Spin-Vorticity Coupling for Massive Vector Mesons

TL;DR

This paper explores how spin couples to vorticity in massive vector mesons using the Proca equation, revealing a non-Hermitian, PT-invariant Hamiltonian with spin-dependent terms relevant for understanding hadron polarization in heavy ion collisions.

Contribution

It provides a detailed theoretical analysis of spin-vorticity coupling in massive vector bosons, including nonrelativistic reduction and quantum corrections, which advances understanding of hadron polarization phenomena.

Findings

Hamiltonian is non-Hermitian but PT-invariant

Leading order spin-vorticity coupling term is (1/2) s_z ħ ω

Includes relativistic and quantum corrections to the Hamiltonian

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.