t tbar W and t tbar Z Hadroproduction at NLO accuracy in QCD with Parton Shower and Hadronization effects

We present theoretical predictions for the hadroproduction of t tbar W+, t tbar W- and t tbar Z at LHC as obtained by matching numerical computations at NLO accuracy in QCD with Shower Monte Carlo programs. The calculation is performed by PowHel, relying on the POWHEG-BOX framework, that allows for the matching between the fixed order computation, with input of matrix elements produced by the HELAC-NLO collection of event generators, and the Parton Shower evolution, followed by hadronization and hadron decays as described by PYTHIA and HERWIG. We focus on the dilepton and trilepton decay channels, studied recently by the CMS Collaboration.


Introduction
The hadroproduction of tt-pairs in association with vector bosons is one of the key processes to constrain top quark properties, in particular top couplings, and to detect if anomalies, possibly related to physics beyond the Standard Model (SM), can manifest themselves. Furthermore, it can be considered a background process for new physics searches. In particular, the dilepton decay channel with two same-sign leptons, accompanied by missing energy and jets, is a relatively rare channel in the SM, but largely exploited in recent supersymmetry searches [1]. From the experimental point of view, these studies are becoming feasible thanks to the increasing amount of data collected at LHC, that has already reached an integrated luminosity large enough to permit the disentangling of tt + V signals over other SM backgrounds [2]. Such an investigation can certainly benefit from high accuracy theoretical tools, involving the inclusion of radiative corrections, at least in QCD, and the matching to Parton Shower (PS) approaches.
The aim of this paper is to provide predictions for tt + V production (with V = W + , W − , Z) at LHC at both NLO and NLO + PS accuracy. In case of NLO we also include uncertainties due to factorization and renormalization scale variation, always assumed equal one to each other in this work. This is achieved by PowHel, an event generator relying on the POWHEG-BOX [3] computer framework designed for matching predictions at NLO accuracy in QCD to a PS evolution, according to the POWHEG method [4,5]. We use as input matrix elements that we compute through codes available in the HELAC-NLO package [6]. With such an input, the POWHEG-BOX is capable to make predictions at both NLO accuracy, and at NLO accuracy matched to a PS evolution. We especially concentrate on the √ s = 7 and 8 TeV energies, but the approach can easily be extended to other ones (and to other colliders). By means of this same framework we were already able to produce predictions for other processes (tt, tt j, tt H/A) at the same accuracy, which can be considered a good test of its robustness [7][8][9][10]. So far, we also presented some theoretical results on tt Z production itself, at NLO accuracy [11], and a phenomenological study limited to its decay channel in six jets plus missing energy, at NLO + PS accuracy [12]. This paper is new with respect to our previous ones, since here for the first time we produce predictions for tt W ± hadroproduction, and we concentrate on the (semi)leptonic decay channels of tt Z, the same channels that are nowadays preferred by the experimental collaborations, as much cleaner signals can be obtained with respect to the fully hadronic decay one. The tt W ± hadroproduction has already been recently investigated by MCFM at the NLO accuracy in QCD [13]. Our study provides a completely independent confirmation of their results at the parton level, with which we found agreement within the quoted uncertainties. Furthermore, we give predictions for the first time for this same process at the hadron level, by the matching the NLO predictions to the PYTHIA [14] and HERWIG [15] Shower Monte Carlo (SMC) programs, describing PS emissions, hadronization and hadron decays.
The paper is organized as follows. In Section 2.1 we provide a short description of the general computing framework, and details on the particular issues we had to face for the implementation of the tt V specific processes. In Section 2.2 we quote our results at NLO accuracy, and we show the checks we did to ensure that the matching between the NLO computation and the PS algorithm is implemented in a correct way. In Section 3 we describe the phenomenological studies we performed at the hadron level and we show predictions for differential distributions both at the inclusive level and in the same exclusive selection channels considered by the CMS Collaboration in their data analysis. In particular, our predictions turn out to be compatible with the experimental data in both the trilepton and the dilepton channels, as recorded in the recently published data analysis at 7 TeV. Finally, in Section 4 we draw our conclusions with mention to future refinements of this computation.

Implementation
We address the problem of matching tt V (V = Z, W ± ) production at NLO level to PS programs, to this end the POWHEG approach [4,5] was chosen as implemented in POWHEG-BOX [3]. While details on the implementation of tt Z in this framework were recorded in our previous papers [11,12], the following ingredients, needed by POWHEG-BOX, were provided in case of tt W ± hadroproduction: • The phase space corresponding to three massive particles in the final state was provided in full analogy with our previous computations of the tt Z and tt H processes at the same accuracy [8,12].
