Testing the Gaussian Ansatz for TMD PDFs Through CMS Measurements

We investigate the differential cross section of the $pp$ Drell-Yan process within the framework of Transverse Momentum Dependent (TMD) factorization. We perform phenomenological calculations of the differential cross section as a function of $q_T$ in different dilepton invariant mass bins and compare it with the measured data from the CMS experiment at $13~$TeV, employing two distinct transverse momentum dependencies of the parton distribution functions: the Collins-Soper-Sterman (CSS) evolution method and the Gaussian Ansatz. The results indicate that the CSS evolution method agrees well with experimental data across the entire energy range, demonstrating its strong predictive capability for the evolution behavior of TMD distribution functions. In contrast, the Gaussian Ansatz of the TMD PDFs is only applicable in the low-energy region and exhibits significant limitations at high energies. This study verifies the effectiveness of the TMD factorization theorem in describing high-energy processes and provides theoretical support for an in-depth exploration of the nucleon's internal structure and non-perturbative QCD dynamics.