Global Analysis of Nuclear Parton Distribution Functions using Markov Chain Monte Carlo

Abstract

Global analyses of nuclear parton distribution functions (nPDFs) have traditionally used the Hessian method for uncertainty estimation, relying on a local quadratic approximation of the chi-squared function. This Gaussian approximation can be inadequate when experimental constraints are limited and parameter correlations are strong, as it cannot fully capture asymmetric uncertainties, flat directions, or multiple minima. This thesis develops a Bayesian framework for nPDF determination using Markov Chain Monte Carlo (MCMC) techniques within the nCTEQ analysis framework. An adaptive Metropolis-Hastings algorithm enables direct sampling of the posterior distribution, revealing pronounced non-Gaussian behavior and secondary minima, particularly in the valence distributions. The analysis presents the first global single-nucleus determination of lead (Pb) PDFs based exclusively on lead data, complemented by a multi-nuclei analysis incorporating different nuclear targets through a standard analytic dependence on the mass number. Including lighter nuclei significantly constrains quark distributions and changes the extracted lead PDFs, while the gluon distribution remains comparatively stable. A comparison with Hessian-based results highlights the limitations of the Gaussian approximation in regions with strong nonlinearity or multimodality. Overall, this work establishes Bayesian MCMC inference as a flexible framework for nPDF determination, providing a more comprehensive characterization of parameter uncertainties and the underlying parameter space.