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  • Open Access

Improved Hessian method in global analysis of parton distribution functions

WenXiao Zhan, Siqi Yang*, Minghui Liu, and Liang Han

Daniel Stump and C.-P. Yuan

  • *Contact author: yangsq@ustc.edu.cn
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Phys. Rev. D 112, 074028 – Published 23 October, 2025

DOI: https://doi.org/10.1103/858l-2x47

Abstract

The Hessian method is widely applied in the global analysis of parton distribution functions (PDFs), which use a set of orthogonal eigenvectors to give predictions of a physical observable. Its uncertainty is estimated based on the assumption that all physical observables can be approximately expressed as linear functions of the nonperturbative parameters in PDF. In this article, we report an improved Hessian method which takes the nonlinear effects into account in the uncertainty estimation. A pseudoglobal analysis is designed to numerically test the new method. The nonlinear uncertainties can significantly enlarge the original linear ones. Such uncertainties can be reduced with high precision data introduced into the global analysis. However, the nonlinear effect could still be sizable corresponding to the current precision of the experimental measurements.

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Phys. Rev. D 112, 074028– Published 23 October, 2025
  • Received 19 November 2024
  • Accepted 29 August 2025
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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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