Heavy quark production in the Aivazis-Collins-Olness-Tung scheme at next-to-next-to-leading and next-to-next-to-next-to-leading order

Abstract

We analyze the properties of the Aivazis-Collins-Olness-Tung (ACOT) scheme for heavy quark production and make use of the $\overline{\mathrm{MS}}$ massless results at next-to-next-to-leading order and ${\mathrm{N}}^{3}\mathrm{LO}$ for the structure functions ${F}_{2}$ and ${F}_{L}$ in neutral current deep-inelastic scattering to estimate the higher order corrections. For this purpose we decouple the heavy quark mass entering the phase space from the one entering the dynamics of the short distance cross section. We show numerically that the phase space mass is generally more important. Therefore, the dominant heavy quark mass effects at higher orders can be taken into account using the massless Wilson coefficients together with an appropriate slow-rescaling prescription implementing the phase space constraints. Combining the exact ACOT scheme at next-to-leading order with these expressions should provide a good approximation to the missing full calculation in the ACOT scheme at next-to-next-to-leading order and ${\mathrm{N}}^{3}\mathrm{LO}$.