O($\alpha_s^2$) polarized heavy flavor corrections to deep-inelastic scattering at Q$^2$ ≫ m$^2$

Abstract

We calculate the quarkonic O($\alpha_s^2$) massive operator matrix elements and for the twist–2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2>>M^2$ 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 derived previously in [1], which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for $g1(x,Q^2)$ to $O(\alpha_s^2)$ for all but the power suppressed terms proportional to ($m^2/Q^2)^k, k>=1$. 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 $O(\epsilon)$.