First $O({\alpha }_s^3)$ heavy flavor contributions to deeply inelastic scattering

Abstract

In the asymptotic limit $Q^2\gg m^2$, the heavy flavor Wilson coefficients for deep--inelastic scattering factorize into the massless Wilson coefficients and the universal heavy flavor operator matrix elements resulting from light--cone expansion. In this way, one can calculate all but the power corrections in $(m^2/Q^2{)}^k,k>0$. The heavy flavor operator matrix elements are known to $\mathsf{NLO}$. We present the last 2--loop result missing in the unpolarized case for the renormalization at 3--loops and first 3--loop results for terms proportional to the color factor $T_F^2$ in Mellin--space. In this calculation, the corresponding parts of the $\mathsf{NNLO}$ anomalous dimensions \cite{LARIN,MVVandim} are obtained as well.

6 pages, Contribution to the Proceedings of "Loops and Legs in Quantum Field Theory", 2008, Sondershausen, Germany, and DIS 2008, London, UK

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Cited by in corpus (7)

• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
• The Gluonic Operator Matrix Elements at O(α_s^2) for DIS Heavy Flavor Production
• Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra
• $O({\alpha }_s^2)$ and $O({\alpha }_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2\gg m^2$
• $O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$
• Heavy Quarks: Lessons Learned from HERA and Tevatron