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We report on the complete computation of the mixed QCD-electroweak corrections to the neutral-current Drell-Yan process. Our calculation holds in the entire range of dilepton invariant masses. We present phenomenological results for several kinematical distributions in the case of bare muons both in the resonant region and for high invariant masses. We also consider the forward-backward asymmetry, which is a key observable to measure the weak mixing angle. We finally extend our calculation to dressed leptons and compare our results in the massless limit to those available in the literature., Comment: 27 pages, 7 Figures, and 2 Tables

We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two different internal massive lines, has been worked out relying on semi-analytical techniques, using complex-valued masses. We can provide, at any arbitrary phase-space point, the solution as a power series in the $W$-boson mass, around a reference value. Starting from these expansions, we can prepare a numerical grid for any value of the $W$-boson mass within their radius of convergence in a negligible amount of time., Comment: 26 pages, 7 figures. arXiv admin note: text overlap with arXiv:2201.01754

We present the computation of the two-loop form factors for diphoton production in the quark annihilation channel. These quantities are relevant for the NNLO QCD corrections to diphoton production at LHC recently presented in arXiv:2308.10885. The computation is performed retaining full dependence on the mass of the heavy quark in the loops. The master integrals are evaluated by means of differential equations which are solved exploiting the generalised power series technique., Comment: 23 pages, 5 figures

In this paper we consider the diphoton production in hadronic collisions at the next-to-next-to-leading order (NNLO) in perturbative QCD, taking into account for the first time the full top quark mass dependence up to two loops (full NNLO). We show selected numerical distributions, highlighting the kinematic regions where the massive corrections are more significant. We make use of the recently computed two-loop massive amplitudes for diphoton production in the quark annihilation channel. The remaining massive contributions at NNLO are also considered, and we comment on the weight of the different types of contributions to the full and complete result., Comment: 14 pages and 5 figures

We compute the next-to-leading-order (NLO) QCD corrections to the Higgs pT distribution in Higgs production in association with a jet via gluon fusion at the LHC, with exact dependence on the mass of the quark circulating in the heavy-quark loops. The NLO corrections are presented including the top-quark mass, and for the first time, the bottom-quark mass as well. Further, besides the on-shell mass scheme, we consider for the first time a running mass renormalisation scheme. The computation is based on amplitudes which are valid for arbitrary heavy-quark masses., Comment: LaTeX, 7 pages, 5 figures

We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package \textsc{SeaSyde}. The implementation solves by series expansions the system of differential equations satisfied by the Master Integrals. At variance with respect to other existing codes, the analytical continuation of the solution is performed in the complex plane associated to each kinematical invariant. We present the results of the evaluation of the Master Integrals relevant for the NNLO QCD-EW corrections to the neutral-current Drell-Yan processes., Comment: 23 pages, 6 figures, 2 tables, Version accepted for publication in CPC

We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, in ancillary files, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses., Comment: 33 pages, 5 figures; Ancillary files attached; Version accepted for publication in JHEP

The analytical expressions of the mixed QCD-EW corrections to on-shell Z boson inclusive production cross section at hadron colliders are presented, together with computational details. The results are given in terms of polylogarithmic functions and elliptic integrals. The impact on the prediction of the Z boson production total cross section is discussed, comparing different proton parton density sets.

We present the analytic evaluation of the two-loop corrections to the amplitude for the scattering of four fermions in Quantum Electrodynamics, $f^- + f^+ + F^- + F^+ \to 0$, with $f$ and $F$ representing a massless and a massive lepton, respectively. Dimensional regularization is employed to evaluate the loop integrals. Ultraviolet divergences are removed by renormalizing the coupling constant in the ${\overline{\text{MS}}}$-scheme, and the lepton mass as well as the external fields in the on-shell scheme. The analytic result for the renormalized amplitude is expressed as Laurent series around $d=4$ space-time dimensions, and contains Generalized Polylogarithms with up to weight four. The structure of the residual infrared divergences of the virtual amplitude is in agreement with the prediction of the Soft Collinear Effective Theory. Our analytic results are an essential ingredient for the computation of the scattering cross section for massive fermion-pair production in massless fermion-pair annihilation, i.e. $f^- f^+ \to F^- F^+$, and crossing related processes such as the elastic scattering $f F \to f F$, with up to Next-to-Next to Leading Order accuracy., Comment: 5 pages, 2 figures, 1 table + supplemental material. v2: references added; plots added; Table 1: finite part of A(2) fixed; matches published version

