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We investigate the transverse momentum weighted Sivers asymmetries in theprocesses with transversely polarized proton target, including the$\frac{P_{hT}}{zM_p}\sin (\phi_h-\phi_S)$ weighted asymmetry in charged hadronproduction in semi-inclusive deeply inelastic scattering (SIDIS) and the$\frac{q_T}{M_p}\sin (\phi_S)$ weighted asymmetry in $\pi^- p$ Drell-Yanprocess. Due to the integration over the transverse momentum, the weightedasymmetries can be expressed as the product of the transverse-moments of thetransverse momentum dependent (TMD) parton distribution functions (PDFs) andfragmentation functions (FFs). Using the parametrization for the Siversfunction of the proton, the unpolarized PDFs of proton and pion, and theunpolarized FF of charged hadron, we present the numerical calculation forweighted Sivers asymmetries in SIDIS and Drell-Yan processes at the kinematicsof COMPASS, and compare them with experimental data. We find that ourprediction on the weighted Sivers asymmetry in SIDIS process is in agreementwith the recent COMPASS measurement. Due to the relatively large uncertaintiesof the preliminary data from COMPASS Drell-Yan program, high precisionexperimental data are needed to test the sign change property of the Siversfunction between SIDIS and Drell-Yan processes and to constrain the sea quarkSivers function.

Transverse momentum weighted Sivers asymmetries in SIDIS and Drell-Yan processes at COMPASS