• The Born and real-emission matrix elements corresponding to the qq tt W ± → 0 and qq tt W ± g → 0 processes, respectively, with q, q ∈ {u, d, c, s}, were provided by HELAC-NLO [6].
• The finite part of the virtual amplitudes was computed by HELAC-1LOOP [16] for the qq tt W ± → 0 processes.
• At both tree-and one-loop-level the remaining matrix elements were obtained by crossing.
• The spin-and color-correlated Born squared matrix elements were also provided by HELAC-NLO.
The PowHel (= POWHEG-BOX + HELAC-NLO) code implemented this way is capable of generating Les Houches Events (LHE's), including up to first radiation emission, for both tt W + and tt W − . A selection between these two cases can simply be achieved by setting the Wmode keyword in the input card to ±1.
In order to make comparison with the available NLO predictions [13], we had to use a non-diagonal CKM matrix in the calculation. We thus extended HELAC-1LOOP in this respect. This process can then be considered the first one, among those computed with HELAC-1LOOP, where a non-diagonal CKM matrix was used. A check of the correctness of the implementation was provided by comparing our results with those already available in literature (see next Subsection), obtained in the same non-diagonal conditions. We make available the PowHel implementation, where the user has the possibility of switching from the diagonal CKM matrix to a non-diagonal one by specifying a positive value of the sin2cabibbo keyword in the input card, which declares sin 2 θ C .

Results at NLO accuracy and Checks
In order to assess the correctness of the implementation, a standard set of checks we are used to doing on the PowHel implementation of any new process, was performed also in this case. The consistency between the real emission matrix elements, the Born part, and the real counterterms automatically computed according to the FKS subtraction scheme [17], was checked by investigating the behavior of these terms in all kinematically degenerate regions of phase space. The original and crossed matrix elements computed by PowHel were checked against those provided by HELAC-Phegas and HELAC-1LOOP standalone in various randomly chosen phase space points. As for tt W ± , the Born results were checked against MCFM [18,19], and the NLO ones against the predictions quoted in Ref. [13], using the same set of parameters mentioned therein and sin 2 θ C = 4.9284 · 10 −2 , as in the default version of MCFM. In all cases we found full agreement.
We also compute NLO tt W ± cross-sections at LHC for a different static central scale choice, by considering the interval [µ 0 /2, 2µ 0 ] centered around µ 0 = m t + m V /2, and the following set of parameters: √ s = 7 and 8 TeV, the CTEQ6.6M PDF set with a 2-loop running α s and 5 active flavours, taken from LHAPDF [20], m b = 0, whereas as for heavy particle masses, the latest available values provided by the PDG [21], i.e. m t = 173.5 GeV, m W = 80.385 GeV and m Z = 91.1876 GeV, were adopted. For the whole calculation a non-diagonal CKM-matrix was used, in the first two families, with sin 2 θ C = 4.9284 · 10 −2 . The renormalization and factorization scales were fixed to µ 0 . The predictions for the total NLO cross-sections in these conditions are shown in Table 1. The considered scale choice turned out to provide a flatter scale dependence with respect to the case µ 0 = m t , as can be understood by comparing the results quoted in Table 1 to those provided in Ref. [13].
Although the K-factor associated to the tt W ± process is close to one, it is also informative to compare NLO differential cross-sections to those obtained from the LHE's, which checks the correctness of the matching procedure. Sample distributions can be found in Figs. 1 and 2, where the transverse momenta and the rapidities of both the t-quark and the tt-pair are shown in case of tt W + and tt W − , respectively, together with the ratio of the predictions from the LHE's to the NLO ones. The agreement between the NLO and the LHE distributions is quite remarkable, as can be seen from the two rapidity plots and from the p ⊥ distribution of the t-quark. The small deviation visible in the p ⊥, t tail is within the increased statistical uncertainty in that region, also plotted in the lower inset of each panel. For the p ⊥, tt distribution the agreement is within 5 % up to 220 GeV, but worsens in dσ dp dσ dp  . Comparison between differential distributions at NLO accuracy (solid line) and from the LHE's (dashed line), in case of tt W + production. As sample distributions, the transverse momentum and rapidity distributions are shown for the t-quark and for the tt-pair. In the lower panels the red dash-dotted line corresponds to the LHE/NLO ratio, whereas the differential Kfactor (NLO/LO) is depicted with a dotted line. The error-bars refer to the statistical uncertainties on the LHE/NLO ratio. In case of transverse momentum distributions, the scale dependence is also superimposed as a light-blue band, which represents a scale variation between µ 0 /2 and 2µ 0 .
