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

Understand

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.