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NLO QCD corrections to off-shell top-antitop production with leptonic decays at hadron colliders
Abstract
We present details of a calculation of the cross section for hadronic top-antitop production in next-to-leading order (NLO) QCD, including the decays of the top and antitop into bottom quarks and leptons. This calculation is based on matrix elements for ν
e
e+μ
−\( {{\overline{\nu}}_{\mu }}\mathrm{b}\overline{\mathrm{b}} \) production and includes all non-resonant diagrams, interferences, and off-shell effects of the top quarks. Such contributions are formally suppressed by the top-quark width and turn out to be small in the inclusive cross section. However, they can be strongly enhanced in exclusive observables that play an important role in Higgs and new-physics searches. Also non-resonant and off-shell effects due to the finite W-boson width are investigated in detail, but their impact is much smaller than naively expected. We also introduce a matching approach to improve NLO calculations involving intermediate unstable particles. Using a fixed QCD scale leads to perturbative instabilities in the high-energy tails of distributions, but an appropriate dynamical scale stabilises NLO predictions. Numerical results for the total cross section, several distributions, and asymmetries are presented for Tevatron and the LHC at 7 TeV, 8 TeV, and 14 TeV.
... On the other hand, bb initial states are neglected as they are at the per-mille level [52] and thus well within NLO scale uncertainties. The numbers of diagrams are independent of the CP-structure of the Higgs boson as long as κ HV V , κ Att , κ Htt = 0. To include Breit-Wigner propagators for the top quark and gauge bosons in a gauge invariant way, we use the complex-mass scheme [55][56][57][58]. In addition to the full off-shell case we also provide results in the NWA, i. are included when employing the NWA, the numbers of considered diagrams for the gg and qq initial states are reduced to 8 and 2, respectively, at LO. ...
... From these input parameters we calculate the top-quark width according to the formulae derived in refs. [58,90]. For the values provided above, the LO and NLO top-quark widths are given by in the NWA. ...
... Generally, in the case of tt production, p T observables constructed from the decay products of both top quarks, like for example p T miss , p T b 1 b 2 and p T e + µ − , are known to have huge K-factors in the tails, see e.g. [58,102]. At LO these observables exhibit a strong suppression of the tt cross-section above 150 GeV. ...
A bstract
Since its discovery at the Large Hadron Collider in 2012 the Higgs boson has arguably become the most famous of the Standard Model particles and many measurements have been performed in order to assess its properties. Among others, these include measurements of the Higgs boson’s $$ \mathcal{CP} $$ CP state which is predicted to be $$ \mathcal{CP} $$ CP -even. Even though a pure $$ \mathcal{CP} $$ CP -odd state has been ruled out, a possible admixture of a $$ \mathcal{CP} $$ CP -odd Higgs state has yet to be excluded. In this work we present predictions for the associated production of a leptonically decaying top quark pair and a stable Higgs boson pp → e ⁺ ν e μ − $$ \overline{\nu} $$ ν ¯ μ b $$ \overline{b} $$ b ¯ H with possible mixing between $$ \mathcal{CP} $$ CP -even and $$ \mathcal{CP} $$ CP -odd states at NLO in QCD for the LHC with $$ \sqrt{s} $$ s = 13 TeV. Finite top-quark and gauge-boson width effects as well as all double-, single- and non-resonant Feynman diagrams including their interference effects are taken into account. We compare the behaviour of the $$ \mathcal{CP} $$ CP -even, -odd and -mixed scenarios for the integrated fiducial cross-sections as well as several key differential distributions. In addition, we show that both NLO corrections and off-shell effects play an important role even at the level of integrated fiducial cross-sections and that these are further enhanced in differential distributions. Even though we focus here on the Standard Model Higgs boson, the calculations could be straightforwardly applied to models that have an extended Higgs-boson sector and predict the existence of $$ \mathcal{CP} $$ CP -odd Higgs-like particles, such as the two-Higgs-doublet model.
... On the other hand, bb initial states are neglected as they are at the per-mille level [50] and thus well within NLO scale uncertainties. The numbers of diagrams are independent of the CP-structure of the Higgs boson as long as κ HV V , κ Att , κ Htt = 0. To include Breit-Wigner propagators for the top quark and gauge bosons in a gauge invariant way, we use the complex-mass scheme [53][54][55][56]. In addition to the full off-shell case we also provide results in the NWA, i.e. the limit in which the unstable intermediate top quarks and W gauge bosons are put on-shell. ...
... From these input parameters we calculate the top-quark width according to the formulae derived in Refs. [56,88]. For the values provided above, the LO and NLO top-quark widths are given by ...
... Generally, in the case of tt production, p T observables constructed from the decay products of both top quarks, like for example p T miss , p T b 1 b 2 and p T e + µ − , are known to have huge K-factors in the tails, see e.g. [56,99]. At LO these observables exhibit a strong suppression of the tt cross-section above 150 GeV. ...
Since its discovery at the Large Hadron Collider in 2012 the Higgs boson has arguably become the most famous of the Standard Model particles and many measurements have been performed in order to assess its properties. Among others, these include measurements of the Higgs boson's ${\cal CP}$ state which is predicted to be ${\cal CP}$-even. Even though a pure ${\cal CP}$-odd state has been ruled out, a possible admixture of a ${\cal CP}$-odd Higgs state has yet to be excluded. In this work we present predictions for the associated production of a leptonically decaying top quark pair and a stable Higgs boson $p p \to e^+ \nu_e\, \mu^- \bar{\nu}_\mu\,b\bar{b}\,H$ with possible mixing between ${\cal CP}$-even and ${\cal CP}$-odd states at NLO in QCD for the LHC with $\sqrt{s} = 13$ TeV. Finite top-quark and gauge boson width effects as well as all double-, single- and non-resonant Feynman diagrams including their interference effects are taken into account. We compare the behaviour of the ${\cal CP}$-even, -odd and -mixed scenarios for the integrated fiducial cross-sections as well as several key differential distributions. In addition, we show that both NLO corrections and off-shell effects play an important role even at the level of integrated fiducial cross-sections and that these are further enhanced in differential distributions. Even though we focus here on the Standard Model Higgs boson, the calculations could be straightforwardly applied to models that have an extended Higgs-boson sector and predict the existence of ${\cal CP}$-odd Higgs-like particles, such as the two-Higgs-doublet model.
... In a first step, we study Higgs boson production in association with top quarks while keeping the Higgs boson stable (Γ H = 0). The complex-mass scheme [36][37][38][39] is used to include all off-shell effects of the top quarks and massive gauge bosons (W ± , Z) in a gauge invariant way. In particular, we consider the following process pp → e + ν e µ −ν µ bb H + X the Dyson-Schwinger off-shell iterative algorithm [40][41][42] instead of the traditional Feynman diagrams approach. ...
... A Higgs boson mass of m H = 126 GeV is used to facilitate the comparison with results from ref. [33]. Even though the current value is closer to m H = 125 GeV, our conclusions do not depend on the specific value used. 2 Furthermore, the top quark width is derived from the equations in ref. [39] using NLO corrections as calculated in ref. [81]. The top quark width is treated as a fixed parameter throughout this work. ...
... Such effects are well known and discussed (also for p T, , that is not shown here), e.g. in refs. [33,39,57], where NLO QCD calculations for top quark pair production with and without heavy bosons are presented. In ref. [92], similar findings are described for the tt production process in the di-lepton top quark decay channel at next-to-next-to-leading order (NNLO) in QCD. ...
A bstract
We report on the calculation of the next-lo-leading order QCD corrections to Higgs boson production and decay in association with top quarks. We consider leptonic decays of top quarks leading to the hadronic process pp → e ⁺ ν e μ − $$ \overline{\nu} $$ ν ¯ μ b $$ \overline{b} $$ b ¯ H ( H → X ) at the LHC with $$ \sqrt{s} $$ s = 13 TeV. All resonant as well as non-resonant Feynman diagrams, interferences and off-shell effects are included for the top quark and W gauge boson. Decays of the Higgs boson, on the other hand, are included in the narrow-width approximation. Specifically, we consider Higgs boson decays into b $$ \overline{b} $$ b ¯ , τ ⁺ τ − , γγ and e ⁺ e − e ⁺ e − . Numerical results are given at the integrated and differential fiducial level for various factorisation and renormalisation scale choices and different PDF sets. We study the main theoretical uncertainties that are associated with neglected higher order terms in the perturbative expansion and with different parametrisations of the PDFs. Furthermore, we examine the size of the off-shell effects by an explicit comparison to the calculation in the full narrow-width approximation. Finally, the impact of the contributions induced by the bottom-quark parton density is investigated.
... In a first step, we study Higgs boson production in association with top quarks while keeping the Higgs boson stable (Γ H = 0). The complex-mass scheme [25][26][27][28] is used to include all off-shell effects of the top quarks and massive gauge bosons (W ± , Z) in a gauge invariant way. In particular, we consider the following process pp → e + ν e µ −ν µ bb H + X (2.1) at NLO QCD, i.e. at O(α 3 s α 5 ). ...
... Even though the current value is closer to m H = 125 GeV, our conclusions do not depend on the specific value used. Furthermore, the top quark width is derived from the equations in Ref. [28] using NLO corrections as calculated in Ref. [70]. The top quark width is treated as a fixed parameter throughout this work. ...
... Such effects are well known and discussed (also for p T, , that is not shown here), e.g. in Refs. [22,28,46], where NLO QCD calculations for top quark pair production with and without heavy bosons are presented. In Ref. [81], similar findings are described for the tt production process in . ...
We report on the calculation of the next-lo-leading order QCD corrections to Higgs boson production and decay in association with top quarks. We consider leptonic decays of top quarks leading to the hadronic process $pp\to e^+\nu_e\, \mu^-\bar{\nu}_\mu \, b\bar{b}\,H\, (H\to X)$ at the LHC with $\sqrt{s}=13$ TeV. All resonant as well as non-resonant Feynman diagrams, interferences and off-shell effects are included for the top quark and $W$ gauge boson. Decays of the Higgs boson, on the other hand, are included in the narrow-width-approximation. Specifically, we consider Higgs boson decays into $b\bar{b}$, $\tau^+\tau^-$, $\gamma\gamma$ and $e^+e^-e^+e^-$. Numerical results are given at the integrated and differential fiducial level for various factorisation and renormalisation scale choices and different PDF sets. We study the main theoretical uncertainties that are associated with neglected higher order terms in the perturbative expansion and with different parametrisations of the PDFs. Furthermore, we examine the size of the off-shell effects by an explicit comparison to the calculation in the full narrow-width-approximation. Finally, the impact of the contributions induced by the bottom-quark parton density is investigated.
... For tt production, finite-width effects at the level of one percent have been found by comparing the offshell calculation with the narrow-top-width limit in Refs. [79][80][81]. It is instructive to perform a similar analysis for the process (2.1). ...
... It is instructive to perform a similar analysis for the process (2.1). To this end, we determine the corresponding narrow-top-width limit in LO as in Ref. [80] by a numerical extrapolation, ...
... While the corrections are of the usual size for low values of this quantity, they steadily increase to exceed 300% above 1200 GeV. Such an effect has already been observed for top-pair production [80]. The quality of the tt-DPA is at the level of −3% at LO around the maximum of the distribution near 500 GeV. ...
In this article, we report on the computation of the next-to-leading order (NLO) QCD corrections to pp→μ−ν¯μe+νeb¯bb¯b at the LHC, which is an irreducible background to pp→tt¯H(→bb¯). This is the first time that a full NLO computation for a 2→8 process with 6 external strongly interacting partons is made public. No approximations are used, and all off-shell and interference effects are taken into account. Cross sections and differential distributions from the full computation are compared to results obtained by using a double-pole approximation for the top quarks. The difference between the full calculation and the one using the double-pole approximation is in general below 5% but can reach 10% in some regions of phase space.