the high momentum tail. We attribute this increasing difference to the increasing K-factor that reaches 2 around 400 GeV (also depicted in the lower panel of the plot). This 10 % deviation however, is well within the NLO scale dependence, as seen from the upper panel, where the uncertainty band, corresponding to a scale-variation in the [µ 0 /2, 2µ 0 ] interval, is shown as well. Differential K-factors and the comparison between NLO and LHE distributions in case of the tt Z process can be found in Ref. [11,12] 3 Phenomenology

PowHel and SMC setup
For our phenomenological studies the following parameters were adopted in PowHel: the CTEQ6.6M PDF set, with a 2-loop running α s , m t = 172.5 GeV, m W = 80.385 GeV, m Z = dσ dp dσ dp   91.1876 GeV, sin 2 θ C = 4.9284 · 10 −2 . The renormalization and factorization scales were fixed to µ R = µ F = m t + m V /2. Although the value of m t is different from the most recent measurements at the LHC and also from that used in our NLO comparisons, it was also used in Ref. [13] and in several measurements performed by the LHC experiments so far.
The PowHel code provides collection of LHE's of two kinds: Born-like events, and events including first radiation emission. According to the POWHEG method, this emission is SMC independent. Further emissions can be simulated by simply showering the events by SMC programs, under the condition that the first emission remains the hardest. We consider the last fortran version of both the PYTHIA and HERWIG SMC, providing a virtuality-ordered and an angular-ordered PS, respectively. As the ordering variable in the POWHEG method is the relative transverse momentum, in case of an angular-ordered PS parton emissions with larger transverse momentum than the first one have to be vetoed explicitly (done in HERWIG automatically). Furthermore, a truncated shower, simulating wide-angle soft emission before the hardest one ought to be included, too. However, the effect of the truncated shower in general turns out to be small, as shown e.g. in Ref. [22] and as we already verified in case of many different multiparticle production processes including a tt pair, where the predictions of PYTHIA and HERWIG turn out to agree one with each other within a few percent. Thus, we neglect truncated shower contributions in this paper, as we already did in our previous ones.
These SMC codes were also used to generate t-quark and heavy boson decays (neglecting spin correlations), as well as hadronization and hadron decays. For consistency, heavy particle masses in the SMC setup were set to the same values used in the PowHel computation, whereas the light quark masses in HERWIG were set to the default values implemented in PYTHIA. Heavy particle decay widths were fixed to Γ t = 1.45775 GeV, Γ W = 2.085 GeV and Γ Z = 2.4952 GeV. Decays of heavy bosons into electrons were assumend to have the same branching ratio as into muons. π 0 's were enforced to be stable in both SMC's, as they can be easily reconstructed in the experiments from their decay products (2 γ), and muon stability was enforced in HERWIG, as in PYTHIA default configuration. All other particles and hadrons were assumed to be stable or to decay according to the default implementation of each SMC. Multiple interactions were neglected in both SMC's.

Inclusive analysis
We now present predictions at the SMC level, i.e. after PS, hadronization and hadron decay, in case of tt W + , tt W − and tt Z in the most general case, i.e. without applying any selection cut. This is possible since these processes are finite at the Born level, so we did not have to introduce any technical cut in the PowHel generation of LHE's. It is useful and instructive to present some theoretical distributions at this level, to better understand how the selection cuts that we will discuss in the following will modify these predictions. In particular, we focus on a few selected distributions that will also be shown again, in presence of cuts, in the following Subsections.
The inclusive cross-sections at the SMC level are the same as at the NLO level as the POWHEG method ensures that the cross-sections from LHE's coincide with the exact NLO ones, i.e. σ LHE = σ NLO . We found that σ tt Z > σ tt W + > σ tt W − , with σ tt Z = 137.21 ± 0.01 fb, σ tt W + = 106.74 ± 0.01 fb and σ tt W − = 43.472 ± 0.005 fb, respectively (uncertainties are statistical only). These values are slightly larger than those quoted in Table 1, due to the slightly smaller value of the t-quark mass (see the beginning of the previous Subsection 3.1).
