Dissecting collinear splittings of quark and gluon jets at NNLL

We examine the problem of the collinear splitting of partons at NNLL in the context of a higher logarithmic accuracy parton shower. Although many of the ingredients for achieving NNLL accuracy have been developed decades ago, and exploited for analytic resummation,  the problem of consistently incorporating them for formulation of higher accuracy parton showers, has only  recently started to be addressed. To this end we derive a suitable anomalous dimension, connected to the NNLL resummation coefficient B2 for both quark and gluon jets. We discuss how this may be exploited in the context of a shower as well as to derive new results for collinear sensitive observables.