Linear response theory for spin alignment of vector mesons in thermal media

TL;DR

This paper develops a linear response theory approach to calculate the spin alignment of vector mesons in a thermal quark-gluon plasma, highlighting the influence of spectral functions and medium interactions.

Contribution

It introduces a first-order expansion method using the Kubo formula to analyze spin alignment in thermal media, incorporating spectral functions from quark-meson interactions.

Findings

Thermal shear tensor causes a small correction to spin alignment (~10^{-4} to 10^{-5}).

Spectral functions are crucial for understanding meson spin behavior in medium.

The correction magnitude depends on the quark-meson coupling constant.

Abstract

We present a calculation of the spin alignment for unflavored vector mesons in thermalized quark-gluon plasma based on the Kubo formula in linear response theory. This is achieved by expanding the system to the first order of the coupling constant and the spatial gradient. The effect strongly relies on the vector meson's spectral functions which are determined by the interaction and medium properties. The spectral functions are calculated for the one-quark-loop self-energy with meson-quark interaction. The numerical results show that the correction to the spin alignment from the thermal shear tensor is of the order $10^{-4}\sim10^{-5}$ for the chosen values of quark-meson coupling constant, if the magnitude of thermal shear tensor is $10^{-2}$.