Transverse momentum dependent splitting functions at work: quark-to-gluon splitting

TL;DR

This paper extends the low x gluon evolution equation by incorporating quark-to-gluon splitting functions, including virtual corrections and regularization, and discusses its generalization to nonlinear regimes with high gluon densities.

Contribution

It introduces a consistent extension of the low x gluon evolution equation with quark-to-gluon splitting, including virtual corrections and regularization, and explores nonlinear generalizations.

Findings

Regularization of Pgq singularity for soft emitted quarks

Extension of low x gluon evolution to include quark-to-gluon splitting

Potential for nonlinear evolution equations in high gluon density regimes

Abstract

Using the recently obtained Pgq splitting function we extend the low x evolution equation for gluons to account for contributions originating from quark-to-gluon splitting. In order to write down a consistent equation we resum virtual corrections coming from the gluon channel and demonstrate that this implies a suitable regularization of the Pgq singularity, corresponding to a soft emitted quark. We also note that the obtained equation is in a straightforward manner generalized to a nonlinear evolution equation which takes into account effects due to the presence of high gluon densities.