The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity

TL;DR

This paper computes 3-loop order heavy flavor contributions and anomalous dimensions for the structure function F2(x,Q^2) and transversity in QCD, providing precise theoretical tools for understanding deep inelastic scattering at high energies.

Contribution

It presents the first calculation of the massive flavor non-singlet Wilson coefficient and operator matrix elements at 3-loop order for general Mellin moments, including transversity and matching in the variable flavor number scheme.

Findings

Calculated 3-loop Wilson coefficients for heavy flavor contributions.

Derived operator matrix elements for transversity at 3-loop order.

Provided numerical results for charm quark contributions to F2(x,Q^2).

Abstract

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function $F_2(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ and the associated operator matrix element $A_{qq,Q}^{(3), \rm NS}(N)$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$. This matrix element is associated to the vector current and axial vector current for the even and the odd moments $N$, respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to $O(N_F)$ and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in $N$ space and harmonic polylogarithms in $x$-space. Numerical results are presented for the non-singlet charm quark contribution to $F_2(x,Q^2)$.