By generalizing the statistical model for particle production to the spin degree of freedom of initially produced J/psi, we study the spin projection J_y of J/psi perpendicular to the reaction plane in peripheral heavy ion collisions at the LHC energy that leads to a strong, albeit of short duration, magnetic field. We find that for J/psis produced directly from charm and anticharm quarks in the color singlet state, like that in the Color-Singlet Model, their yield in the presence of the magnetic field is larger for J_y=0 than for J_y=1 or -1. This leads to a spin asymmetry of finally produced J/psi even after including their final-state scattering in the produced quark-gluon plasma.
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