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

Abstract

We calculate the quarkonic $O({\alpha }_s^2)$ massive operator matrix elements $\Delta A_{Qg}(N),\Delta A_{Qq}^{\mathrm{PS}}(N)$ and $\Delta A_{qq,Q}^{\mathrm{NS}}(N)$ 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 $O({\alpha }_s^2)$ 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

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• NNLO Global Analysis of Polarized Parton Distribution Functions
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Yadism: Yet Another Deep-Inelastic Scattering Module
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• Renormalization of twist-two operators in covariant gauge to three loops in QCD
• General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders
• Toward Precision Helicity PDFs from Global DIS and SIDIS Fits with Projected EIC Measurements