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

TL;DR

This paper introduces a Bayesian inference framework enhanced with artificial intelligence to extract unpolarized quark TMD PDFs from Drell-Yan data, achieving high perturbative accuracy and efficient sampling.

Contribution

It combines AI-driven functional form exploration with machine-learning emulators for scalable Bayesian analysis of TMD PDFs at high perturbative orders.

Findings

Extracted TMD PDFs with quantified uncertainties from diverse Drell-Yan data.

Developed an AI-based iterative procedure for functional form selection.

Created a machine-learning emulator for efficient cross section evaluation.

Abstract

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 ${\rm N^3LO}$ in perturbative QCD combined with ${\rm N^4LL}$ 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.