We present the differential rates and branching ratios of the radiative decays $τ\to l \barν νγ$, with $l=e$ or $μ$, and $μ\to e \barν νγ$ in the Standard Model at next-to-leading order. Radiative corrections are computed taking into account the full depencence on the mass $m_l$ of the final charged leptons, which is necessary for the correct determination of the branching ratios. Only partial agreement is found with previous calculations performed in the $m_l \to 0$ limit. Our results agree with the measurements of the branching ratios $\mathcal{B} (μ\to e \barν νγ)$ and $\mathcal{B} (τ\to μ\barν νγ)$ for a minimum photon energy of 10 MeV in the $μ$ and $τ$ rest frames, respectively. Babar's recent precise measurement of the branching ratio $\mathcal{B} (τ\to e \barν νγ)$, for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.
The computation of the NLO-QCD corrections to the cross sections for W γγproduction in hadronic collisions is presented. We consider the case of real photons in the final state, but include full leptonic decays of the W. Numerical results for the LHC and the Tevatron are obtained through a parton level Monte Carlo based on the structure of the VBFNLO program, allowing an easy implementation of general cuts and distributions. We show the dependence on scale variations of the integrated cross sections and provide evidence of the fact that NLO QCD corrections strongly modify the LO predictions fo…
Precision tests of the Standard Model (SM) require not only accurate experiments, but also precise and reliable theoretical predictions. Triple vector boson production provides a unique opportunity to investigate the quartic gauge couplings and check the validity of the gauge principle in the SM. Since the tree-level predictions alone are inadequate to meet this demand, the next-to-leading order (NLO) calculation becomes compulsory. In this paper, we calculate the NLO QCD + NLO electroweak (EW) corrections to the $W^{\pm}ZZ$ productions with subsequent leptonic decays at the $14~{\rm TeV}$ LHC…
Understanding the polarisation structure and providing precise predictions for multi-boson processes at the LHC is becoming urgent in the light of the upcoming run-3 and high-luminosity data. The CMS and ATLAS collaborations have already started using polarised predictions to perform template fits of the data, getting access to the polarisation of W and Z bosons. So far, only fully-leptonic decay channels have been considered in this perspective. The natural step forward is the investigation of hadronic decays of electroweak bosons. In this work, we compute NLO QCD corrections to the productio…
We present the complete next-to-leading order (NLO) QCD and NLO electroweak (EW) corrections to the $W$-boson pair production associated with a hard jet at the LHC including the spin correlated $W$-boson leptonic decays. The dependence of the leading order (LO) and NLO corrected cross sections on the jet transverse momentum cut is investigated. In dealing with the subsequent resonant $W$-boson decays, we adopt the {\sc MadSpin} method where the spin correlation effect is included. We also provide the LO and NLO corrected distributions of the transverse momenta and rapidities of final products.…
n this letter we investigate the various processes that can contribute to a final state consisting of a lepton, missing transverse momentum and two jets at Next to Leading Order (NLO) at the Tevatron. In particular we consider the production of W/Z + 2 jets, diboson pairs, single top and the tt process with both fully leptonic and semi-leptonic decays. We present distributions for the invariant mass of the dijet system and normalisations of the various processes, accurate to NLO.
We reconsider the complete set of four-quark operators in the Weak Effective Theory (WET) for non-leptonic $ΔF=1$ decays that govern $s\to d$ and $b\to d, s$ transitions in the Standard Model (SM) and beyond, at the Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers $N_f$ of active flavours, intermediate threshold corrections, as well as the issue of transformations between operator bases beyond leading order to facilitate the matching to high-energy completions or the Standard Model Effective Field Theory (SMEFT) at the electroweak scale. As a first step towards a SME…
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.
