Abstract
Recent experiments at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) have indicated that hadrons containing strange quarks produced in non-central 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 ${\cal PT}$ invariant, and involves a spin dependent term $\textstyle{\frac{1}{2}} s_z \hbar \omega$ to leading order in vorticity. We also calculate further relativistic and quantum corrections to the Hamiltonian.
Highlights
Several insightful theoretical papers suggested that the large orbital angular momentum of the matter created in noncentral high energy heavy ion collisions could polarize the quarks and subsequently the hadrons observed in the final state [1,2,3,4]
Measurements by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC) of the polarization of the Λ and Λhyperons were consistent with this idea [5,6,7]
The observed hyperon polarization decreases with increasing beneaemrgyenoef rpgyffisffi,ffiNffibffiNffiffiec1⁄4om20in0gGneeVar.lyMzeearsouaret mtheenmtsaoxfitmheumhyRpeHroICn polarization by the ALICE Collaboration at the much higher beam energies available at the Large Hadron Collider (LHC) are consistent with zero [8]
Summary
Several insightful theoretical papers suggested that the large orbital angular momentum of the matter created in noncentral high energy heavy ion collisions could polarize the quarks and subsequently the hadrons observed in the final state [1,2,3,4]. Massive spin-1 vector mesons should be polarized in noncentral high energy heavy ion collisions [3,4,12,13,14]. Relatively low statistics measurements by the STAR Collaboration at RHIC found no spin alignment of the KÃ0ð892Þ and φð1020Þ vector mesons [15]. ALICE has found no discernable polarization of the J=ψ meson [19] Motivated by these experimental results we investigate in detail the coupling of spin and vorticity for electrically neutral, massive vector bosons using the Proca equation. The description of massive vector mesons in inertial frames of reference, including their interaction with electromagnetic fields if they are charged, is textbook material [20]
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