The O(\alpha_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity

TL;DR

This paper computes the three-loop massive operator matrix elements for heavy flavor contributions to the structure function F_2 and transversity, providing new results for anomalous dimensions using advanced summation techniques.

Contribution

It presents the first complete calculation of certain three-loop operator matrix elements and anomalous dimensions for heavy flavor contributions in deep inelastic scattering.

Findings

Complete results for two matrix elements $A_{qq,Q}^{ ext{PS}}(N)$ and $A_{qg,Q}(N)$.

First independent computation of specific three-loop anomalous dimensions.

Use of advanced summation technologies to handle nested sums and harmonic sums.

Abstract

The contributions $\propto n_f$ to the $O(\alpha_s^3)$ massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit $Q^2 \gg m^2$ are computed for the structure function $F_2(x,Q^2)$ and transversity for general values of the Mellin variable $N$. Here, for two matrix elements, $A_{qq,Q}^{\sf PS}(N)$ and $A_{qg,Q}(N)$, the complete result is obtained. A first independent computation of the contributions to the 3--loop anomalous dimensions $\gamma_{qg}(N)$, $\gamma_{qq}^{\sf PS}(N$ and $\gamma_{qq}^{\sf NS,(TR)}(N)$ is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only.