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The reweighting procedure that using Bayesian statistics incorporates theinformation contained in a new data set, without the need of re-fitting, isapplied to the quark Sivers function extracted from Semi-Inclusive DeepInelastic Scattering (SIDIS) data. We exploit the recently published singlespin asymmetry data for the inclusive jet production in polarized $pp$collisions from the STAR Collaboration at RHIC, which cover a much wider $x$region compared to SIDIS measurements. The reweighting method is extended tothe case of asymmetric errors and the results show a remarkable improvement ofthe knowledge of the quark Sivers function.

Reweighting the Sivers function with jet data from STAR