... Advances and automation in one-loop calculations eventually made it possible to account at NLO for both off-shell effects and non-doubly resonant contributions (i.e. dilepton final states not necessarily mediated by a pair of top quarks) [11,12,[14][15][16][17][18]. ...
... Although the ratio Γ W /m W is larger than the corresponding one for the top quark, it was shown in refs. [11,14] that the effects beyond NWA for the W boson in tt production are very small. ...
... Since our calculation is performed in the NWA approximation one may worry that NWA-breaking effects are affecting this bin. NLO calculations of tt production including all corrections beyond NWA exist [11,12,[14][15][16][17], however, we have not been able to find setting similar to ours that has estimated the size of the beyond-NWA corrections. Similar setup exists [75] for the related [76] process pp → ttγ. ...
A bstract
We calculate a comprehensive set of spin correlations and differential distributions in top-quark pair production and decay to dilepton final states. Our calculation is performed in the Narrow Width Approximation. This is the first time such a complete study is performed at next-to-next-to leading order in QCD. Both inclusive and fiducial distributions are presented and analyzed. Good agreement between NNLO QCD predictions and data is found. We demonstrate that it is possible to perform high-precision comparisons of fixed-order calculations with fiducial-level data. Subtleties of the top quark definition are raised and clarified. Some of those are found to have a very significant impact on top-quark pair production at absolute threshold.
... refs. [72][73][74][75][76], which consistently describes off-shell top-quark contributions by the Breit-Wigner distribution. All matrix elements are evaluated using the complex top-quark mass, µ 2 t = m 2 t − im t Γ t . ...
... The top-quark width is calculated according to ref. [75] and is treated as a fixed parameter throughout this work. Moreover, its value corresponds to a fixed scale setting of µ 0 = m t . 1 In detail, we made comparisons with the following LO processes pp → e + νe µ −ν µ e + νe bb j, pp → e + νe e −ν e e + νe bb j and pp → e + νe e −ν e µ + νµ bb j. ...
A bstract
In view of the persisting tension between theoretical predictions and the LHC data for the pp → $$ t\overline{t}W $$ t t ¯ W ± production process, we present the state-of-the-art full off-shell NLO QCD result for pp → $$ t\overline{t}W $$ t t ¯ W ⁺ j + X . We concentrate on the multi-lepton decay channel at the LHC with $$ \sqrt{s} $$ s = 13 TeV. In our calculation off-shell top quarks and gauge bosons are described by Breit-Wigner propagators, furthermore, double-, single- as well as non-resonant top-quark contributions along with all interference effects are consistently incorporated at the matrix element level. We present results for both integrated and differential fiducial cross sections for various renormalisation and factorisation scale settings and different PDF sets. With a fairly inclusive choice of cuts and regardless of the scale and PDF choice, non-flat differential $$ \mathcal{K} $$ K -factors are obtained for many observables that we have examined. Since from an experimental point of view, both processes pp → $$ t\overline{t}W $$ t t ¯ W ± j + X and pp → $$ t\overline{t}W $$ t t ¯ W ± + X consist of similar final states we investigate the effect of additional jet activity on the integrated and differential fiducial cross sections. For this purpose, the normalised differential distributions for pp → e ⁺ ν e μ − $$ \overline{\nu} $$ ν ¯ μ τ ⁺ ν τ $$ b\overline{b} $$ b b ¯ j + X and pp → e ⁺ ν e μ − $$ \overline{\nu} $$ ν ¯ μ τ ⁺ ν τ $$ b\overline{b} $$ b b ¯ + X are compared. The theoretical results for the latter process are also recalculated.
... The LO and NLO top-quark widths are calculated based on refs. [78,79] and their numerical values are given by ...
... refs. [40,79,[83][84][85]. They are also present for similar observables like p miss ...
A bstract
We report on the computation of NLO QCD corrections to top-quark pair production in association with two photons at the LHC. Higher-order effects and photon bremsstrahlung are taken into account in the production and decays of the top-quark pair. Top-quark and W -boson decays are treated in the Narrow Width Approximation conserving spin correlations up to NLO in QCD. This is the first time that the complete set of NLO QCD corrections to the $$ pp\to t\overline{t}\gamma \gamma $$ pp → t t ¯ γγ process including top-quark decays is calculated. We present results at the integrated and differential cross-section level in the di-lepton and lepton + jet channel. In addition, we investigate the effect of photon bremsstrahlung in $$ t\overline{t} $$ t t ¯ production and top-quark decays, as well as the mixed contribution. The latter contribution, in which two photons occur simultaneously in the production and decay of the $$ t\overline{t} $$ t t ¯ pair, proved to be significant at both the integrated and differential cross-section level.
... The LO and NLO top-quark widths are calculated based on Refs. [70,71] and their numerical values are given by ...
... Refs. [32,71,[75][76][77]. They are also present for similar observables like p miss T = |⃗ p T, ν ℓ + ⃗ p T,ν ℓ | or p T, ℓ + ℓ − . ...
We report on the computation of NLO QCD corrections to top-quark pair production in association with two photons at the LHC. Higher-order effects and photon bremsstrahlung are taken into account in the production and decays of the top-quark pair. Top-quark and $W$-boson decays are treated in the Narrow Width Approximation conserving spin correlations up to NLO in QCD. This is the first time that the complete set of NLO QCD corrections to the $pp \to t\bar{t}\gamma\gamma$ process including top-quark decays is calculated. We present results at the integrated and differential cross-section level in the di-lepton and lepton $+$ jet channel. In addition, we investigate the effect of photon bremsstrahlung in $t\bar{t}$ production and top-quark decays, as well as the mixed contribution. The latter contribution, in which two photons occur simultaneously in the production and decay of the $t\bar{t}$ pair, proved to be significant at both the integrated and differential cross-section level.
... Refs. [72][73][74][75][76], which consistently describes off-shell top-quark contributions by the Breit-Wigner distribution. All matrix elements are evaluated using the complex top-quark mass, ...
... All other leptons and quarks (including the τ lepton and the b quark) are treated as massless. The top-quark width is calculated according to Ref. [75] and is treated as a fixed parameter throughout this work. Moreover, its value corresponds to a fixed scale setting of µ 0 = m t . ...
In view of the persisting tension between theoretical predictions and the LHC data for the $pp \to t\bar{t}W^\pm$ production process, we present the state-of-the-art full off-shell NLO QCD result for $pp \to t\bar{t}W^+\, j+X$. We concentrate on the multi-lepton decay channel at the LHC with $\sqrt{s}= 13$ TeV. In our calculation off-shell top quarks and gauge bosons are described by Breit-Wigner propagators, furthermore, double-, single- as well as non-resonant top-quark contributions along with all interference effects are consistently incorporated at the matrix element level. We present results for both integrated and differential fiducial cross sections for various renormalisation and factorisation scale settings and different PDF sets. With a fairly inclusive choice of cuts and regardless of the scale and PDF choice, non-flat differential ${\cal K}$-factors are obtained for many observables that we have examined. Since from an experimental point of view, both processes $pp \to t\bar{t}W^\pm j+X$ and $pp\to t\bar{t}W^\pm +X$ consist of similar final states we investigate the effect of additional jet activity on the integrated and differential fiducial cross sections. For this purpose, the normalised differential distributions for $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} \,j+X$ and $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} +X$ are compared. The theoretical results for the latter process are recalculated from scratch.
... As a consequence, more events are moved from the resonance or above to below the resonance owing to final-state radiation that is not reconstructed with the decay products of the top/antitop quark forming hence a large radiative tail (see, for instance, Refs. [33,67]). In the case of the hadronically decaying top quark, the effect is so large that the NLO cross section becomes negative above the resonance. ...
... A radiative tail also appears in the invariant-mass distribution of the two hardest light jets (Fig. 5c), which at LO reconstruct a W boson. Again, the effects are extremely large with K factors reaching ten below the resonance. The distribution in the invariant mass of the system formed by the reconstructed bottom quark from the leptonically decaying top quark and the antimuon (Fig. 5d) has been found to be very sensitive to the top-quark mass as it possesses an onshell edge at M 2 [67,68]. While the relative corrections are flat in the on-shell region, they strongly increase above the on-shell edge. ...
The study of top-quark properties will be a central aspect of the physics programme of any future lepton collider. In this article, we investigate the production of top-quark pairs in the semi-leptonic decay channel in $${\textrm{e}}^{+}\textrm{e}^{-}$$ e + e - collisions, whose experimental signature is one charged lepton, jets, and missing energy. We present for the first time fiducial cross sections and differential distributions at next-to-leading-order accuracy in QCD for the full off-shell process. We find that the QCD corrections for the considered process are strongly dependent on the beam energies and range from few per cent up to more than $$100\%$$ 100 % (near threshold and above $$1\,\text {TeV} $$ 1 TeV ). We focus, in particular, on two scenarios: one close to threshold ( $$365\,\text {GeV} $$ 365 GeV ), dominated by top-pair production, and one at the TeV scale ( $$1.5\,\text {TeV} $$ 1.5 TeV ), for which irreducible-background contributions become relevant. An assessment of polarised-beam effects is also provided.
... A similar procedure applies in the NWA case, where in addition the following limit is taken Γ W =m W → 0 as shown in Ref. [59]. In this case we get ...
... This can be done by rescaling the following couplings t − W − b and W − l − ν l by several large factors, as described in Refs. [59,76]. This approach should mimic the Γ t → 0 limit when the scattering cross section factorises into on-shell production and decay. ...
We investigate full off-shell effects in tt¯bb¯ production in the dilepton channel at the LHC with the center-of-mass energy s=13 TeV. Specifically, we compute next-to-leading-order (NLO) QCD corrections to the pp→e+νeμ−ν¯μbb¯bb¯+X process and provide a prescription for b-jet identification to distinguish prompt b jets from b jets originating from the decay of the top quarks. As an important irreducible background to pp→tt¯H(H→bb¯), tt¯ production in association with two prompt b jets is a primary source of uncertainty in the measurement of tt¯H(H→bb¯). In quantifying full off-shell effects, we perform comparisons between the state-of-the-art full off-shell computation and the calculation in the narrow width approximation. The former includes all double-, single- and nonresonant Feynman diagrams, interferences as well as finite-width effects of the top quarks and W gauge bosons. The latter restricts the unstable top quarks and W gauge bosons to on-shell states and includes for the first time NLO QCD corrections to both production and decays. We observe that full off-shell effects are subdominant compared to the scale uncertainties for the integrated fiducial cross section and for the majority of differential observables in the phase-space regions that we investigated. However, for a number of observables related to beyond the Standard Model searches, full off-shell effects are significant. Furthermore, with our b-jet labeling prescription, the prompt b jets and the b jets from top-quark decays can be successfully disentangled.
... We note here, that the state-of-the art theoretical predictions at NLO in QCD with the complete top quark off-shell effects included are also available for other processes at the LHC. Such effects, for example, have been incorporated for pp → tt [31][32][33][34], pp → ttj [35,36], pp → ttH [37], pp → ttγ [38] and for ttZ(Z → ν ν ) [39]. Very recently they have also been incorporated for the pp → ttbb process [40]. ...
... The number of active flavours is set to N F = 5. We employ the following SM input parameters [33]. The top quark width is treated as a fixed parameter throughout this work. ...
Recent discrepancies between theoretical predictions and experimental data in multi-lepton plus $b$-jets analyses for the $t\bar{t}W^\pm$ process, as reported by the ATLAS collaboration, have indicated that more accurate theoretical predictions and high precision observables are needed to constrain numerous new physics scenarios in this channel. To this end we employ the NLO QCD computations with the full off-shell top quark effects included to provide theoretical predictions for the ${\cal R}=\sigma_{t\bar{t}W^+}/\sigma_{t\bar{t}W^-}$ cross section ratio at the LHC with $\sqrt{s}=13$ TeV. Depending on the transverse momentum cut on the $b$-jet we obtain $1\% -2 \%$ theoretical precision on ${\cal R}$, which should help to shed some light on new physics effects that can reveal themselves only once sufficiently precise Standard Model theoretical predictions are available. Furthermore, triggered by these discrepancies we reexamine the top quark charge asymmetry and the charge asymmetries of the top quark decay products in the $t\bar{t}W^\pm$ production process. In the case of charge asymmetries, that are uniquely sensitive to the chiral nature of possible new physics in this channel, theoretical uncertainties below $15\%$ have been obtained. Additionally, for both cases the impact of the top quark modelling is scrutinised by the explicit comparison with the predictions in the narrow-width approximation.
