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

R. Bonciani; P. Mastrolia; E. Remiddi

doi:10.1016/j.nuclphysb.2004.08.009

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arXiv · hep-ph/0301170

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

R. Bonciani·P. Mastrolia·E. Remiddi

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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 $ε= (4-D)/2$ 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.

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R. Bonciani, P. Mastrolia, E. Remiddi. 2004-06-25. Vertex diagrams for the QED form factors at the 2-loop level. https://doi.org/10.1016/j.nuclphysb.2004.08.009

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