The three-loop splitting functions P q g ( 2 ) and P g g ( 2 , N F )

摘要

We calculate the unpolarized twist-2 three-loop splitting functions P q g ( 2 ) ( x ) and P g g ( 2 , N F ) ( x ) and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate P g g ( 2 , N F ) ( x ) directly, P q g ( 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.