... Once this contribution is also taken into account the number of diagrams increases to 564. To regularise intermediate top-quark resonances in a gauge-invariant way we employ the complex-mass scheme [36][37][38][39], which consistently describes off-shell top quark contributions by the Breit-Wigner distribution. All matrix elements are evaluated 1 We shall concentrate here on the ttW + process, however, a similar description applies to ttW − production. ...
... The LO and NLO top quark widths for the off-shell case are calculated according to formulae from refs. [39,72,73] and are given by ...
Recent measurements of the pp → \( t\overline{t}{W}^{\pm } \) process in multi-lepton final states, as performed by the ATLAS collaboration in the context of the Higgs boson studies in the \( t\overline{t}H \) channel, have shown discrepancies between theoretical predictions and experimental data. Such discrepancies have been observed both in the overall normalisation as well as in the modelling of the \( t\overline{t}{W}^{\pm } \) process. With the goal of understanding and resolving the modelling issues within the SM \( t\overline{t}{W}^{\pm } \) process we report on the state-of-the-art NLO QCD computation for this process. Specifically, we calculate higher-order corrections to the \( {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }{e}^{+}{\nu}_eb\overline{b} \) and \( {e}^{-}{\overline{\nu}}_e{\mu}^{+}{\nu}_{\mu }{e}^{-}{\overline{\nu}}_eb\overline{b} \) final state at the LHC with \( \sqrt{s} \) = 13 TeV. In the computation off-shell top quarks are described by Breit-Wigner propagators, furthermore, double-, single- as well as non-resonant top-quark contributions along with all interference effects are consistently incorporated at the matrix element level. Results at NLO QCD accuracy are presented in the form of fiducial integrated and differential cross sections for two selected renormalisation and factorisation scale choices and three different PDF sets. The impact of the top quark off-shell effects on the \( t\overline{t}{W}^{\pm } \) cross section is also examined by an explicit comparison to the narrow-width approximation.A preprint version of the article is available at ArXiv.
... However, both methods introduce theoretical uncertainties and violate gauge invariance. The natural approach is instead to not view single-top and top-pair production as two separable channels and to consider only the fully decayed final state [11][12][13]. In addition to being theoretically robust, this technique matches the reality of performing an experimental measurement, where the Eur. ...
... The subtracted real-emission contributions (RS) were calculated using 10 7 phase-space points. The Born, virtual corrections and integrated subtraction terms (BVI) were calculated using 3 · 10 6 phase-space-points (13) 148.07 (9) 150.55 (9) 230.0 (2) 226.0 (2) 0.15371 (14) 0.15366 (14) 147.55 (9) 147.70 (9) 220.5 (4) 220.7 (2) In the collinear regions, y gb → 0 or y gb → 0, while in the soft limit y gb y gb → 0. We construct ensembles of phasespace points that we refer to as phase-space trajectories as follows: random phase-space points are sampled according to the real-emission cross section in the narrow-width approximation, while requesting three identified jets according to the Durham jet algorithm [30]. For each phase-space point, the kinematical configuration is scaled according to the algorithm described in Appendix A in order to obtain a sequence of points that approach the soft or collinear limit. ...
We present a technique for infrared subtraction in next-to-leading order QCD calculations that preserves the virtuality of resonant propagators. The approach is based on the pseudo-dipole subtraction method proposed by Catani and Seymour in the context of identified particle production. As the first applications, we compute the \(e^+e^- \rightarrow W^+W^-b{\bar{b}}\) and \(pp \rightarrow W^+W^-j_bj_b\) cross-section, which are both dominated by top-quark pair production above the threshold. We compare the efficiency of our approach with a calculation performed using the standard dipole subtraction technique.
... However, given the complex analysis techniques, a precision prediction of the total tth rate falls short of the experimental requirements. Instead, we need a precise prediction of all kinematic distributions for the signal as well as for the irreducible background [480][481][482]. This includes the boosted regime, where we expect any tt analysis to collect most of its significance [483]. ...
... This includes the boosted regime, where we expect any tt analysis to collect most of its significance [483]. Corresponding results are available to NLO in QCD [481] and including electroweak corrections [473]. ...
We review the theoretical underpinning of the Higgs mechanism of electroweak symmetry breaking and the experimental status of Higgs measurements from a pedagogical perspective. The possibilities and motivations for new physics in the symmetry breaking sector are discussed along with current measurements. A focus is on the implications of measurements in the Higgs sector for theoretical insights into extensions of the Standard Model. We also discuss of future prospects for Higgs physics and new analysis techniques.
... Conversely, the LO 2 shows a dip in that region, as a consequence of the negative bottom-interference contributions, which overcompensate the resonance peak of the LO 2 γg term leading to a JHEP09(2023)072 slightly negative LO 2 contribution near the nominal top mass. Our results for the NLO 1 corrections are in line with the results for this observable found in tt [75] and ttW ± [40] production. The QCD corrections are negative (around −40%) on the peak, while they become positive in regions where the antitop quark is off shell: for regions of a reconstructed antitop mass above the peak, i.e. ...
A bstract
Measuring precisely top-pair-associated processes at hadron colliders will become possible with the upcoming LHC running stages. The increased data statistics will especially enable differential measurements leading to an improved characterisation of such processes. Aiming at a consistent data-theory comparison, precise Standard-Model predictions are needed, including higher-order corrections and full off-shell effects. In this work we present NLO-accurate predictions for the production and decay of a top-antitop pair in association with a Z boson at the LHC, in the multi-lepton decay channel. The complete set of LO contributions and NLO corrections of EW and QCD origin is included. The calculation is based on full matrix elements, computed with all resonant and non-resonant contributions, complete spin correlations and interference effects. Integrated and differential cross-sections are presented for a realistic fiducial setup.
... For the LO and NLO top-quark width, based on Refs. [57,58], we use the following values: ...
We report on the calculation of the next-to-leading order (NLO) QCD corrections to top quark pair production in association with two hard jets at the LHC. We take into account higher-order effects in both the production and decays of the top-quark pair. The latter are treated in the narrow width approximation and tt¯ spin correlations are preserved throughout the calculation. This is the first time that such a complete study for this process is conducted at NLO in QCD. We present results for fiducial cross sections at the integrated and differential level. Furthermore, we investigate kinematic properties of the additional light jets and their distribution in the pp→tt¯jj process. We examine jets in production and top-quark decays as well as the mixed contribution, where the two hardest non-b jets are present simultaneously in the production and decay processes.
... While for the full calculation a dynamical scale (H T ) was used, a static scale with µ R = µ F = m t was used for the N W A and N W A P rod approximations. It is well known [1,2,73] that scale variations can lead to sizable effects on the extracted top-quark mass. In addition, the findings of ref. [72] are not directly applicable to the experimental analyses as the experimental approach taken by ATLAS and CMS is rather different from the procedure applied in ref. [72]. ...
A bstract
We present phenomenological results for $$ t\overline{t}j $$ t t ¯ j + X production at the Large Hadron Collider, of interest for designing forthcoming experimental analyses of this process. We focus on those cases where the $$ t\overline{t}j $$ t t ¯ j + X process is considered as a signal. We discuss present theoretical uncertainties and the dependence on relevant input parameters entering the computation. For the $$ \mathcal{R} $$ R distribution, which depends on the invariant mass of the $$ t\overline{t}j $$ t t ¯ j -system, we present reference predictions in the on-shell, $$ \overline{\mathrm{MS}} $$ MS ¯ and MSR top-quark mass renormalization schemes, applying the latter scheme to this process for the first time. Our conclusions are particularly interesting for those analyses aiming at extracting the top-quark mass from cross-section measurements.
... narrow-width approximation [69,70]), full off-shell effects have been studied extensively at the NLO order [71][72][73][74], and electroweak (EW) corrections have been computed up to next-to-leading order (NLO) [75][76][77][78][79]. In certain kinematic regimes, a reliable perturbative description requires the all-order resummation of large logarithmic corrections [80][81][82][83][84][85][86][87]. ...
A bstract
We consider the production of a pair of heavy quarks and illustrate the derivation of the M i NNLOPS method to match next-to-next-to-leading order calculations with parton showers (NNLO+PS) for this class of processes. As a first application, we construct an event generator for the fully differential simulation of hadronic top-quark pair production at NNLO+PS and discuss all details of its implementation in a parton shower Monte Carlo framework. We present new phenomenological results for the Large Hadron Collider obtained by including the tree-level decays of the top quarks, while accounting for spin-correlation effects. A comprehensive comparison to LHC measurements shows an excellent description of experimental data across multiple hadronic and leptonic particle-level observables. The computer code is available for download within the P owheg -B ox .
... Therefore, the top-quark decay width is calculated at NLO QCD accuracy including off-shell W bosons according to formulas given in Refs. [56][57][58], which for our study corresponds to ...
In light of recent discrepancies between the modeling of tt¯W± signatures and measurements reported by the LHC experimental collaborations, we investigate in detail theoretical uncertainties for multilepton signatures. We compare results from the state-of-the-art full off-shell calculation and its narrow-width approximation to results obtained from the on-shell tt¯W± calculation, with approximate spin correlations in top-quark and W decays, matched to parton showers. In the former case double-, single-, and nonresonant contributions together with interference effects are taken into account, while the latter two cases are only based on the double-resonant top-quark contributions. The comparison is performed for the LHC at s=13 TeV for which we study separately the multilepton signatures as predicted from the dominant next-to-leading-order (NLO) contributions at the perturbative orders O(αs3α6) and O(αsα8). Furthermore, we combine both contributions and propose a simple way to approximately incorporate the full off-shell effects in the NLO computation of on-shell pp→tt¯W± matched to parton showers.
... The crucial role of top-quark pair production for the precision physics programme of the LHC has motivated a significant progress in the associated theoretical calculations. Specifically, fixed-order computations of the perturbative expansion in the strong coupling constant α s are known up to NNLO [60][61][62][63][64][65][66][67][68] (also including the top-quark decays in the narrow-width approximation [69,70]), full off-shell effects have been studied extensively at the NLO order [71][72][73][74], and electroweak (EW) corrections have been computed up to next-to-leading order (NLO) [75][76][77][78][79]. In certain kinematic regimes, a reliable perturbative description requires the all-order resummation of large logarithmic corrections [80][81][82][83][84][85][86][87]. ...
We consider the production of a pair of heavy quarks and illustrate the derivation of the MiNNLO method to match next-to-next-to-leading order calculations with parton showers (NNLO+PS) for this class of processes. As a first application, we construct an event generator for the fully differential simulation of hadronic top-quark pair production at NNLO+PS and discuss all details of its implementation in a parton shower Monte Carlo framework. We present new phenomenological results for the Large Hadron Collider obtained by including the tree-level decays of the top quarks, while accounting for spin-correlation effects. A comprehensive comparison to LHC measurements shows an excellent description of experimental data across multiple hadronic and leptonic particle-level observables. The computer code is available for download within the POWHEG-BOX.
... The phase-space integration is performed and optimised with the help of Parni [33] and Kaleu [34]. The produced top quarks are unstable particles, thus, the inclusion of their decays is performed in the complex-mass scheme [35][36][37][38]. It fully respects gauge invariance and is straightforward to apply. ...
