Two-loop Feynman-gauge calculation of the meson nonsinglet evolution potential

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Abstract

Recently, three independent determinations of the two-loop meson nonsinglet evolution potential have been completed. Two of them are an explicit light-cone-gauge calculation while the third is a less direct evaluation based on conformal symmetry. However, all three calculations disagree in the ${C}_{F}$${\mathrm{}}^{2}$ term. In this paper I present the results of a Feynman-gauge evaluation of Gegenbauer matrix elements (${V}_{2}$${)}_{\mathrm{mj}}$ of the ${C}_{F}$${\mathrm{}}^{2}$ part of the two-loop meson nonsinglet evolution potential. The results confirm one of the light-cone-gauge calculations.

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