The invariant mass of all same-flavour ( + , − ) pairs in all events is plotted in Fig. 3.a. Even in absence of cuts, a peak is well visible in the tt Z distribution, around the Z pole mass, due to Z → + − decays. The e + e − and µ + µ − channels both contribute with a similar shape to this distribution. The presence of this peak, absent in the tt W + and tt W − distributions also plotted in Fig. 3.a, will be exploited in the trilepton analysis discussed in the following Sect. 3.3. Looking at the invariant mass of all same-flavour same-sign (anti-)lepton pairs in all events, plotted in Fig. 3.b, an almost monotonically decreasing distribution is found. These lepton combinations can come from any possible source: one from the (anti-)t-quark and the other from the W or Z, a prompt and a secondary (anti-)leptons, two secondary (anti-)leptons.
The predictions using HERWIG as SMC, instead of PYTHIA, agree with the PYTHIA ones well below 5 % in all the dilepton mass range considered (see the ratios plotted in both lower panels of Fig. 3), except for a small window in the range between 65 and 92 GeV in case of opposite-sign and same-flavour dilepton pairs, where a big difference is found, due HERWIG/PYTHIA HERWIG/PYTHIA to the different physics implemented in the default version of the two codes: while PYTHIA includes photon bremsstrahlung from leptons, this effect is absent in HERWIG. Thus, the sharp peak seen by HERWIG due to Z → ( + , − ) decays, is smeared in case of PYTHIA. We will return on this point in more details in the following Sect. 3.3. In Fig. 4.a, the transverse momentum distribution of the hardest lepton of each event is shown. Here it is worth noting the different shapes of the tt W + and tt W − distributions, with the tt W − becoming larger than the tt W + one for p ⊥ > 260 GeV, as expected because the high p ⊥ tail is populated by prompt leptons emitted from primary W − → ν decays, that are absent in case of W + decays. Leptons originated by primary Z decays can have even larger p ⊥ as seen from the shape of the tail of the tt Z distribution, with a slope flatter than both the previous ones.
Finally, the missing transverse momentum distribution due to all neutrinos is plotted in Fig. 4.b. The shape of the tt W + distribution is similar to the tt W − one, with a rescaling factor just due to the different cross-section, whereas the shape of the tt Z distributions differs from the previous ones, with a larger contribution in the first two bins, due to events without neutrinos or with neutrinos from secondary decays with very small transverse energy and a flatter slope than the tt W ± cases. The region around 50 GeV, where the the tt W + and tt Z distributions are closer together, is filled by neutrinos from prompt W + decays, absent in case of tt Z. The first bin is enhanced in all distributions due to the possibility of events without neutrinos (W decays in two light jets are indeed possible and not ruled out by any selection cut in this analysis).
For both distributions plotted in Fig. 4 we found that the differences between the cumulative predictions by PYTHIA and HERWIG, obtained by summing over the three tt V processes, are within 5 % (see the lower panels), with a slightly larger agreement in case of the / p ⊥ -distribution.

Trilepton-channel analysis
The aim of the trilepton channel analysis proposed in Ref. [2] is selecting tt Z events, with Z decaying in two opposite-sign charged leptons, and one of the quarks of the tt-pair decaying leptonically, whereas the other one hadronically. In particular, we considered the following set of cuts: In our simulation, jets were reconstructed using the anti-k ⊥ algorithm, with R = 0.5, using Fastjet 3.0.0 [23]. b-tagging was done by means of the MCTRUTH parameter, allowing to trace back the origin of a jet to a b or ab quark. In case of multiple dilepton pairs with opposite charge and same flavour satisfying cuts 1), 2) and 3), the pair with the invariant mass closest to the nominal Z mass was selected.
