The spin alignment of rho mesons in a pion gas

TL;DR

This paper investigates the spin alignment of neutral rho mesons in a pion gas using spin kinetic equations, finding that interactions produce minimal alignment that quickly diminishes over time.

Contribution

It derives collision terms at leading and next-to-leading order in spin Boltzmann equations and simulates the evolution of rho meson spin alignment under various initial conditions.

Findings

Interaction induces very small spin alignment in the central rapidity region.

Spin alignment rapidly decays over time if initially present.

Deviation of b1_{00} from 1/3 is positive but very small.

Abstract

We study the spin alignment of neutral rho mesons in a pion gas using spin kinetic or Boltzmann equations. The $\rho\pi\pi$ coupling is given by the chiral effective theory. The collision terms at the leading and next-to-leading order in spin Boltzmann equations are derived. The evolution of the spin density matrix of the neutral rho meson is simulated with different initial conditions. The numerical results show that the interaction of pions and neutral rho mesons creates very small spin alignment in the central rapidity region if there is no rho meson in the system at the initial time. Such a small spin alignment in the central rapidity region will decay rapidly toward zero in later time. If there are rho mesons with a sizable spin alignment at the initial time the spin alignment will also decrease rapidly. We also considered the effect on $\rho_{00}$ from the elliptic flow of pions in the blast wave model. With vanishing spin alignment at the initial time, the deviation of $\rho_{00}$ from 1/3 is positive but very small.