A bstract
We report on the calculation of the next-to-leading order QCD corrections to the production of a $$ t\overline{t} $$ t t ¯ pair in association with two heavy-flavour jets. We concentrate on the di-lepton $$ t\overline{t} $$ t t ¯ decay channel at the LHC with $$ \sqrt{s} $$ s = 13 TeV. The computation is based on pp → e ⁺ ν e μ − $$ \overline{\nu} $$ ν ¯ μ $$ b\overline{b}b\overline{b} $$ b b ¯ b b ¯ matrix elements and includes all resonant and non-resonant diagrams, interferences and off-shell effects of the top quark and the W gauge boson. As it is customary for such studies, results are presented in the form of inclusive and differential fiducial cross sections. We extensively investigate the dependence of our results upon variation of renormalisation and factorisation scales and parton distribution functions in the quest for an accurate estimate of the theoretical uncertainties. We additionally study the impact of the contributions induced by the bottom-quark parton density. Results presented here are particularly relevant for measurements of $$ t\overline{t}H $$ t t ¯ H ( H → $$ b\overline{b} $$ b b ¯ ) and the determination of the Higgs coupling to the top quark. In addition, they might be used for precise measurements of the top-quark fiducial cross sections and to investigate top-quark decay modelling at the LHC.
... The phase-space integration is performed and optimised with the help of Parni [33] and Kaleu [34]. The produced top quarks are unstable particles, thus, the inclusion of their decays is performed in the complex-mass scheme [35][36][37][38]. It fully respects gauge invariance and is straightforward to apply. ...
We report on the calculation of the next-to-leading order QCD corrections to the production of a $t\bar{t}$ pair in association with two heavy-flavour jets. We concentrate on the di-lepton $t\bar{t}$ decay channel at the LHC with $\sqrt{s}=13$ TeV. The computation is based on $pp \to e^+ \nu_e\, \mu^-\bar{\nu}_\mu\, b\bar{b} \,b\bar{b}$ matrix elements and includes all resonant and non-resonant diagrams, interferences and off-shell effects of the top quark and the $W$ gauge boson. As it is customary for such studies, results are presented in the form of inclusive and differential fiducial cross sections. We extensively investigate the dependence of our results upon variation of renormalisation and factorisation scales and parton distribution functions in the quest for an accurate estimate of the theoretical uncertainties. We additionally study the impact of the contributions induced by the bottom-quark parton density. Results presented here are particularly relevant for measurements of $t\bar{t}H(H\to b\bar{b})$ and the determination of the Higgs coupling to the top quark. In addition, they might be used for precise measurements of the top-quark fiducial cross sections and to investigate top-quark decay modelling at the LHC.
... One can't remove those top resonant diagrams as it will affect the gauge invariance and we have checked that the interference between resonant and non-resonant diagrams coming from the off-shell region is large which will again ruin the perturbative computations. There are several techniques to remove these on-shell contributions safely [26][27][28][29]. One can also restrict resonant top momenta out of the on-shell region and can have contribution only from the off-shell region. ...
With the standard model working well in describing the collider data, the focus is now on determining the standard model parameters as well as for any hint of deviation. In particular, the determination of the couplings of the Higgs boson with itself and with other particles of the model is important to better understand the electroweak symmetry breaking sector of the model. In this letter, we look at the process $pp \to WWH$, in particular through the fusion of bottom quarks. Due to the non-negligible coupling of the Higgs boson with the bottom quarks, there is a dependence on the $WWHH$ coupling in this process. This sub-process receives largest contribution when the $W$ bosons are longitudinally polarized. We compute one-loop QCD corrections to various final states with polarized $W$ bosons. We find that the corrections to the final state with the longitudinally polarized $W$ bosons are large. It is shown that the measurement of the polarization of the $W$ bosons can be used as a tool to probe the $WWHH$ coupling in this process. We also examine the effect of varying $WWHH$ coupling in the $\kappa$-framework.
... The relative corrections are more moderate for the antitop mass (≈ 70%) in the same region owing to the absence of the reconstruction ambiguity which affects the top quark in the considered process. The general features of the correction to this distribution are similar as for top-antitop production [74]. ...
A bstract
We present results of a computation of NLO QCD corrections to the production of an off-shell top-antitop pair in association with an off-shell W ⁺ boson in proton-proton collisions. As the calculation is based on the full matrix elements for the process $$ \mathrm{pp}\to {\mathrm{e}}^{+}{v}_{\mathrm{e}}{\mu}^{-}{\overline{v}}_{\mu }{\tau}^{+}{v}_{\tau}\mathrm{b}\overline{\mathrm{b}} $$ pp → e + v e μ − v ¯ μ τ + v τ b b ¯ , all off-shell, spin-correlation, and interference effects are included. The NLO QCD corrections are about 20% for the integrated cross-section. Using a dynamical scale, the corrections to most distributions are at the same level, while some distributions show much larger K -factors in suppressed regions of phase space. We have performed a second calculation based on a double-pole approximation. While the corresponding results agree with the full calculation within few per cent for integrated cross-sections, the discrepancy can reach 10% and more in regions of phase space that are not dominated by top-antitop production. As a consequence, on-shell calculations should only be trusted to this level of accuracy.
... The relative corrections are more moderate for the antitop mass (≈ 70%) in the same region owing to the absence of the reconstruction ambiguity which affects the top quark in the considered process. The general features of the correction to this distribution are similar as for top-antitop production [74]. As already seen in Fig. 12, not all distributions receive NLO K-factors that are close to the value of 1.25 for the fiducial cross-section. ...
We present results of a computation of NLO QCD corrections to the production of an off-shell top--antitop pair in association with an off-shell $\text{W}^+$ boson in proton--proton collisions. As the calculation is based on the full matrix elements for the process $\text{p}\text{p}\to {\text{e}}^+\nu_{\text{e}}\,\mu^-\bar{\nu}_\mu\,\tau^+\nu_\tau\,{\text{b}}\,\bar{\text{b}}$, all off-shell, spin-correlation, and interference effects are included. The NLO QCD corrections are about $20\%$ for the integrated cross-section. Using a dynamical scale, the corrections to most distributions are at the same level, while some distributions show much larger $K$-factors in suppressed regions of phase space. We have performed a second calculation based on a double-pole approximation. While the corresponding results agree with the full calculation within few per cent for integrated cross-sections, the discrepancy can reach $10\%$ and more in regions of phase space that are not dominated by top--antitop production. As a consequence, on-shell calculations should only be trusted to this level of accuracy.
... [24][25][26][27][28][29][30][31] up to next-to-next-to-leading logarithmic (NNLL) level, and studies that go beyond the narrow width approximation have been presented in refs. [32][33][34][35][36][37] through higher orders. Taken all together, a picture arises in which the main top quark dynamics can be predicted at the few percent level, from threshold up to highest energies. ...
We calculate the (α) weak corrections to top quark pair production at the LHC and include anomalous electroweak interactions from dimension-six operators. The loop calculation and renormalization are consistently done within the Standard Model Effective Field Theory. Sensitivity to the involved operators is exposed through the virtual corrections, which receive enhancement from electroweak Sudakov logarithms. We investigate the prospects of using this feature for probing New Physics at the LHC that so far has only been studied in final states with on-shell sensitivity such as \( t\overline{t} \) + Z or t → bW. We find that the large \( t\overline{t} \) production rate and the excellent perturbative control allow compensating the loop suppression and yield remarkably strong constraints that are competitive with those from \( t\overline{t} \) + Z.A preprint version of the article is available at ArXiv.
... The top quark width, as calculated from [73][74][75], is taken to be 1.06 Table 1. Integrated cross sections for the pp → e + ν e µ −ν µ bbγ + X production process at the LHC with √ s = 13 TeV. ...
A bstract
We present a comparative study of various approaches for modelling of the $$ {e}^{+}{v}_e{\mu}^{-}{\overline{v}}_{\mu }b\overline{b}\gamma $$ e + v e μ − v ¯ μ b b ¯ γ final state in $$ t\overline{t}\gamma $$ t t ¯ γ production at the LHC. Working at the NLO in QCD we compare the fully realistic description of the top quark decay chain with the one provided by the narrow-width-approximation. The former approach comprises all double, single and non-resonant diagrams, interferences, and off-shell effects of the top quarks. The latter incorporates only double resonant contributions and restricts the unstable top quarks to on-shell states. We confirm that for the integrated cross sections the finite top quark width effects are small and of the order of $$ \mathcal{O}\left({\Gamma}_t/{m}_t\right) $$ O Γ t / m t . We show, however, that they are strongly enhanced for more exclusive observables. In addition, we investigate fractions of events where the photon is radiated either in the production or in the decay stage. We find that large fraction of isolated photons comes from radiative decays of top quarks. Based on our findings, selection criteria might be developed to reduce such contributions, that constitute a background for the measurement of the anomalous couplings in the $$ t\overline{t}\upgamma $$ t t ¯ γ vertex.
... The top quark width, as calculated from [69][70][71], is taken to be ...
We present a comparative study of various approaches for modelling of the $e^+ \nu_e \mu^- \bar{\nu}_\mu b\bar{b} \gamma$ final state in $t\bar{t}\gamma$ production at the LHC. Working at the NLO in QCD we compare the fully realistic description of the top quark decay chain with the one provided by the narrow-width-approximation. The former approach comprises all double, single and non-resonant diagrams, interferences, and off-shell effects of the top quarks. The latter incorporates only double resonant contributions and restricts the unstable top quarks to on-shell states. We confirm that for the integrated cross sections the finite top quark width effects are small and of the order of ${\cal O}(\Gamma_t/m_t)$. We show, however, that they are strongly enhanced for more exclusive observables. In addition, we investigate fractions of events where the photon is radiated either in the production or in the decay stage. We find that large fraction of isolated photons comes from radiative decays of top quarks. Based on our findings, selection criteria might be developed to reduce such contributions, that constitute a background for the measurement of the anomalous couplings in the $t\bar{t}\gamma$ vertex.
... [24][25][26][27][28][29][30][31] up to next-to-next-to-leading logarithmic (NNLL) level, and studies that go beyond the narrow width approximation have been presented in Refs. [32][33][34][35][36][37] through higher orders. Taken all together, a picture arises in which the main top quark dynamics can be predicted at the few percent level, from threshold up to highest energies. ...
We calculate the $\mathcal{O}(\alpha)$ weak corrections to top quark pair production at the LHC and include anomalous electroweak interactions from dimension-six operators. The loop calculation and renormalization are consistently done within the Standard Model Effective Field Theory. Sensitivity to the involved operators is exposed through the virtual corrections, which receive enhancement from electroweak Sudakov logarithms. We investigate the prospects of using this feature for probing New Physics at the LHC that so far has only been studied in final states with on-shell sensitivity such as $t\bar{t}+Z$ or $t \to b W$. We find that the large $t\bar{t}$ production rate and the excellent perturbative control allow compensating the loop suppression and yield remarkably strong constraints that are competitive with those from $t\bar{t}+Z$.
... Phase space integration is performed and optimised with the help of Parni [27] and Kaleu [28]. Since the produced top quarks are unstable particles, the inclusion of the decays is performed in the complex mass scheme [29][30][31][32]. It fully respects gauge invariance and is straightforward to apply. ...
Triggered by ongoing dark matter searches in the top quark sector at the Large Hadron Collider we report on the calculation of the next-to-leading order QCD corrections to the Standard Model process pp → t\( \overline{t} \) + Z (Z → νℓ\( \overline{v} \)ℓ). This calculation is based on matrix elements for \( {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }b\overline{b}\kern0.33em {\nu}_{\tau }{\overline{\nu}}_{\tau } \) production and includes all non-resonant diagrams, interferences, and off-shell effects of the top quarks. Non-resonant and off-shell effects due to the finite W -boson width are also consistently taken into account. As it is common for such studies, we present results for both integrated and differential cross sections for a few renormalisation and factorisation scale choices and three different parton distribution functions. Already with the fairly inclusive cut selection and independently of the scale choice and the parton distribution function non-flat differential \( \mathcal{K} \) -factors are obtained for \( {p}_T^{miss} \), ∆𝜙ℓℓ, ∆𝒴ℓℓ, cos θℓℓ, HT,\( {H}_T^{\prime } \) observables that are relevant for new physics searches. Good theoretical control over the Standard Model background is a fundamental prerequisite for a correct interpretation of possible signals of new physics that may arise in this channel. Thus, these observables need to be carefully reexamined in the presence of more exclusive cuts before any realistic strategies for the detection of new physics signal can be further developed. Since from the experimental point of view both t\( \overline{t} \) and t\( \overline{t} \) + Z (Z → νℓ\( \overline{v} \)ℓ) comprise the same final states, we additionally study the impact of the enlarged missing transverse momentum on various differential cross section distributions. To this end normalised differential distributions for pp →\( {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }b\overline{b}\kern0.33em {\nu}_{\tau }{\overline{\nu}}_{\tau } \) and pp →\( {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }b\overline{b} \) are compared.
