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The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, N_F)}$ (1705.01508v1)

Published 3 May 2017 in hep-ph, hep-ex, and hep-th

Abstract: We calculate the unpolarized twist-2 three-loop splitting functions $P_{qg}{(2)}(x)$ and $P_{gg}{(2,\rm N_F)}(x)$ and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate $P_{gg}{(2,\rm N_F)}(x)$ directly, $P_{qg}{(2)}(x)$ is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.

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