Double quarkonium hadroproduction as a probe of gluon Sivers function

The prediction of single spin asymmetry (SSA) in double $rm J/psi$ 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 $rm p+p^uparrowtopi^0+X$. The color singlet state $rm ^3 S_1^{(1)}$ and color octet state $rm ^3 S_1^{(8)}$ are considered to the SSA contribution in the double $rm J/psi$ hadroproduction. Our result shows that a sizable asymmetry can be estimated as functions of different kinematic variables.