Predictions for the expected number of events after cuts at the √ s = 7 TeV LHC, corresponding to an integrated luminosity L = 4.98 fb −1 , as obtained by our PowHel+ PYTHIA simulations, are shown in Fig. 5, distinguishing the possible decay channels, labelled by the flavours of the two leptons entering the dilepton system plus the third lepton mentioned in cut 4). When more than one additional lepton satisfies cut 4), we choose that with the largest p ⊥ . The sum of the results in all channels is plotted in the last bin of the figure, as well. These predictions can be compared to the experimental results, presented in Ref. [2] for the same luminosity, with the caveat that we still do not include the predictions for background processes (like Z + jets, tt and diboson production) at the same accuracy. For an estimate of these background contributions at a lower accuracy, one can rely on Ref. [2]. One has also to take into account that the CMS Collaboration used an experimental b-jet tagging algorithm, instead of a purely theoretical one, as we did. The contribution in the (e, e) e, (e, e) µ, (µ, µ) e and (µ, µ) µ channels are shown separately, as well as their sum in the last bin. The contributions due to tt Z, tt W + and tt W − are cumulated one over the other. To be compared with the experimental data in Fig. 4 of the CMS technical report [2]. In the lower inset the ratios between cumulative results using different SMC (HERWIG/PYTHIA) and between cumulative results obtained by neglecting and including photon bremsstrahlung from leptons (PYTHIA-no-brem/PYTHIA) are also shown.
As expected, as a result of the selection cuts, and in particular of the cut on the invariant mass of the dilepton system, both in the experiment and in our theoretical predictions the contributions to the total number of events due to the tt W ± processes are highly suppressed. We estimate a suppression factor of about 10 between the cross-sections after the cuts for the processes (tt W + + tt W − ) and tt Z, from our theoretical simulations. The invariant mass of the reconstructed Z is plotted for these three processes in Fig. 6.a, from where it is clear that the largest contribution of the tt Z process is due to the peak around m Z , completely absent in case of both tt W + and tt W − .
In the lower inset of Fig. 5 the ratios of the results using different SMC's are plotted. In particular, using HERWIG instead of PYTHIA as SMC, leads to a larger number of events. This is due to the different physics implemented in the two SMC's. In fact, as already mentioned in Sect. 3.2, while PYTHIA includes by default photon bremsstrahlung from leptons, the stand-alone fortran version of HERWIG does not include it (unless one interfaces it with external packages). The photon bremsstrahlung effect affects the dilepton invariant mass after SMC: as shown in Fig. 6.b, (that is the analogous of Fig. 3.a after cuts), the very narrow peak evident in case of HERWIG simulations is smeared by the effect of photon bremsstrahlung from leptons implemented in default PYTHIA simulations. As a further check, we switched off this kind of emissions even in PYTHIA. The predictions of PYTHIA without lepton bremsstrahlung are superimposed on the same plot and look to be closer to the HERWIG ones. The modification on the number of events after cuts in the different channels, one gets by switching off this effect in PYTHIA, is also shown in the lower panel of Fig. 5. The predictions presented in Fig. 5 are compatible with the experimental data of Ref. [2] within the error-bars of the latter. However, while our simulations predict almost symmetric central values between the (e, e) e and the (µ, µ) µ channels, and between the (e, e) µ and the (µ, µ) e channels, the experimental data show the same pattern for the latter case, but different for the first one: the (µ, µ) µ bin is more populated than the (e, e) e one (although the populations of these two bins can still can still be viewed equal within the large error-bars). From our simulations we verified that a slight asymmetry between the (e, e) e and the (µ, µ) µ bins is generated by the inclusion of photon bremsstrahlung from leptons. In the absence of this effect, the population of these two channels is instead completely symmetric. It is also affected by the different selection cuts on electros and muons (see cut 1). We think that the larger asymmetry effects, as inferred from the experimental data, are due to other experimental details, like limited detection efficiencies and charge misidentification effects. Such effects are neglected in our simulations and their precise implementation is dependent on the experimental analysis detail, beyond the scope of this work.
