The heavy quark-antiquark asymmetry in the variable flavor number scheme

TL;DR

This paper investigates the differences between heavy-quark and antiquark distributions in the variable flavor number scheme, revealing QCD corrections that cause asymmetries starting at three-loop order, with implications for polarized and unpolarized cases.

Contribution

It provides the first calculation of the three-loop heavy-flavor distribution difference, highlighting the asymmetry caused by specific QCD corrections in the variable flavor number scheme.

Findings

Heavy-quark and antiquark distributions differ due to three-loop QCD corrections.

The difference is small but non-zero, affecting both polarized and unpolarized cases.

The calculations are performed in the Larin scheme for polarized distributions.

Abstract

The twist-2 heavy-quark and antiquark distributions, as defined in the variable flavor number scheme, turn out to be different due to QCD corrections from three-loop onward. This is caused by terms containing the color factor $d_{abc} d^{abc}$ in the heavy-flavor massive pure-singlet operator matrix elements (OMEs) $A^{\rm PS, s, (3)}_{Qq}$ for odd moments in the unpolarized case and for $\Delta A^{\rm PS, s, (3)}_{Qq}$ for even moments in the polarized case. The dependence on the factorization scale of the OMEs is ruled by the anomalous dimensions $\gamma^{\rm NS, s, (2)}_{qq}$ and $\Delta \gamma^{\rm NS, s, (2)}_{qq}$. The polarized calculations are performed in the Larin scheme. We compute the corresponding three-loop heavy-flavor distributions $(\Delta) f_Q(x,Q^2) - (\Delta) f_{\overline{Q}}(x,Q^2)$. Compared to the sum of the heavy-quark and antiquark parton distributions, their difference is small, however, non-vanishing.