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

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.