We present a calculation of the O(alpha_s) QCD corrections to the production of a Z boson in association with two photons and to triple photon production at hadron colliders. All final-state photons are taken as real. For the Z boson, we consider the decays both into charged leptons and into neutrinos including all off-shell effects. Numerical results are obtained via a Monte Carlo program based on the structure of the VBFNLO program package. This allows us to implement general cuts and distributions of the final-state particles. We find that the NLO QCD corrections are sizable and significant…
The computation of the NLO QCD corrections to the cross sections for W+W- gamma and ZZgamma production in hadronic collisions is presented. We consider the case of a real photon in the final state, but include full leptonic decays of the W and Z bosons. Numerical results for the LHC and the Tevatron are obtained through a fully flexible parton level Monte Carlo based on the structure of the VBFNLO program, allowing an easy implementation of arbitrary cuts and distributions. We show the dependence on scale variations of the integrated cross sections and provide evidence that NLO QCD corrections…
In various extensions of the Standard Model (SM) tree level non-leptonic decays of hadrons receive contributions from new heavy gauge bosons and scalars. Prominent examples are the right-handed W' bosons in left-right symmetric models and charged Higgs (H^\pm) particles in models with extended scalar sector like two Higgs doublet models and supersymmetric models. Even in the case of decays with four different quark flavours involved, to which penguin operators cannot contribute, twenty linearly independent operators, instead of two in the SM, have to be considered. Anticipating the important r…
In this paper we present the full NLO QCD + NLO EW corrections to the $Z$-boson pair production in association with a hard jet at the LHC. The subsequent $Z$-boson leptonic decays are included by adopting both the naive NWA and MadSpin methods for comparison. Since the $ZZ+{\rm jet}$ production is an important background for single Higgs boson production and new physics search at hadron colliders, the theoretical predictions with high accuracy for the hadronic production of $ZZ+{\rm jet}$ are necessary. We present the numerical results of the integrated cross section and various kinematic dist…
We present a computation of the O(alpha_s) QCD corrections to W^\pm Z γproduction at the Large Hadron Collider. The photon is considered as real, and we include full leptonic decays for the W and Z bosons. Based on the structure of the VBFNLO program package, we obtain numerical results through a fully flexible Monte Carlo program, which allows to implement general cuts and distributions of the final-state particles. The NLO QCD corrections are sizable and strongly exceed the theory error obtained by a scale variation of the leading-order result. Also, the shapes of relevant observables are si…
In this paper we present the NLO QCD + NLO EW corrections to the $ZZZ$ production with subsequent $Z$-boson leptonic decays at the LHC by adopting the improved narrow width approximation, which takes into account off-shell contributions and spin correlations. Integrated cross sections at $13$, $14$, $33$ and $100~{\rm TeV}$ hadron colliders and various kinematic distributions are presented. Our numerical results show that the jet emission correction accounts for a large part of the total QCD correction, especially in the high energy region. By applying a proper cut to the jet transverse moment…
We present the NLO QCD corrections to the processes p p and p anti-p to W+ W- b anti-b including leptonic decays of the W bosons. Non-resonant contributions as well as diagrams with doubly resonant and singly resonant top quark propagators are fully taken into account. We employ the narrow width approximation to perform the decays of the W bosons; spin correlations are however preserved. We also calculate observables relevant for top quark mass measurements, and study the impact of kinematical requirements and different scale choices on t anti-t asymmetries.
The calculation of $t\bar{t}Z$ production including leptonic decays of both $Z$ boson and top quarks via a partially or fully off-shell calculation represents a definite step forward towards a more accurate description of events whose signatures originate from $t\bar{t}Z$ production. In this talk we review two studies that represent the state of the art of theoretical modeling of $t\bar{t}Z$ production by either performing the NLO QCD calculation of the fully decayed $pp\rightarrow e^+ν_eμ^-\barν_μb\bar{b}τ^+τ^-$ process (see Ref. [1]) or matching the NLO QCD calculation of $pp\rightarrow t\ba…
We present for the first time NLO QCD Renormalization Group (RG) evolution matrices for non-leptonic $ΔF=2$ transitions in the Standard Model Effective Field Theory (SMEFT). To this end we transform first the known two-loop QCD anomalous dimension matrices (ADMs) of the BSM operators in the so-called BMU basis into the ones in the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. This allows us subsequently to find the two-loop QCD ADMs for the SMEFT non-leptonic $ΔF=2$ operators in the Warsaw basis. Ha…
We present the QCD radiative corrections to the full off-shell $\rm t\bar{t}W^+$ production, considering a final state with three charged leptons, two b jets and missing energy. All interferences, off-shell effects and spin correlations are included in the calculation. Beyond presenting integrated and differential results for the full off-shell process, we compare them with those obtained applying a double-pole approximation to the virtual corrections.
