Determination of Nuclear PDFs using Markov Chain Monte Carlo

Nuclear parton distribution functions (nPDFs) are a key ingredient in the interpretation of high-energy nuclear collisions. Their uncertainties have traditionally been estimated using the Hessian method, which relies on a local Gaussian approximation of the likelihood. However, the limited constraining power of current nuclear data can lead to non-Gaussian probability distributions and complex parameter-space structures that are not fully captured within this framework. In this seminar, I present a global nPDF analysis based on Markov Chain Monte Carlo (MCMC) techniques implemented within the nCTEQ framework using an adaptive Metropolis–Hastings algorithm. The MCMC approach provides direct access to the full posterior probability distribution and reveals significant non-Gaussian behavior, multiple modes, and strong parameter correlations, particularly in the valence sector. The analysis includes a dedicated determination of lead PDFs using only lead data, as well as a comparison with a multi-nuclei fit employing a standard analytic A-dependence parameterization. The impact of including lighter nuclei on the extracted lead PDFs and their uncertainties is examined. In addition, a parallel Hessian analysis is used to assess the validity of the Gaussian approximation and to highlight its limitations in weakly constrained regions of parameter space. The results demonstrate the advantages of MCMC methods for uncertainty quantification in nPDF analyses and provide new insights into the role of nuclear-data constraints and model assumptions in global fits. This seminar is based on the work presented in arXiv:2603.13150.