On the role of soft and non-perturbative gluons in collinear parton densities and parton shower event generators

The Parton Branching method offers a Monte Carlo solution to the DGLAP evolution equations by incorporating Sudakov form factors. In this approach, the Sudakov form factor can be divided into perturbative and non-perturbative components, with the non-perturbative part being analytically calculable under specific conditions. We first examine forward evolution and demonstrate that including soft and non-perturbative gluons (through the non-perturbative Sudakov form factor) is essential for the proper cancellation of divergent terms in parton density evolution. This non-perturbative component is also important for Transverse Momentum Dependent (TMD) parton distributions, and within the Parton Branching framework, it is constrained by fits to inclusive collinear parton densities. Additionally, we explore the impact of this non-perturbative Sudakov form factor on backward parton evolution and its effects on parton and hadron spectra originating from initial state showers. Our results show that soft and non-perturbative gluons significantly influence inclusive distributions, such as Drell-Yan transverse momentum spectra. However, we found that soft and non-perturbative gluons have a minimal impact on final state hadron spectra and jets.