We compute the 1-loop (alpha_s^2) correction to hard spectator scattering in non-leptonic B decay tree amplitudes. This forms part of the NNLO contribution to the QCD factorization formula for hadronic B decays, and introduces a new rescattering phase that corrects the leading-order result for direct CP asymmetries. Among the technical issues, we discuss the cancellation of infrared divergences, and the treatment of evanescent four-quark operators. The infrared finiteness of our result establishes factorization of spectator scattering at the 1-loop order. Depending on the values of hadronic in…
We report on the calculation of the next-to-leading order QCD corrections to the production of W-boson pairs in association with a hard jet at the Tevatron and the LHC, which is an important source of background for Higgs and new-physics searches. Leptonic decays of the W bosons are included by applying an improved version of the narrow-width approximation that treats the W bosons as on-shell particles, but keeps the information on the W spin. A selection of differential NLO QCD cross sections is provided both for the LHC and the Tevatron. The QCD corrections stabilize the LO prediction for th…
Motivated by ongoing new physics searches in the top-quark sector at the Large Hadron Collider we report on the calculation of NLO QCD corrections to the Standard Model $pp\to t\bar{t}Z+X$ process in the tetra-lepton decay channel. This calculation is based on the matrix elements for the $e^+ ν_e\, μ^-\barν_μ\, b\bar{b} \,τ^+τ^-$ final state and includes all resonant and non-resonant Feynman diagrams, interferences and off-shell effects of the top quark as well as the $W$ and $Z$ gauge bosons. Also incorporated are photon-induced contributions. As it is customary for such studies, we show theo…
We report on the precision predictions for the $e^+e^-\to ZZγ$ process including $Z$-boson leptonic decays at the ILC in the standard model (SM). The calculation includes the full next-to-leading (NLO) electroweak (EW) corrections and high order initial state radiation (h.o.ISR) contributions. We find that the NLO EW corrections heavily suppress the LO cross section, and the h.o.ISR effects are notable near the threshold while become small in high energy region. We present the LO and the NLO EW+h.o.ISR corrected distributions of the transverse momenta of final $Z$-boson and photon as well as t…
Electron--positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies at high luminosity meson factories. A Monte Carlo generator called PHOKHARA has been constructed, which simulates this process at the next-to-leading order accuracy.
The production of top-quark pairs that subsequently decay hadronically and leptonically (lepton+jets channel) is one of the key processes for the study of top-quark properties at the LHC. In this article, NLO QCD corrections of order $\mathcal{O}{\left(α_{\rm s}^3α^{4}\right)}$ to the hadronic process ${\rm p}{\rm p}\to μ^-\barν_μ{\rm b}\bar{\rm b} {\rm j} {\rm j}$ are presented. The computation includes off-shell as well as non-resonant contributions, and experimental event selections are used in order to provide realistic predictions. The results are provided in the form of cross sections an…
We provide Standard Model expectations for the rare radiative decays B->K^* gamma, B->rho gamma and B-> omega gamma, and the electroweak penguin decays B->K^* l^+ l^- and B->rho l^+ l^- at the next-to-leading order (NLO), extending our previous results to b->d transitions. We consider branching fractions, isospin asymmetries and direct CP asymmetries. For the electroweak penguin decays, the lepton-invariant mass spectrum and forward-backward asymmetry is also included. Radiative and electroweak penguin transitions in b->d are mainly interesting in the search for new flavour-changing neutral cu…
We present a general purpose, parton-level Monte Carlo program for the calculation of the radiative ($L\toν\barνl+γ$) and rare ($L\toν\barνl'+ l^+l^-$) muon and tau decays at NLO in the effective Fermi theory. In the case of muon, these processes are irreducible Standard Model backgrounds to searches for lepton flavour violation at the PSI experiments MEG and Mu3e as they become indistinguishable from the corresponding signals when the neutrinos carry little energy. Furthermore, we argue that fully differential NLO corrections are very important for the analysis of measurements aiming at the p…
The measurement of the hadronic cross-section in $e^+ e^-$ annihilation at high luminosity factories using the radiative return method is motivated and discussed. A Monte Carlo generator which simulates the radiative process $e^+ e^- \to γ+hadrons$ at the next-to-leading order accuracy is presented. The analysis is then extended to the description of events with hard photons radiated at very small angle.
