Meson Life Time in the Anisotropic Quark-Gluon Plasma

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.