The transverse momentum distributions of the leading and subleading (anti-)lepton of the ( + , − ) pairs selected by the considered system of cuts are shown separately in Fig. 7. These distributions have different shapes, as expected: those belonging to the leading lepton are peaked at ∼ 65 GeV for both tt Z, tt W + and tt W − while those belonging to the subleding lepton decrease monotonically just above the p ⊥,l > 20 GeV cut. When considered together, the lepton and the anti-lepton give rise to a "reconstructed Z", whose p ⊥ has a shape characterized by a smooth peak in the 50 GeV region.  It is also interesting to separate the behaviour of leptons and anti-leptons. As seen in Fig. 8.a, the p ⊥ -distribution of the hardest lepton of each event has a plateau in the region 20-70 GeV in case of both tt Z and tt W + , whereas for the distribution of the hardest anti-lepton plotted in Fig. 8.b, the plateau appears for tt Z and tt W − , i.e. the situation for tt W + and tt W − is symmetric. This symmetry suggests that these plateaus are generated by the selection cuts and include the contributions of the prompt leptons and anti-leptons originated directly from the decay of the initial Z and W weak-bosons (whereas possible secondary leptons or anti-leptons with the same transverse momentum are cut). The behaviour of the tails of the tt W + and tt W − distributions Fig. 8.b is the same as already observed in Fig. 4.a for the case of the inclusive analysis (see discussion in Subsection 3.2), suggesting that even the high-p ⊥ regions are dominated by prompt leptons, as expected. In case of both HERWIG and PYTHIA where the photon bremsstrahlung effect is switched off, these distributions are just rescaled by a 5-10 % factor, slightly increasing towards the tail of the distributions, indicating that hardest (anti-)leptons are more prone to emit photons than the softer ones. We also repeated the analysis in the trilepton channel in case of an LHC √ s = 8 TeV center-of-mass energy, that can be useful in view of future data analysis on the basis of the events recorded in the present run. For future reference, we report here our cumulative predictions for the cross-section contributions of the three processes tt Z, tt W + and tt W − at √ s = 8 TeV: σ (e,e),e = 0.782 fb, σ (e,e),µ = 0.388 fb, σ (µ,µ),e = 0.420 fb, σ (µ,µ),µ = 0.934 fb, σ = 2.524 fb, all with a statistical uncertainty below 5 · 10 −5 fb. Furthermore, predictions for the same differential distributions already discussed in the √ s = 7 TeV case, were produced in the 8 TeV case, and we have found very similar results, except for a rescaling factor just given by the ratio of the cross-sections at 8 and 7 TeV. The LHE's are freely available at our web repository: http://www.grid.kfki.hu/twiki/bin/view/DbTheory/WebHome.

Dilepton-channel analysis
As mentioned in the introduction, studies of tt V decays in the dilepton channel, with two same-sign leptons plus jets, have their original motivation that this kind of signature is hardly produced by SM processes, and can thus be used in searches for supersymmetry. In this case, tt V can be considered as a background with respect to possible new physics processes. Other sizable backgrounds involve many different diboson and triboson production processes. An exhaustive list of backgrounds in this context can be found in Ref. [13]. New physics searches usually also involve a cut on missing energy. In this paper we explore the dilepton channel, without imposing any missing energy cut, as also done in the very recent CMS technical report [2], where the analysis was optimized on the basis of data collected at LHC at √ s = 7 TeV corresponding to an integrated luminosity L = 4.98 fb −1 . This way the relatively small number of tt V events does not suffer any further suppression due to this cut.
The aim of this analysis is to select the events where one of the quarks of the tt-pair decays leptonically and the other one hadronically, and the vector boson decays leptonically giving rise to a lepton with the same sign of the lepton coming from the (anti-)quark. In case of tt W + -production this means that we are looking for W + → + ν , accompanied by the leptonic decay of the t-quark, whereas, in case of tt W − -production we aim to select events with W − → −ν , accompanied by the leptonic decay of thet-quark. In case of tt Z-production Z → + − , and thus it is sufficient that either the t-or thet-quark decays leptonically.
Following the CMS Collaboration, we considered the following set of cuts: 1. two same-sign isolated leptons with p ⊥, 1 > 55 GeV and p ⊥, 2 > 30 GeV, respectively, within CMS acceptance (|η | < 2. Jets were constructed using of the anti-k ⊥ algorithm, with R = 0.5, as implemented in Fastjet 3.0.0 [23]. Lepton isolation was computed by making use of the standard isolation criterion mentioned in the CMS technical report [1]: we require a lepton relative isolation I rel > 0.15, where I rel is computed as the ratio between the scalar sum of the transverse momenta of all tracks within a distance ∆R < 0.3 with respect to the selected lepton and the transverse momentum of the lepton itself (excluded from the sum at the numerator). Furthermore, in case of multiple dilepton pairs satisfying the cuts mentioned above, the pair was selected with the largest combined transverse momentum.
As also done in the CMS analysis [2], we explicitly exclude from this analysis all events that are selected in the trilepton channel analysis, in order to obtain two statistical independent samples (trilepton veto). As we will see in the following, the final predictions in the dilepton channel as for both the number of events and the shape of the distributions, will indeed be affected by this choice, especially as for the tt Z process.
Differences between our theoretical analysis framework and the experimental conditions are listed in the following: • Contrary to experimental reconstruction of the events, electron and muon detection efficiencies in our theoretical simulations were assumed to be 100 % and charge misidentification effects neglected.