We present a calculation of the next-to-leading-order electroweak corrections to W+γ production, including the leptonic decay of the W boson and taking into account all off-shell effects of the W boson, where the finite width of the W boson is implemented using the complex-mass scheme. Corrections induced by incoming photons are fully included and find particular emphasis in the discussion of phenomenological predictions for the LHC. The corresponding next-to-leading-order QCD corrections are reproduced as well. In order to separate hard photons from jets, a quark-to-photon fragmentation funct…
The branching fractions of radiative leptonic $τ$ decays $(τ\to l ν\barν γ$, $l=e,μ)$ were recently measured by the Babar collaboration with a relative error of about 3%. The measurement of the branching ratio $\mathcal{B} (τ\to e \barν νγ)$, for a minimum photon energy of 10 MeV in the $τ$ rest frame, differs from our recent SM prediction by 3.5 standard deviations, whereas our result agrees with Babar's value for $\mathcal{B} (τ\to μ\barν νγ)$. Our predictions also agree with the measurement of $\mathcal{B} (μ\to e \barν νγ)$ by the MEG collaboration. We also report on a recent proposal to t…
In this work, we investigate the radiative leptonic decays D_(s)^- \to γ\ell \barν(\ell = e, μ) at tree level within the non-relativistic consistuent quark model and the effective Lagrangian for the heavy flavor decays. We find that the contributions for the three Feynman diagrams are all important. With the full calculation, the decay branching ratios are of the order of 10^-5 for D_s^- \to γ\ell \barνand 10^-6 for D^- \to γ\ell \barν, respectively. These decays can be measured at B factories and future CLEO-C experiments to determine the decay constants f_D_s and f_D.
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 νe e+ μ- \barν_μb\bar{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 this work we investigate the effects of the littlest Higgs model (LHM) up to the QCD next-to-leading order (NLO) on the $Z^0H^0$ associated production at the CERN Large Hadron Collider (LHC). We study the dependences of the leading order and NLO QCD corrected integrated cross sections for this process on the factorization/renormalization scale and the LHM parameters. We also provide the distributions of the transverse momenta of final decay products $μ^-$ and $τ^-$. Our results show that the heavy neutral gauge bosons $Z_H$ and $A_H$ could induce significant discrepancies from the standard …
We report on the calculation of the next-to-leading order QCD corrections to the production of W-boson pairs in association with a hard jet at the Tevatron and the LHC, which is an important source of background for Higgs and new-physics searches. Leptonic decays of the W bosons are included by applying an improved version of the narrow-width approximation that treats the W bosons as on-shell particles, but keeps the information on the W spin. Contributions from external bottom quarks are neglected, because they are either numerically suppressed or should be attributed to different processes s…
We complete the computation of the 1-loop (alpha_s^2) corrections to hard spectator scattering in non-leptonic B decays at leading power in Lambda/m_b by evaluating the penguin amplitudes. This extends the knowledge of these next-to-next-to-leading-order contributions in the QCD factorization formula for B decays to a much wider class of final states, including all pseudoscalar-pseudoscalar, pseudoscalar-vector, and longitudinally polarized vector-vector final states, except final states with eta or eta' mesons. The new 1-loop correction is significant for the colour-suppressed amplitudes, but…
We propose a new method to probe the magnetic and electric dipole moments of the $τ$ lepton using precise measurements of the differential rates of radiative leptonic $τ$ decays at high-luminosity $B$ factories. Possible deviations of these moments from the Standard Model values are analyzed in an effective Lagrangian approach, thus providing model-independent results. Analytic expressions for the relevant non-standard contributions to the differential decay rates are presented. Earlier proposals to probe the $τ$ dipole moments are examined. A detailed feasibility study of our method is perfor…
The leptonic asymmetry in semileptonic ttbar decays is measured with the CDF detector using the full Tevatron Run II dataset, which corresponds to 9.4 fb^-1 of integrated luminosity. The measured asymmetry is extrapolated to the full kinematic range and the measured value of A_FB^lep = 0.094^+0.032_-0.029 is compared to the NLO prediction A_FB^lep = 0.038 +/- 0.003.
