Relativistic spin dynamics for vector mesons

TL;DR: In this article , a relativistic theory for spin density matrices of vector mesons based on Kadanoff-Baym equations in the closed-time-path formalism was proposed.

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 ρ 00 for vector mesons on a solid ground. Within the theory we formulate ρ 00 for φ mesons into a factorization form in separation of momentum and space-time variables. We argue that the main contribution to ρ 00 at lower energies should be from the φ 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 φ meson wave function between the φ field that polarizes the strange quark and that polarizes the strange antiquark. This is reflected by the fact that the contributions to ρ 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 ρ 00 of quarkonium vector mesons as links to fundamental properties of quantum chromodynamics.