Double quarkonium hadroproduction as a probe of gluon Sivers function

Abstract

The prediction of single spin asymmetry (SSA) in double $J/\psi$ production in proton-proton collision is given out within the framework of non-relativistic QCD, using the recently obtained best fit parameters for the gluon Sivers function extracted from PHENIX data in $\mathrm{p}+{\mathrm{p}}^{\uparrow }\to {\pi }^0+\mathrm{X}$. The color singlet state ${}^3{\mathrm{S}}_1^{(1)}$ and color octet state ${}^3{\mathrm{S}}_1^{(8)}$ are considered to the SSA contribution in the double $J/\psi$ hadroproduction. Our result shows that a sizable asymmetry can be estimated as functions of different kinematic variables.