have investigated the behaviour of xed order NLO QCD corrections for several distributions and we have analysed their dependence on (the de nition of) the renormalisation and factorisation scales. We have found that QCD corrections on key distributions cannot be described by overall K-factors. However, dynamical scales in general, even though not always, reduce the dependence of the corrections on kinematic variables and thus lead to atter K-factors. In addition, our study shows that while it is not possible to identify a \best scale" choice for all processes and/or di erential distributions in ttV and ttV V , such processes present similar features and can be studied together. For all the processes considered, NLO QCD corrections are in general necessary in order to provide precise and reliable predictions at the LHC. In particular cases they are also essential for a realistic phenomenological description. Notable examples discussed in the text are, e.g., the giant corrections in the tails of pT (tt) distributions for ttV processes and the large decrement of the top-quark central asymmetry for tt production. In the case of future (hadron) colliders also inclusive cross sections receive sizeable corrections, which lead, e.g., to K-factors larger than two at 100 TeV for ttV and ttV V processes with a charged nal state. 14SR2 and especially SR1 involves a rich combinatoric of leptonic and hadronic Z, W and decays, which render the simulation with spin-correlation non-trivial. However, we checked also here for representative cases that spin-correlation e ects do not sensitively alter the results. HJEP02(16)3 In the searches at the LHC for the ttH production with the Higgs boson decaying either into leptons or photons, NLO QCD corrections are important for precise predictions of the signal and the background. We have explicitly studied the sensitivity of NLO+PS QCD corrections on experimental cuts by comparing genuine NLO+PS QCD predictions with LO+PS predictions rescaled by global K-factors from the xed order calculations without cuts. A posteriori, we have veri ed that these two approximations give compatible results for analyses at the 13 TeV Run-II of the LHC with the cuts speci ed in the text. A priori, this feature is not guaranteed for analyses with di erent cuts and/or at di erent energies. In general, a complete NLO+PS prediction for both signal and background processes is more reliable an thus preferable for any kind of simulation. All the results presented in this paper have been obtained automatically in the publicly available MadGraph5 aMC@NLO framework and they can be reproduced starting from the input parameters speci ed in the text. Acknowledgments We thank the ttH subgroup of the LHCHXSWG and in particular Stefano Pozzorini for many stimulating conversations. We thank also all the members of the MadGraph5 aMC@NLO collaboration for their help and for providing a great framework for pursuing this study. 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Fabio Maltoni, Davide Pagani, Ioannis Tsinikos. Associated production of a top-quark pair with vector bosons at NLO in QCD: impact on \( \mathrm{t}\overline{\mathrm{t}}\mathrm{H} \) searches at the LHC, Journal of High Energy Physics, 2016, 113, DOI: 10.1007/JHEP02(2016)113