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

Abstract

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 $t=-Q^2$ and finite squared electron mass $m_e^2=a$. We identify all the Master Integrals (MI's) of the problem and write the differential equations in $Q^2$ which they satisfy. The equations are expanded in powers of $ϵ=(4-D)/2$ 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 $ϵ$ of the MI's up to zeroth order expressed in close analytic form in terms of Harmonic Polylogarithms.

Comments: A few misprints have been corrected. The results are now available at http://pheno.physik.uni-freiburg.de/~bhabha, as FORM input files