Intrinsic $k_T$ in shower-based event generators: focus on PYTHIA

We explore the role of intrinsic transverse momentum - intrinsic-$k_T$ and its energy dependence in parton shower models used in Monte Carlo event generators. Understanding intrinsic-$k_T$ has long been a challenge: it is typically modeled with a Gaussian distribution, yet in practice, Monte Carlo generators require an intrinsic width that increases with collision energy, reaching unphysical values at high energies. We investigate this behavior in Pythia8 and demonstrate that it arises from the interplay between two non-perturbative effects: the intrinsic transverse motion of partons and soft-gluon emissions. These effects become particularly significant in Drell-Yan production at low transverse momentum, which serves as one of the most sensitive probes of initial-state parton evolution. By analyzing the impact of the Sudakov form factor on the required intrinsic-$k_T$ width, we clarify the origin of this unexpected energy dependence and provide new insights into parton shower modeling.