The two-mass contribution to the three-loop pure singlet operator matrix element

TL;DR

This paper calculates the two-mass contributions to the three-loop pure singlet operator matrix element in QCD, essential for precise structure function and heavy quark distribution predictions.

Contribution

It provides the first calculation of two-mass three-loop contributions to the pure singlet operator matrix element in x-space, including generalized iterated integrals with square root letters.

Findings

Numerical results for the two-mass contributions are presented.

The results are relevant for $F_2(x,Q^2)$ at $O( ext{alpha}_s^3)$.

The calculation includes mass ratio dependence through generalized integrals.

Abstract

We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function $F_2(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.