AI-assisted modeling and Bayesian inference of unpolarized quark transverse momentum distributions from Drell-Yan data

We present an extraction of unpolarized quark transverse-momentum-dependent parton distribution functions (TMD PDFs) from Drell-Yan data within a Bayesian inference framework, incorporating artificial intelligence at multiple stages of the analysis. Our analysis is performed at ${\mathrm{N}}^3\mathrm{L}\mathrm{O}$ in perturbative QCD combined with ${\mathrm{N}}^4\mathrm{L}\mathrm{L}$ resummation accuracy. We first employ an AI-driven iterative procedure to explore and rank candidate functional forms for the nonperturbative contributions to TMD PDFs at the initial scale, as well as for the Collins-Soper evolution kernel, using ${\chi }^2$ fits and physics constraints. To enable efficient Bayesian inference, we construct a surrogate model for TMD cross sections by training a machine-learning emulator over the parameter space, replacing computationally expensive repeated evaluations and allowing scalable sampling with an affine-invariant Markov Chain Monte Carlo (MCMC) ensemble. Using this framework, we perform a global analysis of Drell-Yan data from fixed-target, RHIC, and LHC experiments and extract TMD PDFs with quantified uncertainties. We compare the results with those obtained using the replica method and highlight differences in the resulting uncertainty estimates.