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

Paper

Abstract

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous

-dimensional regularization scheme, for on-shell electrons, momentum transfer

and finite squared electron mass

. We identify all the Master Integrals (MI's) of the problem and write the differential equations in

which they satisfy. The equations are expanded in powers of

and solved by the Euler's method of the variation of the constants. As a result, we obtain the coefficients of the Laurent expansion in

of the MI's up to zeroth order expressed in close analytic form in terms of Harmonic Polylogarithms.