Improved Hessian method in global analysis of parton distribution functions

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.