Master integrals for the 2-loop QCD virtual corrections to the forward–backward asymmetry

Abstract

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q 2 and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The Master Integrals are Laurent-expanded around D = 4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

“…The MIs needed for the calculation presented in this paper were already known in the literature [73,74,[100][101][102][103][104][105][106][107][108][109][110][111][112][113]. In particular, all of the two-loop four-point MIs encountered in the calculation of the leading color coefficient in the gluon-fusion channel coincide with the ones needed for the corresponding calculation in the quark-antiquark annihilation channel [74], or can be obtained by the latter by replacing the Mandelstam variable t with u.…”

Heavy quark form factors at two loops

“…This technique has already been applied to massive form factor integrals at two and three loops in [25,77,78]. In this work, we calculate the two-loop master integrals up to a sufficiently high order in ε to obtain Oðε 2 Þ accuracy in the form factors.…”

Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

“…The master integrals in the third, fourth and fifth line in figure 3 are non-factorizable. Integrals in the third and fourth line were calculated already in [18] 1 and [22,21,19]. respectively.…”