Singlet and non-singlet three-loop massive form factors

TL;DR

This paper computes three-loop corrections to massive form factors in QCD for various currents, using a semi-numerical method that ensures high precision across all kinematic regimes, aiding practical applications.

Contribution

It introduces a semi-numerical approach for calculating three-loop massive form factors in QCD, achieving high precision and broad kinematic coverage.

Findings

At least seven significant digits in form factor calculations.

Method covers entire kinematic range for both negative and positive s.

Results are provided as series expansions and interpolation functions.

Abstract

We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a semi-numerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy $s$ which allows to cover the whole kinematic range for negative and positive values of $s$. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current set-up we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.