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PDF reweighting in the Hessian matrix approach

We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an existing set of PDFs. By construction, the method discussed here applies to the PDF fits that carried out a Hessian error analysis using a non-zero tolerance $Δχ^2$. The principle is validated by considering a simple, transparent example. We are also able to establish an agreement with the Bayesian technique provided that the tolerance criterion is appropriately accounted for and that a purely exponential Bayesian likelihood is assumed. As a practical example, we discuss the inclusive jet production at the LHC.