Interplay of intrinsic motion of partons and soft gluon emissions in Drell-Yan production studied with PYTHIA

Understanding the intrinsic transverse momentum (intrinsic-$k_T$) of partons within colliding hadrons, typically modeled with a Gaussian distribution characterized by a specific width (the intrinsic-$k_T$ width), has been an extremely challenging issue. This difficulty arises because event generators like Pythia require an intrinsic-$k_T$ width that unexpectedly varies with collision energy, reaching unphysical values at high energies. This paper investigates the underlying physics behind this energy dependence in Pythia, revealing that it arises from an interplay between two non-perturbative processes: the internal transverse motion of partons and non-perturbative soft gluon emissions. These contributions are most constrained in the production of Drell-Yan pairs with very low transverse momentum, where soft gluon effects become increasingly prominent with rising collision energy-contrary to initial expectations. Through a detailed analysis of the non-perturbative Sudakov form factor and its influence on intrinsic-$k_T$ width, we clarify the observed energy scaling behavior in Pythia, providing insight into a longstanding issue in parton shower modeling.