Top quark contribution to two-loop helicity amplitudes for ZZ boson pair production in gluon fusion

We compute the top quark contribution to the two-loop amplitude for on-shell $Z$ boson pair production in gluon fusion, $gg \to ZZ$. Exact dependence on the top quark mass is retained. For each phase space point the integral reduction is performed numerically and the master integrals are evaluated using the auxiliary mass flow method, allowing fast computation of the amplitude with very high precision

Virtual corrections to gg→ZHgg\to ZH via a transverse momentum expansion

We compute the next-to-leading virtual QCD corrections to the partonic cross section of the production of a Higgs boson in association with a $Z$ boson in gluon fusion. The calculation is based on the recently introduced method of evaluating the amplitude via an expansion in terms of a small transverse momentum. We generalize the method to the case of different masses in the final state and of a process not symmetric in the forward-backward direction exchange. Our analytic approach gives a very good approximation (better than percent) of the partonic cross section in the center of mass energy region up to $\sim 750 \,\textrm{GeV}$, where at the LHC $\sim 98\%$ of the total hadronic cross section is concentrated.Comment: 21 pages, 3 Figures and 1 Tabl

Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion

We compute the contribution of third generation quarks ($t,\ b$) to the two-loop amplitude for on-shell $W$ boson pair production in gluon fusion $gg \to WW$. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations

Toward three-loop Feynman massive diagram calculations

There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in e+e collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observables, such as scattering asymmetries, effective weak mixing angles, and decay widths, related to the Z-boson will meet severe experimental requirements at the planned e+e colliders and will increase the chance to detect non-standard effects in experimental analysis. To reach this goal, one has to calculate the next order of perturbative SM theory, namely three-loop Feynman integrals. We discuss the complexity of the problem, as well as the methods crucial for completing three-loop calculations. We show several numerical solutions for some three-loop Feynman integrals using sector decomposition, Mellin–Barnes (MB), and differential equation methods

Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion

We compute the contribution of third generation quarks (t, b) to the two-loop amplitude for on-shell W boson pair production in gluon fusion gg -> WW. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations

Numerical scattering amplitudes with pySecDec

We present a major update of the program pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The new version enables the evaluation of multi-loop integrals as well as amplitudes in a highly distributed and flexible way, optionally on GPUs. The program has been optimised and runs up to an order of magnitude faster than the previous release. A new integration procedure that utilises construction-free median Quasi-Monte Carlo rules is implemented. The median lattice rules can outperform our previous component-by-component rules by a factor of 5 and remove the limitation on the maximum number of sampling points. The expansion by regions procedures have been extended to support Feynman integrals with numerators, and functions for automatically determining when and how analytic regulators should be introduced are now available. The new features and performance are illustrated with several examples

Two-loop QCD-EW master integrals for Z plus jet production at large transverse momentum

The production of electroweak Z bosons that decay to neutrinos and recoil against jets with large transverse momentum p$_{⊥}$ is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benet from opportunities offered by the future high-luminosity LHC, the theoretical description of the pp → Z + j process should be extended to include mixed QCD-electroweak corrections. The goal of this paper is to initiate the computation of such corrections starting with the calculation of the Feynman integrals needed to describe two-loop QCD-electroweak contributions to qq̅ → Z + g scattering amplitudes. Making use of the hierarchy between the large transverse momenta of the recoiling jet, relevant for heavy dark matter searches, and the Z boson mass m$_{Z}$, we present the relevant master integrals as a series expansion in m$_{Z}$/p$_{⊥}$