The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O(\alpha_s^3)$

TL;DR

This paper analytically computes the polarized massive operator matrix element $A_{gq}^{(3)}(N)$ at three-loop order in QCD for general Mellin variable $N$, crucial for the variable flavor number scheme at $O( ext{alpha}_s^3)$, including single- and double-mass cases.

Contribution

It provides the first analytical calculation of the polarized massive operator matrix element $A_{gq}^{(3)}(N)$ at three-loop order in QCD for general $N$, in both single- and double-mass scenarios.

Findings

Analytical expressions for $A_{gq}^{(3)}(N)$ in Mellin space.

Results in momentum fraction space.

Applicable to variable flavor number scheme at $O( ext{alpha}_s^3)$.

Abstract

We calculate the polarized massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable $N$ both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at $O(\alpha_s^3)$. We also present the results in momentum fraction space.