$O(\alpha_s^2)$ and $O(\alpha_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2 \gg m^2$

TL;DR

This paper computes high-order heavy flavor contributions to the transversity distribution in deep-inelastic scattering, providing new analytical results for operator matrix elements and anomalous dimensions at two and three loops.

Contribution

It presents the first calculation of $O(eta_s^2)$ and $O(eta_s^3)$ massive operator matrix elements for transversity, extending previous knowledge to higher orders.

Findings

Calculated $O(eta_s^2)$ OME for general Mellin N

Computed moments N=1 to 13 at $O(eta_s^3)$

Confirmed terms in the 3-loop transversity anomalous dimension

Abstract

In deep-inelastic processes the heavy flavor Wilson coefficients factorize for $Q^2 \gg m^2$ into the light flavor Wilson coefficients of the corresponding process and the massive operator matrix elements (OMEs). We calculate the $O(\alpha_s^2)$ and $O(\alpha_s^3)$ massive OME for the flavor non-singlet transversity distribution. At $O(\alpha_s^2)$ the OME is obtained for general values of the Mellin variable $N$, while at $O(\alpha_s^3)$ the moments $N = 1$ to 13 are computed. The terms $\propto T_F$ of the 3--loop transversity anomalous dimension are obtained and results in the literature are confirmed. We discuss the relation of these contributions to the Soffer bound for transversity.