MCMC-based Nuclear PDFs for Lead (Pb) – Posterior Samples and LHAPDF Grids

This repository contains the data outputs related to the publication "Determination of Nuclear PDFs using Markov Chain Monte Carlo Methods": https://arxiv.org/abs/2603.13150v1 The dataset includes posterior samples of fitted nuclear PDF parameters and corresponding LHAPDF grids for both the $\texttt{Pb-only}$ and $\texttt{Multi-nuclei}$ analyses. Parameter Samples The parameter samples are provided in the files: ordered_parameter_samples_Pb.csv ordered_parameter_samples_Nu.csv They contain the posterior samples of the fitted nuclear PDF parameters for the $\texttt{Pb-only}$ and $\texttt{Multi-nuclei}$ analyses, respectively. Each row contains the $\chi^2$ value and the corresponding sampled parameter vector $\{a_k\}$, which defines a nuclear PDF through the parameterization described in Sec. II.A of the paper. The samples are ordered in ascending order with respect to their $\chi^2$ value. The first entry corresponds to the parameter set with the lowest $\chi^2$, while the last entry corresponds to the highest value in the sample. The fixed parameters are not included in the files and follow the setup specified in the publication. The ordering of the samples is identical to that used in the corresponding LHAPDF sets. LHAPDF Files The archives Pb_combined_order_208_82.zip Nuclei_combine_order_208_82.zip contain the LHAPDF grid files corresponding to the parameter samples provided in the CSV files for the $\texttt{Pb-only}$ and $\texttt{Multi-nuclei}$ analyses, respectively. Each archive includes a complete LHAPDF set, where each member corresponds to a PDF constructed from one parameter sample. The structure of the LHAPDF Sets is as follows: Member 0: Reference PDF (not used in analysis) Defined from the average of the parameters, $PDF(\langle\{p_k\}\rangle)$. This member is provided for reference only and is not used in the analysis Members 1–N: PDF samples (MCMC replicas) Each member corresponds to a single parameter sample from the CSV files. The PDF members are ordered identically to the parameter samples, i.e., in ascending order of $\chi^2$. In particular: Member 1: PDF corresponding to the lowest $\chi^2$ sample (best-fit for the cumulative-$\chi^2$ method) Member N: PDF corresponding to the highest $\chi^2$ sample