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

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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

e p s i l o n = (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

e p s i l o n

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

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