Nuclear parton distributions from lepton-nucleus scattering and the impact of an electron-ion collider

Rabah Abdul Khalek,Jacob J Ethier,Juan Rojo

doi:10.1140/epjc/s10052-019-6983-1

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 xsimeq 5times 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.

Highlights

NPDF extractions can sharpen the physics case of future high-energy lepton-nucleus colliders such as the Electron-Ion Collider (EIC) [13] and the Large Hadron electron Collider (LHeC) [14,15], which will probe nuclear structure deep in the region of small parton momentum fractions, x, and aim to unravel novel QCD dynamics such as nonlinear effects. The latter will only be possible provided that a faithful estimate of the nuclear parton distribution functions (nPDF) uncertainties at small x can be attained, similar to what was required for the recent discovery of BFKL dynamics from the HERA structure function data [16]
While a detailed and systematic comparison between the performances of the Tensor Flow-based stochastic gradient descent optimization used in nNNPDF1.0 and that of the Genetic Algorithm (GA) and Covariance Matrix AdaptationEvolutionary Strategy (CMA-ES) minimizers used in previous NNPDF analyses is beyond the scope of this work, here we provide a qualitative estimate for improvement in performance that has been achieved as a result of using the former strategy
We present the main results of our analysis, namely the nNNPDF1.0 sets of nuclear parton distributions

Summary

Introduction

NPDF extractions can sharpen the physics case of future high-energy lepton-nucleus colliders such as the Electron-Ion Collider (EIC) [13] and the Large Hadron electron Collider (LHeC) [14,15], which will probe nuclear structure deep in the region of small parton momentum fractions, x, and aim to unravel novel QCD dynamics such as nonlinear (saturation) effects. The latter will only be possible provided that a faithful estimate of the nPDF uncertainties at small x can be attained, similar to what was required for the recent discovery of BFKL dynamics from the HERA structure function data [16]. PDF uncertainties are often estimated using the Hessian method, which is restricted to a Gaussian approximation with ad hoc tolerances, introducing a level of arbitrariness in their statistical interpretation

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Conclusion