Flavor Factorization at Two-Loops

Recently, a factorization theorem was proposed for partonic flavor evolution as defined by the net flavor of the Winner-Take-All axis of a jet. We validate the factorization theorem through explicit calculation at two-loop order, and in the process extract all anomalous dimensions and renormalization factors for any ultraviolet-to-infrared flavor transition at this order. These results can then be used to extract the renormalized hard function for flavored jet production at next-to-next-to-leading order for any process of interest.