The O(\alpha_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer

TL;DR

This paper computes three-loop order heavy flavor contributions to the charged current structure function in deep-inelastic scattering, providing detailed numerical results and implications for the Gross-Llewellyn Smith sum rule.

Contribution

It introduces the calculation of massive Wilson coefficients for heavy flavor contributions at three-loop order in QCD for the structure function $xF_3$, extending previous lower-order results.

Findings

Numerical results for charm quark contributions are provided.

Implications for the Gross-Llewellyn Smith sum rule are discussed.

The calculation includes both heavy quark pair production and single heavy flavor excitation.

Abstract

We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure function $xF_3^{W^+}(x,Q^2)+xF_3^{W^-}(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics (QCD) at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production also the single heavy flavor excitation $s \rightarrow c$ contributes. Numerical results are presented for the charm quark contributions and consequences on the Gross-Llewellyn Smith sum rule are discussed.