Vertex diagrams for the QED form factors at the 2-loop level Original Research Article

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous D-dimensional regularization scheme, for on-shell electrons, momentum transfer t=−Q2 and finite squared electron mass me2=a. We identify all the master integrals (MIs) of the problem and write the differential equations in Q2 which they satisfy. The equations are expanded in powers of ϵ=(4−D)/2 and solved by the Eulerʹs method of the variation of the constants. As a result, we obtain the coefficients of the Laurent expansion in ϵ of the MIs up to zeroth order expressed in close analytic form in terms of harmonic polylogarithms.