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

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 $d_{abc} d<sup>{abc}$ in the heavy-flavor massive pure-singlet operator matrix elements (OMEs) $A^{\rm PS, s, (3)}<em>{Qq}$ for odd moments in the unpolarized case and for $ΔA^{\rm PS, s, (3)}</em>{Qq}$ for even moments in the polarized case. The dependence on the factorization scale of the OMEs is ruled by the anomalous dimensions $γ^{\rm NS, s, (2)}<em>{qq}$ and $Δγ^{\rm NS, s, (2)}</em>{qq}$. The polarized calculations are performed in the Larin scheme. We compute the corresponding three-loop heavy-flavor distributions $$(Δ) f_Q(x,Q²⁾ - (Δ) f_{\overline{Q}}(x,Q<sup>2)$$. Compared to the sum of the heavy-quark and antiquark parton distributions, their difference is small, however, non-vanishing.