Simultaneous reweighting of Transverse Momentum Dependent distributions

The Bayesian reweighting procedure is extended to the case of multiple independent extractions of transverse momentum dependent parton distributions (TMDs). By exploiting the data on transverse single spin asymmetries, $A_N$, for inclusive pion production in polarized proton-proton collisions measured at RHIC, we perform a simultaneous reweighting of the quark Sivers, transversity and Collins TMD functions extracted from semi-inclusive deep inelastic scattering (SIDIS) and $e^+ e^-$ annihilation into hadron pairs. The impact of the implementation of the Soffer bound, as well as the differences between older and newer $A_N$ data, are investigated. The agreement with $A_N$ data at large-$x_F$ values, a kinematical region complementary to those explored in SIDIS measurements, is enhanced, improving the knowledge of the polarized quark TMDs in the large-$x$ region.