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Determination of nuclear PDFs using Markov chain Monte Carlo methods

N. Derakhshanian ^1,*, P. Risse ^2,3,†, T. Ježo ^4,‡, M. Klasen ⁴, K. Kovařík ⁴, and A. Kusina ^1,§

¹Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 Krakow, Poland
²Department of Physics, Southern Methodist University, Dallas, Texas 75275-0175, USA
³Theory Center, Jefferson Lab, Newport News, Virginia 23606, USA
⁴Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, D-48149 Münster, Germany

^*Contact author: nasim.derakhshanian@ifj.edu.pl
^†Contact author: rissep@jlab.org
^‡Contact author: tomas.jezo@uni-muenster.de
^§Contact author: aleksander.kusina@ifj.edu.pl

Phys. Rev. D 114, 034037 – Published 18 August, 2026

DOI: https://doi.org/10.1103/6bpd-yrm4

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 nontrivial 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.

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Phys. Rev. D 114, 034037– Published 18 August, 2026

Vol. 114, Iss. 3 — 1 August 2026

Received 30 March 2026
Accepted 20 July 2026

DOI: https://doi.org/10.1103/6bpd-yrm4

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Determination of nuclear PDFs using Markov chain Monte Carlo methods

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