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

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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).