Meson Life Time in the Anisotropic Quark-Gluon Plasma

TL;DR

This paper investigates how meson lifetimes in an anisotropic quark-gluon plasma vary with temperature and anisotropy, using gauge/gravity duality and quasinormal mode analysis, revealing a polynomial relation and a Padé approximant connection.

Contribution

It introduces a numerical method to relate meson lifetime to anisotropy and temperature, and finds a novel polynomial and Padé approximant description of the plasma properties.

Findings

Meson lifetime decreases with increased anisotropy at fixed temperature.

A polynomial function describes the imaginary part of quasinormal mode frequencies.

The ratio (s/T^3)^6 can be expressed as a Padé approximant of the anisotropy parameter.

Abstract

In the hot (an)isotropic plasma the meson life time $\tau$ is defined as a time scale after which the meson dissociates. According to the gauge/gravity duality, this time can be identified with the inverse of the imaginary part of the frequency of the quasinormal modes, $\omega_I$, in the (an)isotropic black hole background. In the high temperature limit, we numerically show that at fixed temperature(entropy density) the life time of the mesons decreases(increases) as the anisotropy parameter raises. For general case, at fixed temperature we introduce a polynomial function for $\omega_I$ and observe that the meson life time decreases. Moreover, we realize that $(s/T^3)^6$, where $s$ and $T$ are entropy density and temperature of the plasma respectively, can be expressed as a function of anisotropy parameter over temperature. Interestingly, this function is a Pad\'{e} approximant.