... Conventionally, in processes with a single hard scale Q, one chooses μ R ¼ Q on dimensional grounds. Although not essential for the goals of the present work, we would like to mention that more refined arguments for choosing this scale have been given in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Such arguments tend to modify the choice μ R ¼ Q by a factor of Oð1Þ and are especially relevant for observables with several kinematic scales. ...
In any calculation in perturbative quantum chromodynamics (QCD) a choice needs to be made for the unphysical renormalization scale, μR. The Brodsky-Lepage-Mackenzie/principle of maximum conformality (BLM/PMC) scale-setting procedure is one proposed method for selecting this scale. In this work we identify three ambiguities in the BLM/PMC procedure itself. Their numerical impact is studied using the example of the total cross section for tt¯ production through next-to-next-to-leading order in QCD. One ambiguity is the arbitrary choice of the value of the highest-order PMC scale. The numerical impact of this choice on the BLM/PMC prediction for the cross section is found to be comparable to the impact of the choice of μR in the conventional scale-setting approach. Another ambiguity relates to the definitions of the other PMC scales and is similarly found to have a large impact on the cross section.
... As in Ref. [28], where top-pair production was included in approximate NNLO, the present calculation is performed within the narrow width approximation for both the top quark and the W boson. This approximation is known to work well [29] for distributions that are away from kinematic boundaries, which is the case considered in this Letter. Below we also compare our calculation with a more recent NLO study [30]. ...
We calculate, for the first time, the next-to-next-to-leading order (NNLO) QCD corrections to spin correlations in top quark pair production at the LHC. The NNLO corrections play an important role in the description of the corresponding differential distributions. We observe that the standard model calculation describes the available Δϕℓℓ data in the fiducial region but does not agree with the Δϕℓℓ measurement extrapolated to full phase space. Most likely this discrepancy is due to the difference in precision between existing event generators and NNLO calculations for dilepton top-pair final states.
... Phase space integration is performed and optimised with the help of Parni [18] and Kaleu [19]. Since the produced top quarks are unstable particles, the inclusion of the decays is performed in the complex mass scheme [20][21][22][23]. It fully re- ...
Triggered by ongoing dark matter searches in the top quark sector at the Large Hadron Collider we report on the calculation of the next-to-leading order QCD corrections to the Standard Model process $pp\to t\bar{t}+ Z(\to \nu_\ell \bar{\nu}_\ell)$. This calculation is based on matrix elements for $e^+\nu_e \, \mu^- \bar{\nu}_\mu \, b\bar{b} \, \nu_\tau \bar{\nu}_\tau$ production and includes all non-resonant diagrams, interferences, and off-shell effects of the top quarks. Non-resonant and off-shell effects due to the finite $W$-boson width are also consistently taken into account. As it is common for such studies, we present results for both integrated and differential cross sections for a few renormalisation and factorisation scale choices and three different parton distribution functions. Already with the fairly inclusive cut selection and independently of the scale choice and the parton distribution function non-flat differential ${\cal K}$-factors are obtained for $p_T^{miss}, \Delta \phi_{\ell\ell}, \Delta y_{\ell\ell}, \cos\theta_{\ell\ell}, H_T, H^\prime_T$ observables that are relevant for new physics searches. Good theoretical control over the Standard Model background is a fundamental prerequisite for a correct interpretation of possible signals of new physics that may arise in this channel. Thus, these observables need to be carefully reexamined in the presence of more exclusive cuts before any realistic strategies for the detection of new physics signal can be further developed.
... We also show results obtained by using central scales that are lowered by a factor of 1/2. A reduced central scale, such as H T /4, was considered in the studies of ref. [97] on the basis of features of fastest perturbative convergence of some observables, and it was also already suggested in ref. [21]. ...
A bstract
We report on a new fully differential calculation of the next-to-next-to-leading-order (NNLO) QCD radiative corrections to the production of top-quark pairs at hadron colliders. The calculation is performed by using the q T subtraction formalism to handle and cancel infrared singularities in real and virtual contributions. The computation is implemented in the Matrix framework, thereby allowing us to efficiently compute arbitrary infrared-safe observables for stable top quarks. We present NNLO predictions for several single- and double-differential kinematical distributions in pp collisions at the centre-of-mass energy $$ \sqrt{s}=13 $$ s = 13 TeV, and we compare them with recent LHC data by the CMS collaboration.
... , the top-quark pair process at LO enters only through off-shell effects and tWb contributions become important. In this high-m minimax bl region, the NLO calculation of bbl þ ν l l −ν l including interference effects [44][45][46][47][48][49] and parton showering [43], provides an excellent description of the data. ...
In the context of the standard model of particle physics, the relationship between the top-quark mass and width (Γt) has been precisely calculated. However, the uncertainty from current direct measurements of the width is nearly 50%. A new approach for directly measuring the top-quark width using events away from the resonance peak is presented. By using an orthogonal dataset to traditional top-quark width extractions, this new method may enable significant improvements in the experimental sensitivity in a method combination. Recasting a recent ATLAS differential cross section measurement, we find Γt=1.28±0.30 GeV (1.33±0.29 GeV expected), providing the most precise direct measurement of the width.
... The measurement probed the interference between tt and tW b by comparing the data with state-of-the-art interference models [39][40][41][42]. The target observable was the minimax pairing of lepton-jet invariant masses m b , region, the NLO calculation of bb + ν l − ν l including interference effects [43][44][45][46][47][48] and parton showering [42], provides an excellent description of the data. ...
In the context of the Standard Model (SM) of particle physics, the relationship between the top-quark mass and width ($\Gamma_t$) has been precisely calculated. However, the uncertainty from current direct measurements of the width is nearly 50%. A new approach for directly measuring the top-quark width using events away from the resonance peak is presented. By using an orthogonal dataset to traditional top-quark width extractions, this new method may enable significant improvements in the experimental sensitivity in a method combination. Recasting a recent ATLAS differential cross section measurement, we find $\Gamma_t$ = 1.28 $\pm$ 0.30 GeV (1.33 $\pm$ 0.29 GeV expected), providing the most precise direct measurement of the width.
... To this end a process that is under excellent theoretical control must to be employed in the denominator of the ratio. The tt production process, albeit in the same decay channel, seems to be the best candidate for the job due to its large cross section and similar behaviour with regard to radiative corrections [7][8][9]. Consequently, the following cross section ratio ...
A bstract
With the goal of increasing the precision of NLO QCD predictions for the $$ pp\to t\overline{t}\gamma $$ pp → t t ¯ γ process in the di-lepton top quark decay channel we present theoretical predictions for the $$ \mathrm{\mathcal{R}}={\sigma}_{t\overline{t}\gamma }/{\sigma}_{t\overline{t}} $$ ℛ = σ t t ¯ γ / σ t t ¯ cross section ratio. Results for the latter together with various differential cross section ratios are given for the LHC with the Run II energy of $$ \sqrt{s}=13 $$ s = 13 TeV. Fully realistic NLO computations for $$ t\overline{t} $$ t t ¯ and $$ t\overline{t}\gamma $$ t t ¯ γ production are employed. They are based on matrix elements for $$ {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }b\overline{b} $$ e + ν e μ − ν ¯ μ b b ¯ and $$ {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }b\overline{b}\gamma $$ e + ν e μ − ν ¯ μ b b ¯ γ processes and include all resonant and non-resonant diagrams, interferences, and off-shell effects of the top quarks and the W gauge bosons. Various renormalisation and factorisation scale choices and parton density functions are examined to assess their impact on the cross section ratio. Depending on the transverse momentum cut on the hard photon a judicious choice of a dynamical scale allows us to obtain 1%–3% percent precision on $$ \mathrm{\mathcal{R}} $$ ℛ . Moreover, for differential cross section ratios theoretical uncertainties in the range of 1%-6% have been estimated. Until now such high precision predictions have only been reserved for the top quark pair production at NNLO QCD. Thus, $$ \mathrm{\mathcal{R}} $$ ℛ at NLO in QCD represents a very precise observable to be measured at the LHC for example to study the top quark charge asymmetry or to probe the strength and the structure of the t - $$ \overline{t} $$ t ¯ -γ vertex. The latter can shed some light on possible new physics that can reveal itself only once sufficiently precise theoretical predictions are available.
... The NLO QCD corrections for the process pp → W þ W − bb were computed [18] showing an impact on various kinematic distributions and making results more stable with respect to the QCD scale variation. The NLO corrections to the complete 2 → 6 process involving offshell W bosons were calculated [19][20][21][22] and the k-factor for 13 TeV LHC energy was found to be 1.16. At this stage of our analysis, which aims to show the main effect caused by the width change, the complete leading order contributions have been taken into account, and the impact of the NLO corrections has been included in the assumed systematic uncertainties, as will be explained below. ...
Though the top quark was discovered more than twenty years ago, measurement of its width is still a challenging task. Most measurements either have rather low precision or they are made under the assumption of the SM top quark interactions. We consider model-independent parametrization of the top quark width and provide estimations on achievable accuracy using a combination of fiducial cross sections in double-resonant, single-resonant and nonresonant regions.
... Traditional measurements of production of a single top quark with an associated W boson (tW) are designed to be insensitive to such effects [19][20][21]. Recent fixed-order calculations of the full next-to-leading-order (NLO) pp → l þ νl −ν bb process [22][23][24][25][26] include proper treatment of the interference and have set the stage for corresponding predictions matched to a parton shower [27]. However, there are no measurements available to assess the modeling in a region sensitive to interference effects. ...
This Letter presents a normalized differential cross-section measurement in a fiducial phase-space region where interference effects between top-quark pair production and associated production of a single top quark with a W boson and a b-quark are significant. Events with exactly two leptons (ee, μμ, or eμ) and two b-tagged jets that satisfy a multiparticle invariant mass requirement are selected from 36.1 fb−1 of proton-proton collision data taken at s=13 TeV with the ATLAS detector at the LHC in 2015 and 2016. The results are compared with predictions from simulations using various strategies for the interference. The standard prescriptions for interference modeling are significantly different from each other but are within 2σ of the data. State-of-the-art predictions that naturally incorporate interference effects provide the best description of the data in the measured region of phase space most sensitive to these effects. These results provide an important constraint on interference models and will guide future model development and tuning.
... To this end a process that is under excellent theoretical control must to be employed in the denominator of the ratio. The tt production process, albeit in the same decay channel, seems to be the best candidate for the job due to its large cross section and similar behaviour with regard to radiative corrections [5][6][7]. Consequently, the following cross section ratio ...
