$O(\alpha_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2 \gg m^2$
| Autor: | Bierenbaum, I., Blümlein, J., De Freitas, A., Goedicke, A., Klein, S., Schönwald, K. |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2023.116114 |
| Popis: | We calculate the quarkonic $O(\alpha_s^2)$ massive operator matrix elements $\Delta A_{Qg}(N), \Delta A_{Qq}^{\rm PS}(N)$ and $\Delta A_{qq,Q}^{\rm NS}(N)$ 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 $O(\varepsilon)$ 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 $\propto (m^2/Q^2)^k, k \geq 1$. 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 $O(\varepsilon)$. Comment: 58 pages Latex, 12 Figures |
| Databáze: | arXiv |
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