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

Abstract

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.

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

“…We employ the same renormalisation scheme as used in ref. [13] where the gluon field G µ and the top quark mass m t are computed in the on-shell scheme while the strong coupling constant, α s , is renormalised in the MS scheme. The relations between bare and renormalised quantities read…”

“…The approach to integral reduction described here is in variance to our approach in previous work [13] where reductions were performed with s and t as free parameters. We kept the reductions tractable by projecting integrals onto one master integral at a time which, however, in turn made bookkeeping more involved.…”

“…To compute the 205 two-loop master integrals we follow the same procedure as described in ref. [13] and employ the auxiliary mass flow method [14,15]. We construct a JHEP05(2021)244…”

“…To compute the gg → ZZ amplitude, we largely follow the method described in our paper on a similar process, gg → W W [13]. The main difference lies in the integral reduction.…”

Two-loop helicity amplitudes for gg → ZZ with full top-quark mass effects

“…Higgs mediated two-loop contributions to ZZ production involving a closed top-quark loop were calculated some time ago [37][38][39][40]. Contributions of the third generation quarks to W + W − production with exact mass dependence were computed recently in [41].…”