• Also, while in the experiment b-jets were reconstructed as displaced vertices, making use of spatial tracking information, and a b-tagging algorithm was applied, ensuring a limited efficiency in the reconstruction of b-jets, accompanied by a non-negligible fake rate, in our simulations we identified b-jets using the MCTRUTH parameter which allows for tracking back b andb quarks from tt-decay, but we lacked spatial information concerning the position of displaced vertices.
Despite the differences in the analysis, and perhaps other experimental detail we are not aware of, the theoretical predictions, shown in Fig. 9, are compatible with the experimental results. The largest contribution to the total number of events is from the tt W + process, followed by the tt Z and the tt W − ones. The contribution of the tt W + process is larger than the tt W − one already at the inclusive level (see Sect. 3.3), with the ratio between the two remaining almost the same after cuts (2.45 for the inclusive predictions and 2.42 after cuts). The contribution of tt W + is enhanced with respect to that of tt Z after cuts is an effect of the selection cuts and of the trilepton veto. For the tt W ± processes, the contribution in the (e, µ) channel turns out to be almost twice the average of the (e, e) and (µ, µ) ones, as naively expected on the basis of the possible charge and flavour combinations. (An electron can come from the W and a muon with the same sign from one of the t-quarks, or viceversa.) For the tt Z process, the contribution in the (e, µ) channel turns out to be 3.5 times the average of the (e, e) and (µ, µ) ones, i.e. larger than expected on the basis of the charge and flavour combinatorics. The reason has to be attributed to the trilepton veto. As seen in Fig. 5, the number of events in the trilepton channel in case of the (e, e) e and (µ, µ) µ combinations are larger than those in the (e, e) µ and (µ, µ) e bins. The former affect the (e, e) and (µ, µ) bins of the dilepton analysis, while the latter affect the (e, µ) bins of the dilepton analysis. As a consequence, the contribution to the (e, µ) channel of the dilepton analysis is less suppressed than those in the (e, e) and (µ, µ) channels due to the trilepton veto. The predictions by different SMC programs, i.e. HERWIG and PYTHIA where the photon bremsstrahlung from leptons is switched off, are up to 8 % and 5 % larger than those of PYTHIA, as can be seen from the lower panel of Fig. 9. These differences have the same sign, but are smaller, than those found in case of the trilepton analysis (see the lower panel of Fig. 5 for comparison).
As for the comparison with the experimental data, we note that in the CMS technical report [2] a contribution to the number of events was assigned to the effect of charge misidentification for the leptons, in particular the electrons, and another additional contribution to the effect of non-prompt leptons, i.e. leptons not coming directly from heavy bosons decays. In our theoretical simulations the background due to charge misidentification vanishes, whereas a possible contribution of non-prompt leptons to our final results relies on the effectiveness of the isolation criteria we adopted. In this respect, even if we lack a precise estimate, it can be interesting to observe the differential distributions of the hardest isolated (anti-)leptons of each event after cuts, plotted in Fig. 10.
We see from Fig. 10.a, in case of tt W + the hardest isolated anti-lepton after cuts has a minimum p ⊥ of 50 GeV and a peak slightly above it, whereas in case of tt W − it has a minimum p ⊥ of 30 GeV without a peak. In case of the hardest isolated lepton, instead, the behaviour of tt W + and tt W − is the opposite, as can be seen in Fig. 10.b. This behaviour is compatible with cut 1) and means that the system of proposed cuts is effective in selecting prompt leptons, i.e. the selection of ( + , + ) pair in case of tt W − decay, or of ( − , − ) pair in the tt W + decay are actually suppressed by orders of magnitude, even if several leptons and anti-leptons can be present after PS, hadronization and hadron decays. In case of tt Z decays, two opposite-charge leptons are produced by Z-decays, so both ( + , + ) and ( − , − ) pairs of prompt leptons could be selected. Thus a peak above 50 GeV is present in both the lepton and the anti-lepton distributions. In all cases, the peaks slightly above 50 GeV are related to the request of having at least one (anti-)lepton with p ⊥ > 55 GeV in the selection cuts.
As examples of further distributions that can be measured in the experiment, the cumulative transverse momentum distributions of the leading and subleading lepton or anti-lepton of the ( , ) selected pairs are plotted in Fig. 11. At low p ⊥ the sum is dominated by the tt W + contribution, whereas in the high p ⊥ tail (i.e. above 300 GeV in case of the leading lepton and above 150 GeV in case of the subleading one), the contributions of tt Z and tt W + become almost equal.
