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arXiv · 2411.11645

Improved Hessian Method in Global Analysis of Parton Distribution Functions

Wenxiao Zhan·Siqi Yang·Minghui Liu·Liang Han·Daniel Stump·C. -P. Yuan
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Abstract

The Hessian method is widely applied in the global analysis of parton distribution functions (PDFs), which uses 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 non-perturbative parameters in PDF. In this article, we report an improved Hessian method which takes the non-linear effects into account in the uncertainty estimation. A pseudo global analysis is designed to numerically test the new method. The non-linear uncertainties can significantly enlarge the original linear ones. Such uncertainties can be reduced with high precision data introduced into the global analysis. However, the non-linear effect could still be sizable corresponding to the current precision of the experimental measurements.

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Wenxiao Zhan, Siqi Yang, Minghui Liu, Liang Han, Daniel Stump, C. -P. Yuan. 2024-11-18. Improved Hessian Method in Global Analysis of Parton Distribution Functions. https://arxiv.org/abs/2411.11645

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