Spin alignment of vector mesons in local equilibrium by Zubarev's approach

TL;DR

This paper calculates the spin alignment of vector mesons in local equilibrium using Zubarev's approach, revealing that non-zero effects appear only at second order in gradients and discussing the properties under time reversal.

Contribution

It provides a second-order gradient expansion calculation of spin alignment in local equilibrium, highlighting the first order vanishing and the T-odd nature of the shear-induced effect.

Findings

First order spin alignment $ ho_{00}=1/3$ with vanishing contributions.

Non-zero second order contributions from thermal shear stress.

First order effect is dissipative due to T-odd transport coefficient.

Abstract

We compute the $00$ element of the spin density matrix, denoted as $\rho_{00}$ and called the spin alignment, up to the second order of the gradient expansion in local equilibrium by Zubarev's approach. In the first order, we obtain $\rho_{00}=1/3$, meaning that the contributions from thermal vorticity and shear stress tensor are vanishing. The non-vanishing contributions to $\rho_{00}-1/3$ appear in the second order of gradients in the Belinfante and canonical cases. We also discuss the properties of the spin density matrix under the time reversal transformation. The effective transport coefficient for the spin alignment induced by the thermal shear stress tensor is T-odd in the first order, implying that the first order effect is dissipative.