The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension

TL;DR

This paper computes the 3-loop pure singlet heavy flavor corrections to the structure function F2(x,Q^2) in deep-inelastic scattering, providing new calculations of anomalous dimensions and numerical results for Wilson coefficients and operator matrix elements.

Contribution

It presents the first calculation of the complete 3-loop pure singlet anomalous dimension and detailed results for heavy flavor contributions in the variable flavor number scheme.

Findings

Computed 3-loop pure singlet heavy flavor corrections to F2.

Recalculated the complete 3-loop pure singlet anomalous dimension.

Provided numerical results for Wilson coefficients and operator matrix elements.

Abstract

The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function $F_2(x,Q^2)$ and the corresponding transition matrix element $A_{Qq}^{(3), \sf PS}$ in the variable flavor number scheme are computed. In Mellin-$N$ space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function $F_2(x,Q^2)$ are presented.