Two-Loop Four-Fermion Scattering Amplitude in QED

Understand

We present the analytic evaluation of the two-loop corrections to the amplitude for the scattering of four fermions in Quantum Electrodynamics, $f^- + f^+ + F^- + F^+ \to 0$, with $f$ and $F$ representing a massless and a massive lepton, respectively.

• Dimensional regularization is employed to evaluate the loop integrals.
• Ultraviolet divergences are removed by renormalizing the coupling constant in the ${\overline{\text{MS}}}$-scheme, and the lepton mass as well as the external fields in the on-shell scheme.
• The analytic result for the renormalized amplitude is expressed as Laurent series around $d=4$ space-time dimensions, and contains Generalized Polylogarithms with up to weight four.