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.
Categories: hep-ph hep-ex hep-th