The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)

TL;DR

This work computes the heavy-quark contributions to the longitudinal structure function F_L in deep inelastic scattering in the asymptotic region Q^2 ≫ m^2 at O(α_s^3) using mass-factorization in Mellin space. It provides the full expressions for heavy-quark Wilson coefficients, decomposed into light-flavor Coefficients and universal operator-matrix elements, and analyzes their small-x behavior, including leading 1/x and log-enhanced terms. Numerical illustrations show gluon and pure-singlet terms dominate the heavy-flavor impact on F_L at small x, with NNLO corrections larger than NLO, and indicate the asymptotic results are reliable for Q^2 around 10^3 GeV^2 or higher. The findings enhance the precision of heavy-flavor effects in F_L and inform future phenomenology at high Q^2 where heavy-quark contributions are significant.

Abstract

The logarithmic and constant contributions to the Wilson coefficient of the longitudinal heavy quark structure function to $O(α_s^3)$ are calculated using mass factorization techniques in Mellin space. The small $x$ behaviour of the Wilson coefficient is determined. Numerical illustrations are presented.