In view of the searches for new physics in the dilepton channel another interesting distribution is that of the missing transverse energy, plotted in Fig. 12. In Fig. 12.a, different shapes characterize the three tt V processes. The distribution for tt Z is peaked around 30 GeV, while that for tt W ± is peaked around 50 GeV. This difference is related to the W → ν decay events selected in the dilepton analysis, that populate the peak region.
PY1/PY0 HW/PY0 Figure 11. Transverse momentum distribution of a) the leading and b) the subleading (anti)lepton of each same-sign ( , ) pair after the dilepton analysis. Predictions by PowHel + PYTHIA at √ s = 7 TeV LHC corresponding to the different tt Z, tt W + and tt W − processes are shown separately. In the lower inset the ratios between cumulative results using different SMC HERWIG and PYTHIA (HW/PY0) and between cumulative results obtained by neglecting and including photon bremsstrahlung from leptons in PYTHIA (PY1/PY0) are also shown.
The suppression in the first few bins, not present in the analogous inclusive / p ⊥ -distribution plotted in Fig. 4.b, is an effect of the set of cuts, aiming at the selection of two same-sign prompt (anti-)leptons. With this selection both the primary boson and either the t-or thē t-quark should decay leptonically, leading to a non-zero / p ⊥ . As expected, including further cuts on / p ⊥ , will enhance the relative contribution of the tt W ± process with respect to the tt Z one, and will reduce the number of observed tt V events. In particular, integrating over the cumulative / p ⊥ -distribution, plotted in Fig. 12.b, we find that a cut of / p ⊥ > 50 GeV corresponds to a reduction on the total number of events, plotted in Fig. 9, by a factor of 4 and a cut of / p ⊥ > 100 GeV to a further reduction by a similar factor. Looking forward to an analysis of data collected in the recent LHC energy upgrade, we repeated the whole analysis at √ s = 8 TeV LHC. For future reference, we list our predictions for the cross-sections after cuts at this energy for each dilepton channel, together with their sum. We found σ (e,e) = 0.907 fb, σ (e,µ) = 0.991 fb, σ (µ,µ) = 2.289 fb, σ = 4.187 fb, all with a statistical uncertainty < 5 · 10 −5 . As for differential distributions at 8 TeV, we found that their general qualitative behaviour and their shapes are similar to those already shown at 7 TeV, thus we do not present them again here. These can just be obtained by a proper rescaling factor given by the ratio of the cross-sections at 8 and 7 TeV. The LHE's are freely available at our web repository.

Conclusions
In this paper we provided predictions for tt V hadroproduction at LHC. Our NLO predictions in the tt W ± channel provide a confirmation, by a completely independent method, of those already presented by Ref.
[13] at 7, 8 and 14 TeV center-of-mass energies. In case of both tt Z and tt W ± we quote the uncertainties on the cross-sections due to scale variation at NLO. Furthermore, we provide predictions for differential distributions due to these same processes at the hadron level, thanks to the matching of the NLO computation with a SMC approach, through the POWHEG method as implemented in the PowHel framework, on the basis of the interface of the POWHEG-BOX and the HELAC-NLO event generators. In case of tt W ± these are the first predictions provided at such a level of accuracy in the literature, whereas in case of tt Z this paper can be considered a sequel to our previous ones, exploring different decay channels in the phenomenological analysis. In particular, we concentrate on the dilepton and trilepton channels, also recently studied by the CMS Collaboration. At 7 TeV our predictions turn out to be compatible with the experimental data, taking into account the slightly different selection conditions, whereas, in case of 8 TeV, where the experimental data have not yet been analyzed, we provide new predictions, both for the total and differential cross-sections, that we hope can be useful for the experimental analysis. For this purpose all LHE files with sets of several millions of events at the first radiation emission level used for the analysis presented in this paper, are freely available at our web repository: http://www.grid.kfki.hu/twiki/bin/view/DbTheory/WebHome.
In the future, when the accumulated data will reach the necessary statistics that allows for a more detailed comparison of the theory with the experiment, the inclusion of spin correlations effects and radiative corrections in top quark and heavy bosons decays, as well as the evaluation of the different backgrounds at the same level of accuracy, will be possible and indispensable. Moreover the estimate of the theoretical uncertainty will require further studies of the scale variation at the NLO and SMC levels, as well as a systematic study of the effect of different PDF sets and parameters.