Abstract
We showcase the calculation of the master integrals needed for the two loop mixed QCD-QED virtual corrections to the neutral current Drell-Yan process ( qoverline{q} → l+l−). After establishing a basis of 51 master integrals, we cast the latter into canonical form by using the Magnus algorithm. The dependence on the lepton mass is then expanded such that potentially large logarithmic contributions are kept. After determining all boundary constants, we give the coefficients of the Taylor series around four space-time dimensions in terms of generalized polylogarithms up to weight four.
Highlights
JHEP11(2020)107 (a) Neutral Current (b) Charged Current were computed for the W and Z boson decay [23, 24] and the Z boson production [25]
As a first step towards the calculation of the relevant master integrals we identify a special set of master integrals, for which the dimensional regularization parameter factorizes from the kinematics
The lepton mass dependence was kept up to logarithmic terms, such that the incomplete cancellation of these potentially large contributions can be studied in cross sections which are not fully inclusive due to lepton identification cuts
Summary
This article considers the mixed QCD-QED two-loop corrections to the Drell-Yan process q(p1) + q(p2) → l+(p3) + l−(p4) ,. Specified by the following kinematics p21 = p22 = 0 , s = (p1 + p2) , p23 = p24 = m2l , t = (p1 − p3) , u = (p2 − p3)2 = 2m2l − s − t ,. Where the lepton mass ml was kept non-zero throughout the calculation. In particular our work is concerned with the quantum corrections involving the exchange of a photon and a Z boson between the initial and final state, depicted in figure 2. The appearing integrals are of the form. In the above definitions ki denote the loop momenta and the normalization factor C( ) has been chosen such that the canonical integral I9 is set to one
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