Transverse-momentum-dependent quark splitting functions in $k_T$-factorization: real contributions

TL;DR

This paper computes the transverse momentum dependent quark splitting functions within $k_T$-factorization, completing the set of kernels needed for evolution equations and parton shower algorithms in high-energy QCD.

Contribution

It provides the missing quark splitting functions $P_{gq}$ and $P_{qq}$, essential for a complete TMD evolution framework.

Findings

Calculated $P_{gq}$ and $P_{qq}$ splitting kernels.

Completed the set of TMD splitting functions.

Facilitated development of TMD evolution equations and parton showers.

Abstract

We calculate transverse momentum dependent quark splitting kernels $P_{gq}$ and $P_{qq}$ within $k_T$-factorization, completing earlier results which concentrated on gluon splitting functions $P_{gg}$ and $P_{qg}$. The complete set of splitting kernels is an essential requirement for the formulation of a complete set of evolution equations for transverse momentum dependent parton distribution functions and the development of corresponding parton shower algorithms.