${\mathcal{O}(\alpha_s^2 \alpha)}$ corrections to quark form factor

TL;DR

This paper computes the three-loop mixed strong-electroweak corrections to quark form factors, addressing complex integrals involving massive vector bosons and providing finite results expressed through advanced polylogarithms.

Contribution

It provides the first analytic calculation of non-singlet three-loop mixed QCD-electroweak corrections to quark form factors with massive vector bosons.

Findings

Analytic expressions for three-loop mixed corrections obtained.

Results expressed in Harmonic and Generalized Polylogarithms.

Addresses complexities of massive vector boson loops in high-order calculations.

Abstract

We present the analytic results for the non-singlet contributions to the three-loop mixed strong-electroweak ${\mathcal{O}}(\alpha_s^2\alpha)$ virtual corrections to the quark form factors. The primary challenge of this computation arises from the presence of massive vector bosons within the loops. This significantly increases the complexity of the integration-by-parts reduction of the scalar integrals and complicates their evaluation via the method of differential equations. To obtain the physical results, we perform the appropriate ultraviolet renormalization and subtract the universal infrared divergences. The resulting finite remainders are expressed in terms of Harmonic Polylogarithms and Generalized Polylogarithms.