Spin-vorticity coupling for massive vector mesons

Recent experiments at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) have indicated that hadrons containing strange quarks produced in noncentral heavy ion collisions can be polarized. We investigate in detail the coupling of spin and vorticity for electrically neutral, massive vector bosons using the Proca equation, and provide the nonrelativistic reduction of the field equations via a single Foldy-Wouthuysen transformation. We find that the resulting Hamiltonian is not Hermitian, but PT invariant, and involves a spin dependent term 1/2 s(z) (h) over bar omega to leading order in vorticity. We also calculate further relativistic and quantum corrections to the Hamiltonian.