With the goal of increasing the precision of NLO QCD predictions for the $pp\to t\bar{t} \gamma$ process in the di-lepton top quark decay channel we present theoretical predictions for the ${\cal R}= \sigma_{t\bar{t}\gamma}/\sigma_{t\bar{t}}$ cross section ratio. Results for the latter together with various differential cross section ratios are given for the LHC with the Run II energy of $\sqrt{s} = 13$ TeV. Fully realistic NLO computations for $t\bar{t}$ and $t\bar{t}\gamma$ production are employed. They are based on matrix elements for $e^+\nu_e \mu^- \bar{\nu}_\mu b\bar{b}$ and $e^+\nu_e \mu^- \bar{\nu}_\mu b\bar{b}\gamma$ processes and include all resonant and non-resonant diagrams, interferences, and off-shell effects of the top quarks and the $W$ gauge bosons. Various renormalisation and factorisation scale choices and parton density functions are examined to assess their impact on the cross section ratio. Depending on the transverse momentum cut on the hard photon a judicious choice of a dynamical scale allows us to obtain $1\%-3\%$ percent precision on ${\cal R}$. Moreover, for differential cross section ratios theoretical uncertainties in the range of $1\%-6\%$ have been estimated. Until now such high precision predictions have only been reserved for the top quark pair production at NNLO QCD. Thus, ${\cal R}$ at NLO in QCD represents a very precise observable to be measured at the LHC for example to study the top quark charge asymmetry or to probe the strength and the structure of the $t$-$\bar{t}$-$\gamma$ vertex. The latter can shed some light on possible new physics that can reveal itself only once sufficiently precise theoretical predictions are available.
... where Γ NLO t refers to the top quark width with W gauge boson off-shell effects included and Γ NLO tW to the top quark width with an on-shell W gauge boson as used in the NWA [39,40]. Both values are derived for massless b quarks since all leptons and u, d, c, s, b partons are considered to be massless. ...
A precise measurement of the top quark mass, a fundamental parameter of the Standard Model, is among the most important goals of top quark studies at the Large Hadron Collider. Apart from the standard methods, numerous new observables and reconstruction techniques are employed to improve the overall precision and to provide different sensitivities to various systematic uncertainties. Recently, the normalised inverse invariant mass distribution of the tt¯ system and the leading extra jet not coming from the top quark decays has been proposed for the pp→tt¯j production process, denoted as ℛ(mtpole, ρs). In this paper, a thorough study of different theoretical predictions for this observable, however, with top quark decays included, is carried out. We focus on fixed order NLO QCD calculations for the di-lepton top quark decay channel at the LHC with s=13 TeV. First, the impact on the extraction of mt is investigated and afterwards the associated uncertainties are quantified. In one approach we include all interferences, off-shell effects and non-resonant backgrounds. This is contrasted with a different approach with top quark decays in the narrow width approximation. In the latter case, two cases are employed: NLO QCD corrections to the pp→tt¯j production process with leading order decays and the more sophisticated case with QCD corrections and jet radiation present also in top quark decays. The top quark mass sensitivity of ℛ(mtpole, ρs) is investigated and compared to other observables: the invariant mass of the top anti-top pair, the minimal invariant mass of the b-jet and a charged lepton as well as the total transverse momentum of the tt¯j system. Once top quark decays are included the invariant mass of the tt¯ system shows better sensitivity to the top quark mass extraction and smaller dependence on the off-shell effects and non-resonant contributions of the top quark and the W gauge boson than the ℛ(mtpole, ρs) observable.
... A few examples of Feynman diagrams contributing at O(α 2 s α 5 ) for the gg initial state are presented in Fig. 1. As a final comment, we note that NLO QCD corrections with complete top quark off-shell effects are also known for tt, ttH and ttj productions [15][16][17][18][19][20][21][22][23]. In case of tt and ttH NLO electroweak corrections have been added as well [24,25]. ...
A bstract
We present a complete description of top quark pair production in association with a hard photon in the dilepton channel. Our calculation is accurate to NLO in QCD. It is based on matrix elements for $$ {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }b\overline{b}\upgamma $$ e + ν e μ − ν ¯ μ b b ¯ γ production and includes all resonant and non-resonant diagrams, interferences, and off-shell effects of the top quarks and the W gauge bosons. This calculation constitutes the first full computation for top quark pair production with a final state photon in hadronic collisions at NLO in QCD. Numerical results for total and differential cross sections are presented for the LHC at a centre-of-mass energy of $$ \sqrt{s}=13 $$ s = 13 TeV. For a few observables relevant for new physics searches, beyond some kinematic bounds, we observe shape distortions of more than 100%. In addition, we confirm that the size of the top quark off-shell effects for the total cross section is consistent with the expected uncertainties of the narrow width approximation. Results presented here are not only relevant for beyond the Standard Model physics searches but also important for precise measurements of the top-quark fiducial cross sections and top-quark properties at the LHC.
A bstract
The increasingly high accuracy of top-quark studies at the LHC calls for a theoretical description of $$ t\overline{t} $$ t t ¯ production and decay in terms of exact matrix elements for the full 2 → 6 process that includes the off-shell production and the chain decays of $$ t\overline{t} $$ t t ¯ and tW intermediate states, together with their quantum interference. Corresponding NLO QCD calculations matched to parton showers are available for the case of dileptonic channels and are implemented in the bb4l Monte Carlo generator, which is based on the resonance-aware POWHEG method. In this paper, we present the first NLOPS predictions of this kind for the case of semileptonic channels. In this context, the interplay of off-shell $$ t\overline{t} $$ t t ¯ + tW production with various other QCD and electroweak subprocesses that yield the same semileptonic final state is discussed in detail. On the technical side, we improve the resonance-aware POWHEG procedure by means of new resonance histories based on matrix elements, which enable a realistic separation of $$ t\overline{t} $$ t t ¯ and tW contributions. Moreover, we introduce a general approach which makes it possible to avoid certain spurious terms that arise from the perturbative expansion of decay widths in any off-shell higher-order calculation, and which are large enough to jeopardise physical finite-width effects. These methods are implemented in a new version of the bb4l Monte Carlo generator, which is applicable to all dileptonic and semileptonic channels, and can be extended to fully hadronic channels. The presented results include a NLOPS comparison of off-shell against on-shell $$ t\overline{t} $$ t t ¯ + tW production and decay, where we highlight various non-trivial aspects related to NLO and parton-shower radiation in leptonic and hadronic top decays.
New Physics searches at the LHC rely very heavily on the precision and accuracy of Standard Model background predictions. Applying the spin-0 s -channel mediator model, we assess the importance of properly modelling such backgrounds in $$t{\bar{t}}$$ t t ¯ associated Dark Matter production. Specifically, we discuss higher-order corrections and off-shell effects for the two dominant background processes $$t{\bar{t}}$$ t t ¯ and $$t{\bar{t}}Z$$ t t ¯ Z in the presence of extremely exclusive cuts. Exclusion limits are calculated for state-of-the-art NLO full off-shell $$t{\bar{t}}$$ t t ¯ and $$t{\bar{t}}Z$$ t t ¯ Z predictions and compared to those computed with backgrounds in the NWA and / or at LO. We perform the same comparison for several new-physics sensitive observables and evaluate which of them are affected by the top-quark modelling. Additionally, we make suggestions as to which observables should be used to obtain the most stringent limits assuming integrated luminosities of 300 fb $$^{-1}$$ - 1 and 3000 fb $$^{-1}$$ - 1 .
Recent discrepancies between theoretical predictions and experimental data in multi-lepton plus b -jets analyses for the $$t{\bar{t}}W^\pm $$ t t ¯ W ± process, as reported by the ATLAS collaboration, have indicated that more accurate theoretical predictions and high precision observables are needed to constrain numerous new physics scenarios in this channel. To this end we employ NLO QCD computations with full off-shell top quark effects included to provide theoretical predictions for the $$\mathcal{R}= \sigma _{t{\bar{t}}W^+}/\sigma _{t{\bar{t}}W^-}$$ R = σ t t ¯ W + / σ t t ¯ W - cross section ratio at the LHC with $$\sqrt{s}=13$$ s = 13 TeV. Depending on the transverse momentum cut on the b -jet we obtain 2–3% theoretical precision on $$\mathcal{R}$$ R , which should help to shed some light on new physics effects that can reveal themselves only once sufficiently precise Standard Model theoretical predictions are available. Furthermore, triggered by these discrepancies we reexamine the charge asymmetry of the top quark and its decay products in the $$t{\bar{t}}W^\pm $$ t t ¯ W ± production process. In the case of charge asymmetries, that are uniquely sensitive to the chiral nature of possible new physics in this channel, theoretical uncertainties below 15% are obtained. Additionally, the impact of the top quark decay modelling is scrutinised by explicit comparison with predictions in the narrow-width approximation.
With the standard model working well in describing the collider data, the focus is now on determining the standard model parameters as well as for any hint of deviation. In particular, the determination of the couplings of the Higgs boson with itself and with other particles of the model is important to better understand the electroweak symmetry breaking sector of the model. In this letter, we look at the process pp→WWH, in particular through the fusion of bottom quarks. Due to the non-negligible coupling of the Higgs boson with the bottom quarks, there is a dependence on the WWHH coupling in this process. This sub-process receives largest contribution when the W bosons are longitudinally polarized. We compute one-loop QCD corrections to various final states with polarized W bosons. We find that the corrections to the final state with the longitudinally polarized W bosons are large. It is shown that the measurement of the polarization of the W bosons can be used as a tool to probe the WWHH coupling in this process. We also examine the effect of varying WWHH coupling in the κ-framework.
Current particle phenomenology is characterized by the spectacular agreement of the predictions of the Standard Model of particle physics (SM) with all results from collider experiments and by the absence of significant signals of non-standard physics, despite the fact that we know that the SM cannot be the ultimate theory of nature. In this situation, confronting theory and experiment with high precision is a promising direction to look for potential traces of physics beyond the SM. On the theory side, the calculation of radiative corrections of the strong and electroweak interactions is at the heart of this task, a field that has seen tremendous conceptual and technical progress in the last decades. This review aims at a coherent introduction to the field of electroweak corrections and tries to fill gaps in the literature between standard textbook knowledge and the current state of the art. The SM and the machinery for its perturbative evaluation are reviewed in detail, putting particular emphasis on renormalization, on one-loop techniques, on modern amplitude methods and tools, on the separation of infrared singularities in real-emission corrections, on electroweak issues connected with hadronic initial or final states in collisions, and on the issue of unstable particles in quantum field theory together with corresponding practical solutions.
A bstract
We construct predictions for top quark pair differential distributions at hadron colliders that combine state-of-the-art NNLO QCD calculations with double resummation at NNLL ′ accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms. This is the first time a resummed calculation at full NNLO+NNLL ′ accuracy in QCD for a process with non-trivial color structure has been completed at the differential level. Of main interest to us is the stability of the $$ {M}_{t\overline{t}} $$ M t t ¯ and top-quark p T distributions in the boosted regime where fixed order calculations may become strongly dependent on the choice of dynamic scales. With the help of numeric and analytic arguments we confirm that the choice for the factorization and renormalization scales advocated recently by some of the authors is indeed optimal. We further derive a set of optimized kinematics-dependent scales for the matching functions which appear in the resummed calculations. Our NNLO+NNLL ′ prediction for the top-pair invariant mass is significantly less sensitive to the choice of factorization scale than the fixed order prediction, even at NNLO. Notably, the resummed and fixed order calculations are in nearly perfect agreement with each other in the full $$ {M}_{t\overline{t}} $$ M t t ¯ range when the optimal dynamic scale is used. For the top-quark p T distribution the resummation performed here has less of an impact and instead we find that upgrading the matching with fixed-order from NLO+NNLL ′ to NNLO+NNLL ′ to be an important effect, a point to be kept in mind when using NLO-based Monte Carlo event generators to calculate this distribution.
We present the results of a next-to-leading order calculation of QCD corrections to the production of an on-shell top-anti-top quark pair in association with two flavored b-jets. Besides studying the total cross section and its scale dependence, we give several differential distributions. Where comparable, our results agree with a previous analysis. While the process under scrutiny is of major relevance for Higgs boson searches at the LHC, we use it to demonstrate the ability of our system built around Helac-Phegas to tackle complete calculations at the frontier of current studies for the LHC. On the technical side, we show how the virtual corrections are efficiently computed with Helac-1Loop, based on the OPP method and the reduction code CutTools, using reweighting and Monte Carlo over color configurations and polarizations. As far as the real corrections are concerned, we use the recently published Helac-Dipoles package. In connection with improvements of the latter, we give the last missing integrated dipole formulae necessary for a complete implementation of phase space restriction dependence in the massive dipole subtraction formalism.