We report on the first complete computation of the mixed QCD$-$electroweak (EW) corrections to the neutral-current Drell$-$Yan process. Superseding previously applied approximations, our calculation provides the first result at this order that is valid in the entire range of dilepton invariant masses. The two-loop virtual contribution is computed by using semi-analytical techniques, overcoming the technical problems in the evaluation of the relevant master integrals. The cancellation of soft and collinear singularities is achieved by a formulation of the $q_T$ subtraction formalism valid in presence of charged massive particles in the final state. We present numerical results for the fiducial cross section and selected kinematical distributions. At large values of the lepton $p_T$ the mixed QCD$-$EW corrections are negative and increase in size, to about $-15\%$ with respect to the next-to-leading-order QCD result at $p_T=500\,$GeV. Up to dilepton invariant masses of 1 TeV the computed corrections amount to about $-1.5\%$ with respect to the next-to-leading-order QCD result., Comment: 8 pages, 2 figures and 1 table

We present for the first time the exact NLO QCD corrections to the light-quark part of the mixed QCD-EW contributions to Higgs production via gluon fusion at LHC13, with exact EW-boson mass dependence. The relevant two-loop real-emission matrix element is computed using a dynamic one-dimensional series expansion strategy whose stability and speed allows for a numerical phase-space integration using local IR subtraction counterterms. For $\mu_R=\mu_F=M_H$, we find: \begin{equation}\sigma^{(\alpha_s^2\alpha^2+\alpha_s^3\alpha^2)}_{g g\rightarrow H+X} = 1.467(2)^{\;+18.7\%}_{\;-14.6\%}\;(\mu_R\;\text{var.})\;\pm 2\%\;(\text{PDF}) \ \textrm{pb},\end{equation} which we use to provide the best result including an estimate of suppressed contributions: \begin{equation}\sigma^{(\text{EW},\textrm{best})}_{p p\rightarrow H+X} = 2.11 \pm 0.28 \ (\textrm{theory}) \ \mathrm{pb}.\end{equation}, Comment: 7 pages, 4 figures

We present the first analytical results for the ${\cal O}(\alpha\alpha_s)$ corrections to the total cross section for the inclusive production of an on-shell $Z$ boson at hadron colliders. We include the complete set of contributions, with photonic and massive weak gauge boson effects, which have been computed in analytical form and expressed in terms of polylogarithmic and elliptic integrals. We present numerical results, relevant for the precision studies at the LHC. These corrections increase the accuracy of the predictions and contribute to the reduction of the QCD component of the theoretical uncertainty., Comment: 6 pages, 4 tables

We outline the computational details to obtain mixed EW-QCD corrections to on-shell production of a single vector boson at the LHC at two-loop level. We use the method of differential equation to obtain the pure virtual, real-virtual and double-real master integrals. Finally, we obtain the ${\cal O}(\alpha \alpha_s)$ corrections to the total partonic cross section of the process $q \bar{q} \rightarrow Z + X$., Comment: 12 pages; To appear in the proceedings of RADCOR 2019, 9th - 13th September 2019, Avignon, France

We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the quark-annihilation channel, which are not yet known analytically. The master integrals have been computed exploiting the differential equations method in canonical form. The solution is given as a series expansion in the dimensional regularization parameter through to weight four, the expansion coefficients are given in terms of multiple polylogarithms., Comment: 11 pages, 2 figures, talk given at RADCOR2019, based on arXiv:1904.10834

