Two-loop vertices with vacuum polarization insertion

Abstract

We present the analytic evaluation of the second-order corrections to the massive form factors, due to two-loop vertex diagrams with a vacuum polarization insertion, with exact dependence on the external and internal fermion masses, and on the squared momentum transfer. We consider vector, axial-vector, scalar and pseudoscalar interactions between the external fermion and the external field. After renormalization, the finite expressions of the form factors are expressed in terms of polylogarithms up to weight three.

Theory for the MUonE experiment

“…The precision goal of the MUonE experiment requires a theoretical computation of the muonelectron elastic scattering with an accuracy of 10 ppm on the differential cross section [12]. In order to achieve this level of precision, the calculation must include QED corrections at least at the Next-to-Next-to-Leading Order (NNLO) accuracy [13][14][15][16][17][18][19][20][21][22], as well as electroweak [13] and hadronic [23,24] contributions. Since the electron mass 𝑚 𝑒 cannot be neglected, a significant…”