Since the smallest leptonic mixing angle theta_{13} has been measured to be relatively large, it is quite promising to constrain or determine the leptonic Dirac CP-violating phase delta in future neutrino oscillation experiments. Given some typical values of delta = pi/2, pi, and 3pi/2 at the low-energy scale, as well as current experimental results of the other neutrino parameters, we perform a systematic study of the radiative corrections to delta by using the one-loop renormalization group equations in the minimal supersymmetric standard model and the universal extra-dimensional model. It t…
For the first time the next-to-leading-order electroweak corrections to the full off-shell production of two top quarks that decay leptonically are presented. This calculation includes all off-shell, non-resonant, and interference effects for the 6-particle phase space. While the electroweak corrections are below one per cent for the integrated cross section, they reach up to 15% in the high-transverse-momentum region of distributions. To support the results of the complete one-loop calculation, we have in addition evaluated the electroweak corrections in two different pole approximations, one…
We compute the hadronic production of top-antitop pairs in association with a Higgs boson at next-to-leading-order QCD, including the decay of the top and antitop quark into bottom quarks and leptons. Our computation is based on full leading and next-to-leading-order matrix elements for $e^+ ν_e μ^-\barν_μb \bar{b} H(j)$ and includes all non-resonant contributions, off-shell effects and interferences. Numerical results for the integrated cross section and several differential distributions are given for the LHC operating at 13 TeV using a fixed and a dynamical factorization and renormalization…
Rare radiative leptonic decay $B\to l\bar ν_l γ$ is studied in the instantaneous Bethe-Salpeter approach. The results are compared to other relativistic quark model predictions.
We show that the so-called parity-conserving amplitudes predicted in the a priori mixing scheme for non-leptonic and weak radiative decays of hyperons vanish in the strong-flavor symmetry limit.
We present a general purpose Monte Carlo program for the calculation of the radiative muon decay $μ\to e\,ν\barνγ$ and the radiative decays $τ\to e\, ν\barνγ$ and $τ\toμ\,ν\barνγ$ at next-to-leading order in the Fermi theory. The full dependence on the lepton masses and polarization of the initial-sate lepton are kept. We study the branching ratios for these processes and show that fully-differential next-to-leading order corrections are important for addressing a tension between BaBar's recent measurement of the branching ratio $\mathcal{B}(τ\to e\, ν\barνγ)$ and the Standard Model prediction…
In this work we investigate the NLO QCD+EW corrections to the top quark pair production and their effects on the spin correlation coefficients and asymmetries at fixed-order top quark pair production and LO decay in the dilepton channel, within the narrow-width approximation. The spin correlations are implicitly measured through the lepton kinematics. Moreover we study the EW effects to the leptonic differential distributions. We find that the EW corrections to the $t \bar t$ production are within the NLO QCD theoretical uncertainties for the spin correlation coefficients and the leptonic asym…
We study the radiative leptonic $B_c\to γ\ell\barν$ decays in the nonrelativistic QCD effective field theory, and consider a fast-moving photon. As a result the interactions with the heavy quarks can be integrated out, and thus we arrive at a factorization formula for the decay amplitude. We calculate not only the relevant short-distance coefficients at leading order and next-to-leading order in $α_s$, but also the nonrelativistic corrections at the order $|\bold{v}|^2$ in our analysis. We find out that the QCD corrections can sizably decrease the branching ratio and thus is of great importanc…
Exclusive non-leptonic two-body decays of $B$ mesons have been studied extensively in the past two decades within the framework of factorization. However, the exploration of the corresponding three-body case has only started recently, in part motivated by new data. We consider here the simplest non-leptonic three-body $B$ decays from the point of view of factorization, namely heavy-to-heavy transitions. We provide a careful derivation of the SCET/QCDF factorized amplitudes to NNLO in $α_s$, and discuss the numerical impact of NLO and NNLO corrections. We then study the narrow-width limit, show…
We discuss the next to the leading order (NLO) electroweak radiative corrections to the $e^- e^+ \rightarrow f^- f^+ (γ)$ cross section asymmetry, for polarized and unpolarized beam scenario. The left-right and forward-backward amplitudes, with and without radiative corrections, are evaluated and compared for various kinematics. The hard bremsstrahlung is included for arbitrary energy cuts. The radiative corrections are shown to be significant and having a non-trivial dependency on the kinematic conditions. The calculations are relevant for the ultra-precise low-energy experiment Belle~II plan…
I discuss recent developments on non-leptonic and radiative kaon decays mainly related to direct CP-violation within the combined ChPT and 1/N_c expansion approaches. In particular, I review the status of K -> pi pi, epsilon_K', direct CP-violating K+ -> 3 pi Dalitz plot slope g and decay rate asymmetries, and the Standard Model prediction for Br(K_L -> pi0 e+ e-).
