The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O({\alpha }_s^3)$

Abstract

We calculate the polarized massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable $N$ both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at $O({\alpha }_s^3)$. We also present the results in momentum fraction space.

26 pages Latex

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Cited by in corpus (12)

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• The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering
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• $O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$
• Yadism: Yet Another Deep-Inelastic Scattering Module
• The inverse Mellin transform via analytic continuation
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• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• 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