The {{mathcal{O}}}(alpha) electroweak radiative corrections to {gammagammato WWto 4f} within the electroweak standard model are calculated in double-pole approximation (DPA). Virtual corrections are treated in DPA, leading to a classification into factorizable and non-factorizable contributions, and real-photonic corrections are based on complete lowest-order matrix elements for {gammagammato 4f}{ + }gamma. Soft and collinear singularities appearing in the virtual and real corrections are combined alternatively in two different ways, namely by using the dipole subtraction method or by applying phase-space slicing. The radiative corrections are implemented in a Monte Carlo generator called Coffer gammagamma - the computer code can be obtained from the authors upon request - which optionally includes anomalous triple and quartic gauge-boson couplings in addition and performs a convolution over realistic spectra of the photon beams. A detailed survey of numerical results comprises {{mathcal{O}}}(alpha) corrections to integrated cross sections as well as to angular, energy, and invariant-mass distributions. Particular attention is paid to the issue of collinear safety in the observables.
Using BlackHat in conjunction with SHERPA, we have computed next-to-leading order QCD predictions for a variety of distributions in Z,*+1, 2, 3-jet production at the Tevatron, where the Z boson or off-shell photon decays into an electron-positron pair. We find good agreement between the next-to-leading order results for jet p{sub T} distributions and measurements by CDF and D0. We also present jet-production ratios, or probabilities of finding one additional jet. As a function of vector-boson p{sub T}, the ratios have distinctive features which we describe in terms of a simple model capturing leading logarithms and phase-space and parton-distribution-function suppression.
We present a measurement of forward-backward asymmetry in top quark-antiquark production in proton-antiproton collisions in the final state containing a lepton and at least four jets. Using a data set corresponding to an integrated luminosity of 5.4 fb-1, collected by the D0 experiment at the Fermilab Tevatron Collider, we measure the tt̅ forward-backward asymmetry to be (9.2±3.7)% at the reconstruction level. When corrected for detector acceptance and resolution, the asymmetry is found to be (19.6±6.5)%. We also measure a corrected asymmetry based on the lepton from a top quark decay, found to be (15.2±4.0)%. The results are compared to predictions based on the next-to-leading-order QCD generator mc@nlo. The sensitivity of the measured and predicted asymmetries to the modeling of gluon radiation is discussed.
We present the cross section for production of a Z boson in association with four jets at the Large Hadron Collider, at next-to-leading order in the QCD coupling. When the Z decays to neutrinos, this process is a key irreducible background to many searches for new physics. Its computation has been made feasible through the development of the on-shell approach to perturbative quantum field theory. We present the total cross section for pp collisions at √s=7 TeV, after folding in the decay of the Z boson, or virtual photon, to a charged-lepton pair. We also provide distributions of the transverse momenta of the four jets, and we compare cross sections and distributions to the corresponding ones for the production of a W boson with accompanying jets.
This is an Erratum to a Letter of ours [S. Moretti, M.R. Nolten, D.A.
Ross, Phys. Lett. B 639 (2006) 513]. After its publication, we have
discovered a mistake in a numerical program that affects the results
presented therein. We provide here the corrected version.
The new web-based version of the automatized process and event generator Mad-Graph/MadEvent is now available. Recent developments are: New models, notably MSSM, 2HDM and a framework for addition of user-defined models, inclusive sam-ple generation and on-line hadronization and detector simulation. Event generation can be done on-line on any of our clusters.
Results for next-to-leading order QCD corrections to the pp( p[`(p)] ) ® t[`(t)] ® W+ W- b[`(b)] ® e+ nem- [`(n)]m b[`(b)] + X pp\left( {p\bar{p}} \right) \to t\bar{t} \to {W^{+} }{W^{-} }b\bar{b} \to {e^{+} }{\nu_e}{\mu^{-} }{\bar{\nu }_\mu }b\bar{b} + X processes with complete off-shell effects are presented for the first time. Double-, single-and non-resonant top contributions
of the order O( as3a4 ) \mathcal{O}\left( {\alpha_s^3{\alpha^4}} \right) are consistently taken into account, which requires the introduction of a complex-mass scheme for unstable top quarks. Moreover,
the intermediate W bosons are treated off-shell. Comparison to the narrow width approximation for top quarks, where non-factorizable corrections
are not accounted for is performed. Besides the total cross section and its scale dependence, several differential distributions
at the TeVatron run II and the LHC are given. In case of the TeVatron the forward-backward asymmetry of the top is recalculated
afresh. With inclusive selection cuts, the forward-backward asymmetry amounts to AFBt = 0.051±0.0013 A_{FB}^t = 0.051\pm 0.0013 . Furthermore, the corrections with respect to leading order are positive and of the order 2.3% for the TeVatron and 47% for
the LHC. A study of the scale dependence of our NLO predictions indicates that the residual theoretical uncertainty due to
higher order corrections is 8% for the TeVatron and 9% for the LHC.
KeywordsJets–NLO Computations–Hadronic Colliders–QCD
Top-quark physics plays an important role at hadron colliders such as the Tevatron at Fermilab or the upcoming Large Hadron
Collider (LHC) at CERN. Given the planned experimental precision, detailed theoretical predictions are mandatory. In this
article we present analytic results for the complete weak corrections to gluon-induced top-quark pair production – neglecting
purely photonic corrections, completing our earlier results for the quark-induced reaction. As an application we discuss top-quark
pair production at the Tevatron and LHC. In particular we show that, although they are small for inclusive quantities, weak
corrections can be sizeable for differential distributions.
We compute the next-to-leading order QCD corrections to WZ+jet production at the Tevatron and the LHC, including decays of
the electroweak bosons to light leptons with all off-shell effects taken into account. The corrections are sizable and have
significant impact on the differential distributions.
KeywordsNLO Computations-QCD-Jets
I present the two-loop QCD corrections to the production of a massive quark–anti-quark pair in the massless quark–anti-quark annihilation channel. The result is obtained as a combination of a deep expansion in the mass around the high energy limit and of a numerical integration of a system of differential equations. The primary application of the outcome and developed methods is top quark pair production at the Large Hadron Collider.
We present a measurement of forward-backward asymmetry in top quark-antiquark production in proton-antiproton collisions in the final state containing a lepton and at least four jets. Using a data set corresponding to an integrated luminosity of 5.4 fb-1, collected by the D0 experiment at the Fermilab Tevatron Collider, we measure the tt̅ forward-backward asymmetry to be (9.2 ± 3.7)% at the reconstruction level. When corrected for detector acceptance and resolution, the asymmetry is found to be (19.6 ± 6.5)%. We also measure a corrected asymmetry based on the lepton from a top quark decay, found to be (15.2± 4.0)%. The results are compared to predictions based on the next-to-leading-order QCD generator MC@NLO. The sensitivity of the measured and predicted asymmetries to the modeling of gluon radiation is discussed.
Until recently it was thought that for Higgs boson searches at the Large Hadron Collider, W H and ZH production where the Higgs boson decays to b ¯ b would be poor search channels due to large backgrounds. Recent phenomenological stud-ies have indicated that at high transverse momenta, employing state-of-the-art jet reconstruction and decomposition techniques, these processes can be recovered as promising search channels for the Standard Model Higgs boson around 120 GeV in mass. We investigate this claim using a realistic simulation of the ATLAS detector.
We present predictions for
$ {\text{t}}\overline {\text{t}} {\text{b}}\overline {\text{b}} $
production at the LHC in next-to-leading order QCD. The precise description of this background process is a prerequisite to observe associated
$ {\text{t}}\overline {\text{t}} {\text{H}} $
production in the
$ {\text{H}} \to {\text{b}}\overline {\text{b}} $
decay channel and to directly measure the top-quark Yukawa coupling at the LHC. The leading-order cross section is extremely sensitive to scale variations. We observe that the traditional scale choice adopted in ATLAS simulations underestimates the
$ {\text{t}}\overline {\text{t}} {\text{b}}\overline {\text{b}} $
background by a factor two and introduce a new dynamical scale that stabilizes the perturbative predictions. We study various kinematic distributions and observe that the corrections have little impact on their shapes if standard cuts are applied. In the regime of highly boosted Higgs bosons, which offers better perspectives to observe the
$ {\text{t}}\overline {\text{t}} {\text{H}} $
signal, we find significant distortions of the kinematic distributions. The one-loop amplitudes are computed using process-independent algebraic manipulations of Feynman diagrams and numerical tensor reduction. We find that this approach provides very high numerical stability and CPU efficiency.
We present a new general algorithm for calculating arbitrary jet cross sections in arbitrary scattering processes to next-to-leading accuracy in perturbative QCD. The algorithm is based on the subtraction method. The key ingredients are new factorization formulae, called dipole formulae, which implement in a Lorentz covariant way both the usual soft and collinear approximations, smoothly interpolating the two. The corresponding dipole phase space obeys exact factorization, so that the dipole contributions to the cross section can be exactly integrated analytically over the whole of phase space. We obtain explicit analytic results for any jet observable in any scattering or fragmentation process in lepton, lepton-hadron or hadron-hadron collisions. All the analytical formulae necessary to construct a numerical program for next-to-leading order QCD calculations are provided. The algorithm is straightforwardly implementable in general purpose Monte Carlo programs.
We calculate the next-to-next-to-leading-order O({sub s}) one-loop squared corrections to the production of heavy-quark pairs in the gluon-gluon fusion process. Together with the previously derived results on the qq production channel, the results of this paper complete the calculation of the one-loop squared contributions of the next-to-next-to-leading-order O({sub s}) radiative QCD corrections to the hadroproduction of heavy flavors. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization.
We compute the leading color, next-to-leading order QCD
corrections to the dominant partonic channels for the production of a
W boson in association with three jets at the Tevatron and the LHC.
This is the first application of generalized unitarity for realistic
one-loop calculations. The method performs well in this non-trivial
test and offers great promise for the future.
The kt and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance measure. We examine some properties of a new member of this class, for which the power is negative. This ``anti-kt'' algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid boundary and the Milan factor is universal. None of these properties hold for existing sequential recombination algorithms, nor for cone algorithms with split-merge steps, such as SISCone. They are however the identifying characteristics of the collinear unsafe plain ``iterative cone'' algorithm, for which the anti-kt algorithm provides a natural, fast, infrared and collinear safe replacement.
It has been argued that higher order 2-->3 O(alphas3 QCD processes play an important role in the hadroproduction of heavy quarks. We propose forward-backward or charge conjugation asymmetry as a distinctive signature of the higher-order QCS production mechanism. We analyse the physical origin of the asymmetries and show that observed forward-backward asymmetries for the heavy quark or decay lepton are 5% or less for realistic experimental conditions. Observation of asymmetries in excess of our calculated values would signal the production of heavy quarks via unconventional mechanisms.
We compute the NLO QCD corrections to the pair production of W-bosons in
association with two jets at the Tevatron and the LHC. This process is an
important background to heavy Higgs-boson production in association with two
jets, either in gluon or weak boson fusion. We consider leptonic decays of
W-bosons and include all the spin correlations exactly. For natural choices of
the renormalization scale, the NLO QCD corrections to pp(ppbar) -> W^+W^-jj are
moderate but different for various values of the center-of-mass collision
energy at the LHC and the Tevatron, emphasizing the need to compute them
explicitly.
We compute the one-loop QCD amplitude for the process gg→QQ̅ in dimensional regularization through order ϵ2 in the dimensional regulator and for arbitrary quark mass values. This result is an ingredient of the next-to-next-to-leading order cross section for heavy-quark production at hadron colliders. The calculation is performed in conventional dimensional regularization using well-known reduction techniques as well as a method based on recent ideas for the functional form of one-loop integrands in four dimensions.