Università di Pavia（帕维亚大学）；INFN, Sezione di Pavia（意大利国家核物理研究所帕维亚分部）；Università di Pisa（比萨大学）；INFN, Sezione di Pisa（意大利国家核物理研究所比萨分部）；Università di Ferrara（费拉拉大学）；INFN, Sezione di Ferrara（意大利国家核物理研究所费拉拉分部）；INFN, Galileo Galilei Institute for Theoretical Physics（意大利国家核物理研究所伽利略·伽利莱理论物理研究所）
A priori mixings of eigenstates in physical states are quantum mechanical effects well known in several realms of physics. The possibility that such effects are also present in particle physics, in the form of flavor and parity mixings, is studied. Applications to weak radiative and non-leptonic decays of hyperons are discussed.
The radiative leptonic $B_{c}\toτ\bar{ν_τ}γ$ decay is analysed in context of 2HDM. It is shown that with large values of $tanβ$, the contributions of Model II to the decay rate exceeds considerably the Standard Model ones, while the contributions of Model I overlap with the Standard Model predictions.
We propose a method to determine the leptonic decay constant $f_{B^*}$ in the infinite heavy quark mass limit from the analysis of the radiative decay mode $B^- \to \ell^- {\bar ν}_\ell γ$. The method relies on HQET symmetries and on experimental data from $D^{*0} \to D^0 γ$.
We study the forward-backward and the CP-violating asymmetries (both time-independent and time-dependent) in rare semileptonic and radiative leptonic B_{d,s}-decays and investigate the sensitivity of these asymmetries to the extensions of the Standard model.
The next-to-leading-order electroweak corrections to $pp\to l^+l^-/\barνν+γ+X$ production, including all off-shell effects of intermediate Z bosons in the complex-mass scheme, are calculated for LHC energies, revealing the typically expected large corrections of tens of percent in the TeV range. Contributions from quark-photon and photon-photon initial states are taken into account as well, but their impact is found to be moderate or small. Moreover, the known next-to-leading-order QCD corrections are reproduced. In order to separate hard photons from jets, both a quark-to-photon fragmentation…
Three CP-violating phases of the $3\times 3$ lepton flavor mixing matrix $V$ are entangled with one another in the renormalization-group evolution from the seesaw scale ($Λ_{\rm SS} \sim 10^{14}$ GeV) to the electroweak scale ($Λ_{\rm EW} \sim 10^2$ GeV). Concerning the Dirac phase $δ$, we show that $δ=90^\circ$ at $Λ_{\rm EW}$ can be radiatively generated from $δ=0^\circ$ at $Λ_{\rm SS}$ in the minimal supersymmetric standard model, if three neutrino masses are nearly degenerate. As for the Majorana phases $ρ$ and $σ$, it is also possible to radiatively generate $ρ=90^\circ$ or $σ= 90^\circ$ …
In this work we study the radiative leptonic decays of $B^-$, $D^-$ and $D_s^-\to γl \barν$, including both the short-distance and long-distance contributions. The short-distance contribution is calculated by using the relativistic quark model, where the bound state wave function we used is that obtained in the relativistic potential model. The long-distance contribution is estimated by using vector meson dominance model.
We discuss top-quark physics at the ILC with a focus on the full off-shell processes for $t\bar{t}$ and $t\bar{t}H$ production, including top-quark decays and also leptonic $W$ decays. A special focus is on the matching of the resummed vNRQCD threshold calculation and the fixed-order NLO QCD continuum calculation, where we present an update on the validation of the matching. All of the calculations have been performed in the \wz event generator framework.
