Pgg TMD splitting function in kT factorization

TL;DR

This paper derives a transverse momentum dependent gluon-to-gluon splitting function within kT-factorization, unifying various known kernels and extending previous work on quark splittings.

Contribution

It introduces a generalized TMD gluon splitting function that interpolates between BFKL, DGLAP, and CCFM kernels, extending the theoretical framework of kT-factorization.

Findings

Splitting function reduces to BFKL kernel at low z.

Splitting function matches DGLAP in collinear limit.

Splitting function aligns with CCFM in angular ordered region.

Abstract

We calculate the transverse momentum dependent gluon-to-gluon splitting function within kT-factorization [EPJC 78 (2018) 174], generalizing the framework of [NPB 175 (1980) 27; NPB 427 (1994) 475] and extending our previous works [JHEP 01 (2016) 181; PRD 94 (2016) 114013] for the quark splittings. While existing versions of kT factorized evolution equations contain already a gluon-to-gluon splitting function i.e. the leading order BFKL kernel or the CCFM kernel, the obtained splitting function has the important property that it reduces to the leading order BFKL kernel in the low z limit, to the DGLAP gluon-to-gluon splitting function in the collinear limit as well as to the CCFM kernel in the angular ordered region.