Two-loop Vertices with Vacuum Polarization Insertion

TL;DR

This paper analytically computes second-order corrections to massive form factors involving two-loop vertex diagrams with vacuum polarization, accounting for exact mass and momentum transfer dependencies.

Contribution

It provides the first exact analytic expressions for these two-loop form factors with vacuum polarization insertions, including all mass and momentum transfer effects.

Findings

Finite expressions in terms of polylogarithms up to weight three.

Applicable to vector, axial-vector, scalar, and pseudoscalar interactions.

Enhances precision in theoretical predictions of fermion interactions.

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.