The $O(\alpha_s^3 n_f T_F^2 C_{A,F})$} Contributions to the Gluonic Massive Operator Matrix Elements

TL;DR

This paper computes specific third-order quantum chromodynamics corrections to gluonic operator matrix elements for general Mellin variables, crucial for precise theoretical predictions in particle physics.

Contribution

It introduces a novel calculation of $O( ext{ extit{alpha}}_s^3 n_f T_F^2 C_{A,F})$ terms for massive gluonic matrix elements at NNLO, using hypergeometric series and harmonic sums.

Findings

Analytic expressions for the matrix elements are obtained.

The results are valid for complex Mellin variable N.

Provides tools for improved precision in QCD calculations.

Abstract

The $O(\alpha_s^3 n_f T_F^2 C_{A,F})$ terms to the massive gluonic operator matrix elements are calculated for general values of the Mellin variable $N$. These twist-2 matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of $N$ is provided.