Most calculations of the electroweak radiative corrections to e+e− annihilation near the Z0 resonance contain spurious higher-order gauge-dependent contributions. It is shown how to develop, to arbitrary accuracy, a perturbative expansion that is exactly gauge invariant at each order and produces expressions that are particularly simple in form. Experiments at LEP currently extract the value of the renormalized mass in the on-shell scheme for the physical Z0 mass. It is shown that this definition differs from the traditional one based on the position of the pole of the scattering amplitude by 35 MeV or more than 1 σ of the present experimental accuracy. The gauge-invariant expansion proposed here makes the latter definition the natural choice.
We compute the next-to-next-to-leading order QCD corrections to the partonic reaction that dominates top-pair production at the Tevatron. This is the first ever next-to-next-to-leading order calculation of an observable with more than two colored partons and/or massive fermions at hadron colliders. Augmenting our fixed order calculation with soft-gluon resummation through next-to-next-to-leading logarithmic accuracy, we observe that the predicted total inclusive cross section exhibits a very small perturbative uncertainty, estimated at ±2.7%. We expect that once all subdominant partonic reactions are accounted for, and work in this direction is ongoing, the perturbative theoretical uncertainty for this observable could drop below ±2%. Our calculation demonstrates the power of our computational approach and proves it can be successfully applied to all processes at hadron colliders for which high-precision analyses are needed.
The process pp → + X represents a very important background reaction to searches at the LHC, in particular to production where the Higgs boson decays into a pair. A successful analysis of at the LHC requires the knowledge of direct production at next-to-leading order in QCD. We take the first step in this direction upon calculating the next-to-leading-order QCD corrections to the subprocess initiated by q annihilation. We devote an appendix to the general issue of rational terms resulting from ultraviolet or infrared (soft or collinear) singularities within dimensional regularization. There we show that, for arbitrary processes, in the Feynman gauge, rational terms of infrared origin cancel in truncated one-loop diagrams and result only from trivial self-energy corrections.
Many theories, from Supersymmetry to models of Strong Electroweak Symmetry Breaking, look at the production of four top quarks as an interesting channel to evidentiate signals of new physics beyond the Standard Model. The production of four-top final states requires large partonic energies, above the 4m
t
threshold, that are available at the CERN Large Hadron Collider and will become more and more accessible with increasing energy and luminosity of the proton beams. A good theoretical control on the Standard Model background is a fundamental prerequisite for a correct interpretation of the possible signals of new physics that may arise in this channel. In this paper we report on the calculation of the next-to-leading order QCD corrections to the Standard Model process \( pp \to t\overline t t\overline t + X \). As it is customary for such studies, we present results for both integrated and differential cross sections. A judicious choice of a dynamical scale allows us to obtain nearly constant \( \mathcal{K} - {\text{factors}} \) in most distributions.
Formulae expressing the amplitude for a Feynman diagram consisting of a single internal loop withn sides andn external lines as a sum of its reduced diagrams are derived by applying restrictions imposed by the finite dimensionality
of space-time on the unparametrized amplitude. In 4-dimensional space-time these formulae express the amplitude for then-sided diagram as i) a sum of all its 5-sided reduced diagrams; this can be further expressed as ii) a sum of all its 4-sided
reduced diagrams. The coefficients in each sum depend only on the external invariants and internal masses.
Applicando le restrizioni imposte alla ampiezza non parametrizzata dalla dimensionalità finita dello spazio-tempo, si deducono
le formule che esprimono l'ampiezza di un diagramma di Feynman composto di un solo nodo interno conn lati edn linee esterne come somma dei suoi diagrammi ridotti. Nello spazio-tempo quadridimensionale queste formule esprimono l'ampiezza
dei diagrammi conn lati come i) una somma dei loro diagrammi ridotti con 5 lati; questi possono essere inoltre espressi come ii) una somma di
tutti i loro diagrammi ridotti con 4 lati. I coefficienti di ciascuna somma dipendono solo dagli invarianti esterni e dalle
masse interne.
We compute, for $t \bar t$ production at the LHC and at the Tevatron, several
charge asymmetries to NLO QCD, including also the electromagnetic and
weak-interaction corrections. We calculate these asymmetries both inclusively
and with additional kinematic cuts and compare our results, where possible,
with recent experimental results and with SM predictions. The $t \bar t$
asymmetries induce also corresponding asymmetries for the charged leptons from
semileptonic top-quark decay. Although these asymmetries are, in the SM,
smaller than the corresponding ones for top quarks, they are expected to be
measurable quite precisely. In fact, measurement of a lepton asymmetry in
$\ell$ + jets events was reported by the D$\emptyset$ and CDF experiments. We
analyze and compute to NLO in the gauge couplings leptonic charge asymmetries
for dileptonic and semileptonic $\ttbar$ events, with and without acceptance
cuts, at the Tevatron and the LHC.
We give a detailed presentation of the electroweak one-loop contributions to the production mechanisms of top quark pairs, , for the energy range of future hadron colliders. The full gauge-invariant set of loop diagrams with Higgs, Z0 and W± bosons is considered including strong Yukawa couplings. The parton cross sections get sizeable modifications up to 40% and are sensitive to the Higgs boson mass and the Yukawa coupling. Results are also given for the observable hadronic cross section , where the large corrections at the parton level are substantially reduced to the order of a few percent. For the electroweak Standard Model the maximum contribution is about 7% for a light Higgs boson with Mη = 60 GeV. For Higgs bosons with Mη > 200 GeV, the electroweak contributions are typically (2–3)%.
Analytical experessions for the e+e− → μ+μ− cross section including all the one-loop radiative corrections in the context of the Weinberg model are presented. The systematic calculation of one-loop diagrams has been carried out using a recently proposed scheme. Numerical results are shown in a region from 40–200 GeV c.m. energy and different values of the scattering angle; they indicate that the percentage corrections are mainly due to soft photons. The only departure from QED-like correction can be seen in a region where the lowest-order cross section is lowered by weak-e.m. interference. In that region hard photon contributions are relatively prominent and perhaps within experimental possibilities.
We have written Feyn Arts, a program which generates all tree and one-loop graphs for processes with given external particles in a given renormalizable field theory without mixing propagators. Successively all topologies are created, particles and Feynman rules are inserted and the graphs are drawn. The obtained amplitudes are suited for evaluation by the program Feyn Calc. We have entered the Feynman rules for the electroweak standard model and have applied the program to different processes within this model.
We describe the implementation of top production and decay processes in the
parton-level Monte Carlo program MCFM. By treating the top quark as being
on-shell, we can factorize the amplitudes for top-pair production, s-channel
single-top production, and t-channel single-top production into the product of
an amplitude for production and an amplitude for decay. In this way we can
retain all spin correlations. Both the production and the decay amplitudes are
calculated consistently at next-to-leading order in alpha_s. The full
dependence on the b-quark mass is also kept. Phenomenological results are
presented for various kinematic distributions at the LHC and for the top quark
forward-backward asymmetry at the Tevatron.
We investigate the QCD corrections to the cross section and single-particle inclusive differential distributions for p + p̄ → Q(Q̄) + X where Q and Q̄ are heavy quarks. We calculate the order αS corrections to the parton reaction q + q̄ → Q + Q̄ which involves the computation of the virtual gluon contributions and the soft and hard contributions from the reaction q + q̄ → Q + Q̄ + g. The contributions from the channels g + q(q̄) → Q + Q̄ + q(q̄) are also calculated. Including the order αS corrections to g + g → Q + Q̄ from our previous paper, we give exact results for the order α3S cross sections and single-particle inclusive differential distributions for the production of t and b quarks in pp̄ collisions at energies presently available at the CERN Spp̄S and the Fermilab tevatron. Results for future pp colliders are also presented. Finally we compare the results of the simple approximations to the order αS corrections with the exact results.
A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly) singular points in phase space. No particular restriction is imposed on kinematics, and complex masses (poles) are allowed.
A new method for the reduction of one-loop tensor 5-point integrals to related 4-point integrals is proposed. In contrast to the usual Passarino–Veltman reduction and other methods used in the literature, this reduction avoids the occurrence of inverse Gram determinants, which potentially cause severe numerical instabilities in practical calculations. Explicit results for the 5-point tensor coefficients are presented up to rank 4. The expressions for the reduction of the relevant 1-, 2-, 3-, and 4-point tensor coefficients to scalar integrals are also included; apart from these standard integrals no other integrals are needed.
Lusifer is a Monte Carlo event generator for all processes e+e−→6 fermions, which is based on the multi-channel Monte Carlo integration technique and employs the full set of tree-level diagrams. External fermions are taken to be massless, but can be arbitrarily polarized. The calculation of the helicity amplitudes and of the squared matrix elements is presented in a compact way. Initial-state radiation is included at the leading logarithmic level using the structure-function approach. The discussion of numerical results contains a comprehensive list of cross sections relevant for a collider, including a tuned comparison to results obtained with the combination of the Whizard and Madgraph packages as far as possible. Moreover, for off-shell top-quark pair production and the production of a Higgs boson in the intermediate mass range we additionally discuss some phenomenologically interesting distributions. Finally, we numerically analyze the effects of gauge-invariance violation by comparing various ways of introducing decay widths of intermediate top quarks, gauge and Higgs bosons.
The complete electroweak O(α) corrections are calculated for the charged-current four-fermion production processes , , and . The calculation is performed using complex gauge-boson masses, supplemented by complex couplings to restore gauge invariance. The evaluation of the occurring one-loop tensor integrals, which include 5- and 6-point functions, requires new techniques. Explicit numerical results are presented for total cross sections in the energy range from the W-pair-production threshold region up to a scattering energy of 2 TeV. A comparison with the predictions based on the “double-pole approximation” (DPA) provided by the generator RacoonWW reveals corrections beyond DPA of ≲0.5% in the energy range 170–300 GeV, in agreement with previous estimates for the intrinsic DPA uncertainty. The difference to the DPA increases to 1–2% for . At threshold, where the DPA becomes unreliable, the full O(α) calculation corrects an improved Born approximation (IBA) by about 1.6%, also consistent with an error estimate of the IBA.
We consider the total production cross section of heavy coloured particle pairs in hadronic collisions at the production threshold. We construct a basis in colour space that diagonalizes to all orders in perturbation theory the soft function, which appears in a new factorization formula for the combined resummation of soft gluon and Coulomb gluon effects. This extends recent results on the structure of soft anomalous dimensions and allows us to determine an analytic expression for the two-loop soft anomalous dimension at threshold for all production processes of interest.
We provide a complete set of results for the scalar 4-point function appearing in one-loop calculations in QCD, QED, the electroweak Standard Model and popular extensions thereof. Complex internal masses, which are needed for calculations involving unstable particles, are supported throughout, whereas complex momenta are not supported. In particular, for the most general, regular case we present two independent results in terms of 72 and 32 dilogarithms. In addition we list explicit results for all soft- and/or collinear-singular cases in dimensional regularization, mass regularization, and in regularizations of mixed type. The exceptional case with a vanishing modified Cayley determinant, which hardly appears in applications, is not considered.
In ongoing and upcoming hadron collider experiments, top quark physics will play an important role in testing the Standard Model and its possible extensions. In this work we present analytic results for the differential cross sections of top quark pair production in hadronic collisions at next-to-leading order in the QCD coupling, keeping the full dependence on the spins of the top quarks. These results are combined with the corresponding next-to-leading order results for the decay of polarized top quarks into dilepton, lepton plus jets, and all jets final states. As an application we predict double differential angular distributions which are due to the QCD-induced top quark spin correlations in the intermediate state. In addition to the analytic results, we give numerical results in terms of fit functions that can easily be used in an experimental analysis.
General IR-divergent scalar box integrals, as present in calculations of radiative corrections, are calculated, using a photon mass λ as regulator. Also special “mass singular” cases and examples thereof occuring in the electroweak theory are listed. It is also shown how these IR-divergent integrals appear in the reduction of the corresponding tensor integrals.