Determination of Nuclear PDFs using Markov Chain Monte Carlo Methods

TL;DR

This paper introduces a novel Markov Chain Monte Carlo approach for determining nuclear parton distribution functions, revealing complex parameter structures and improving uncertainty estimates over traditional methods.

Contribution

It is the first to apply MCMC techniques to nPDF analysis, capturing non-Gaussian features and multiple modes in the parameter space, enhancing the reliability of uncertainty quantification.

Findings

MCMC reveals non-Gaussian behavior and multiple modes in nPDF parameters.

Including lighter nuclei reduces quark uncertainties and alters lead PDFs.

MCMC provides more reliable uncertainty estimates than Hessian methods.

Abstract

Global QCD analyses of nuclear parton distribution functions (nPDFs) have traditionally relied on the Hessian method for uncertainty estimation. However, the inherent Gaussian approximation and reliance on local curvature often prove insufficient for nPDF fits, which are frequently characterized by limited data constraints and non-Gaussian likelihoods. In this paper, we present the first nPDF determination based on Markov Chain Monte Carlo (MCMC) techniques, implemented within the nCTEQ framework using an adaptive Metropolis-Hastings algorithm. The MCMC approach enables a direct mapping of the posterior distribution and reveals a highly non-trivial parameter-space structure, including multiple modes and pronounced non-Gaussian behavior, particularly for the valence PDFs. We perform the first single-nucleus global analysis of lead PDFs using exclusively lead data and compare it to a multi-nuclei fit employing a standard analytic A dependence. The inclusion of lighter nuclei reduces quark uncertainties and modifies the shape of the lead PDFs, while leaving the gluon distribution largely unaffected. A complementary Hessian analysis exposes systematic limitations of the Gaussian approximation. Our results demonstrate that MCMC methods provide a more reliable framework for uncertainty quantification in nPDF determinations.