# Nuclear Parton Distributions from Lepton-Nucleus Scattering and the Impact of an Electron-Ion Collider

## TL;DR

This paper introduces the first Monte Carlo-based nuclear parton distribution functions (nPDFs) using NNPDF methodology, validated with high-precision deep-inelastic scattering data and explores the potential impact of future Electron-Ion Collider measurements.

## Contribution

It presents the first nPDF analysis employing a Monte Carlo approach consistent with proton PDF fits, incorporating NNLO QCD and heavy quark effects, and evaluates EIC data impact.

## Key findings

- nNNPDF1.0 provides robust nuclear PDFs validated by closure tests.
- EIC measurements could significantly improve nPDF constraints at low x.
- The methodology achieves $oldsymbol{ ext{chi}^2}$ minimization via stochastic gradient descent with backpropagation.

## Abstract

We present a first determination of the nuclear parton distribution functions (nPDF) based on the NNPDF methodology: nNNPDF1.0. This analysis is based on neutral-current deep-inelastic structure function data and is performed up to NNLO in QCD calculations with heavy quark mass effects. For the first time in the NNPDF fits, the $\chi^2$ minimization is achieved using stochastic gradient descent with reverse-mode automatic differentiation (backpropagation). We validate the robustness of the fitting methodology through closure tests, assess the perturbative stability of the resulting nPDFs, and compare them with other recent analyses. The nNNPDF1.0 distributions satisfy the boundary condition whereby the NNPDF3.1 proton PDF central values and uncertainties are reproduced at $A=1$, which introduces important constraints particularly for low-$A$ nuclei. We also investigate the information that would be provided by an Electron-Ion Collider (EIC), finding that EIC measurements would significantly constrain the nPDFs down to $x\simeq 5\times 10^{-4}$. Our results represent the first-ever nPDF determination obtained using a Monte Carlo methodology consistent with that of state-of-the-art proton PDF fits, and provide the foundation for a subsequent global nPDF analyses including also proton-nucleus data.