3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$

TL;DR

This paper calculates 3-loop order contributions to the heavy flavor operator matrix element $A_{gg}$ in the variable flavor number scheme, revealing complex nested sums and integrals involving square-root letters.

Contribution

It provides the first calculation of two-mass 3-loop contributions to $A_{gg}$, including novel nested sums and iterated integrals with square-root letters.

Findings

Finite nested binomial sums in Mellin space.

Iterated integrals with square-root valued letters in x-space.

Enhanced understanding of heavy flavor contributions at 3-loop order.

Abstract

Contributions to heavy flavour transition matrix elements in the variable flavour number scheme are considered at 3-loop order. In particular a calculation of the diagrams with two equal masses that contribute to the massive operator matrix element $A_{gg,Q}^{(3)}$ is performed. In the Mellin space result one finds finite nested binomial sums. In $x$-space these sums correspond to iterated integrals over an alphabet containing also square-root valued letters.