Massive vector form factors to three loops

TL;DR

This paper presents a detailed three-loop calculation of photon-quark form factors, incorporating full mass and virtuality dependence, achieving high precision across all kinematic regimes.

Contribution

It introduces a novel combination of differential equations and expansion techniques to compute form factors with unprecedented accuracy at three loops.

Findings

Achieved high-precision results for form factors across all kinematic ranges.

Successfully incorporated full mass and virtuality dependence in three-loop calculations.

Enhanced computational methods for multi-loop form factor evaluations.

Abstract

We compute the three-loop non-singlet corrections to the photon-quark form factors taking into account the full dependence on the virtuality of the photon and the quark mass. We combine the method of differential equations in an effective way with expansions around regular and singular points. This allows us to obtain results for the form factors with an accuracy of about eight to twelve digits in the whole kinematic range.