$O(α_s^2)$ corrections to polarized heavy flavour production at $Q^2\gg m^2$

TL;DR

This work delivers analytic, spin-dependent heavy-quark coefficient functions for polarized DIS in the high-$Q^2$ regime, grounded in the two-loop spin-operator matrix elements. By factorizing the heavy-quark effects into operator matrix elements and light-parton coefficient functions, it provides explicit $O(\alpha_s^2)$ corrections to polarized charm production and establishes exact results for certain terms (e.g., $L_q^{\rm NS,(2)}$) with asymptotic formulae for the rest. It also introduces threshold-improved approximations to broaden applicability to lower $Q^2$ and assesses the phenomenological impact on the polarized structure function $g_1$, finding the charm component to be modest at HERA energies. These results enable more precise predictions for polarized DIS and cross-checks of perturbative QCD in the spin sector.

Abstract

We present analytic formulae for the heavy flavour coefficient functions for polarized deep inelastic lepton-hadron scattering. The expressions are valid in the kinematical regime $Q^2\gg m^2$ where $Q^2$ and $m^2$ stand for the masses squared of the virtual photon and heavy quark respectively. Using these coefficient functions we have computed the next-to-leading order $α_s$ corrections to polarized charm production at HERA collider energies, where both the electron and proton beams are polarized. We also give an estimate of these corrections at fixed target experiments where the typical $Q^2$ values are much smaller than at HERA.