Relativistic spin dynamics for vector mesons

TL;DR

This paper develops a relativistic theoretical framework for analyzing the spin density matrices of vector mesons, enabling more accurate calculations of spin observables like $ ho_{00}$, and links these to fundamental QCD properties through field fluctuations.

Contribution

It introduces a relativistic theory based on Kadanoff-Baym equations for spin density matrices of vector mesons, with a novel factorization of $ ho_{00}$ and insights into field correlations within the meson.

Findings

Formulation of $ ho_{00}$ for $phi$ mesons in a factorized form.

Identification of the main contribution to $ ho_{00}$ from $phi$ field polarization.

Connection between field fluctuations and QCD properties via $ ho_{00}$ measurements.

Abstract

We propose a relativistic theory for spin density matrices of vector mesons based on Kadanoff-Baym equations in the closed-time-path formalism. The theory puts the calculation of spin observables such as the spin density matrix element $\rho_{00}$ for vector mesons on a solid ground. Within the theory we formulate $\rho_{00}$ for $\phi$ mesons into a factorization form in separation of momentum and space-time variables. We argue that the main contribution to $\rho_{00}$ at lower energies should be from the $\phi$ fields that can polarize the strange quark and antiquark in the same way as electromagnetic fields. The key observation is that there is correlation inside the $\phi$ meson wave function between the $\phi$ field that polarizes the strange quark and that polarizes the strange antiquark. This is reflected by the fact that the contributions to $\rho_{00}$ are all in squares of fields which are nonvanishing even if the fields may strongly fluctuate in space-time. The fluctuation of strong force fields can be extracted from $\rho_{00}$ of quarkonium vector mesons as links to fundamental properties of quantum chromodynamics.