$O(\hat{I}{\pm }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$

Abstract

We calculate the quarkonic $O(\hat{I}{\pm }_s^2)$ massive operator matrix elements $\hat{I}”A_{Qg}(N),\hat{I}”A_{Qq}^{\mathrm{PS}}(N)$ and $\hat{I}”A_{qq,Q}^{\mathrm{NS}}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2\gg m^2$ to $O(\epsilon )$ in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region $Q^2\gg m^2$ derived previously in \cite{BUZA2}, which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for $g_1(x,Q^2)$ to $O(\hat{I}{\pm }_s^2)$ for all but the power suppressed terms $\propto (m^2/Q^2{)}^k,k\ge 1$. The results in momentum fraction $z$-space are also presented. We also discuss the small $x$ effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two--mass variable flavor number scheme to $O(\epsilon )$.

58 pages Latex, 12 Figures