Planar box diagram for the (NF=1) 2-loop QED virtual corrections to Bhabha scattering Original Research Article

In this paper we present the master integrals necessary for the analytic calculation of the box diagrams with one electron loop (NF=1) entering in the 2-loop (α3) QED virtual corrections to the Bhabha scattering amplitude of the electron. We consider on-shell electrons and positrons of finite mass m, arbitrary squared c.m. energy s, and momentum transfer t; both UV and soft IR divergences are regulated within the continuous D-dimensional regularization scheme. After a brief overview of the method employed in the calculation, we give the results, for s and t in the Euclidean region, in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3. The corresponding results in the physical region can be recovered by analytical continuation. For completeness, we also provide the analytic expression of the 1-loop scalar box diagram including the first order in (D−4).