We present the first results for the ${\cal O}(\alpha\alpha_s)$ corrections to the total partonic cross section of the process $q\bar q\to Z+X$, with the complete set of contributions, that include photonic and massive weak gauge boson effects. The results are relevant for the precise determination of the hadronic $Z$ boson production cross section. Virtual and real corrections are calculated analytically using the reduction to the master integrals and their evaluation through differential equations. Real corrections are dealt with using the reverse-unitarity method. They require the evaluation of a new set of two-loop master integrals, with up to three internal massive lines. In particular, three of them are expressed in terms of elliptic integrals. We verify the absence, at this perturbative order, of initial state mass singularities proportional to a weak massive virtual correction to the quark-gluon splitting., Comment: 6 pages, 1 figure

We present the analytic computation of a family of non-planar master integrals which contribute to the two-loop scattering amplitudes for Higgs plus one jet production, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to inclusive Higgs production and for the NLO corrections to Higgs production in association with a jet, in QCD. The computation of the integrals is performed with the method of differential equations. We provide a choice of basis for the polylogarithmic sectors, that puts the system of differential equations in canonical form. Solutions up to weight 2 are provided in terms of logarithms and dilogarithms, and 1-fold integral solutions are provided at weight 3 and 4. There are two elliptic sectors in the family, which are computed by solving their associated set of differential equations in terms of generalized power series. The resulting series may be truncated to obtain numerical results with high precision. The series solution renders the analytic continuation to the physical region straightforward. Moreover, we show how the series expansion method can be used to obtain accurate numerical results for all the master integrals of the family in all kinematic regions.

We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator $\epsilon$ and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four., Comment: 28 pages, 2 figures, ancillary files included

We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular points. The different series are then matched numerically with high accuracy in intermediate points. The expansions allow a fast and precise numerical calculation of the two master integrals in all the regions of the phase space. A numerical routine that implements these expansions is presented., Comment: 23 pages, 2 figures, numerical routine available with submission

We present the analytic calculation of the planar master integrals which contribute to compute the two-loop light-fermion electroweak corrections to the production of a Higgs boson in association with a jet in gluon-gluon fusion. The complete dependence on the electroweak-boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic results are expressed in terms of multiple polylogarithms up to weight four., Comment: 21 pages, ancillary files

We evaluate analytically the master integrals for double real radiation emission in the b --> u W* decay, where b and u are a massive and massless quark, respectively, while W* is an off-shell charged weak boson. Since the W boson can subsequently decay in a lepton anti-neutrino pair, the results of the present paper constitute a further step toward a fully analytic computation of differential distributions for the semileptonic decay of a b quark at NNLO in QCD. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B mesons. Our results are expressed in terms of multiple polylogarithms of maximum weight four., Comment: 21 pages, 6 figures, 2 tables

We propose a new method to calculate analytically higher-order perturbative corrections and we apply it to the calculation of the two-loop virtual corrections to Higgs pair production through gluon fusion. The method is based on the expansion of the amplitudes in terms of a small Higgs transverse momentum. This approach gives a very good approximation (better than per-mille) of the partonic cross section in the center of mass energy region $\sqrt{\hat{s}} \lesssim 750$ GeV, where $\sim95\%$ of the total hadronic cross section is concentrated. The presented method is general and can be applied in a straightforward way to the computation of virtual higher-order corrections to other $2\to2$ processes, representing an improvement with respect to calculations based on heavy mass expansions., Comment: 6 pages, 2 figures; V2: Version accepted for publication

We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The masters are evaluated by means of the differential equations method and expressed in terms of multiple polylogarithms and one- or two-fold integrals of polylogarithms and irrational functions, up to transcendentality four., Comment: 20 pages, ancillary files