Mesons in a soft-wall AdS-Schwarzschild approach at low temperature

Abstract

We derive a holographic soft-wall approach in five dimensional AdS-Schwarzschild space for the description of mesons at finite temperature. In this first application we consider the small temperature limit and derive analytical expression for the mass spectrum of mesons with adjustable quantum numbers $n$ (radial number), $L$ (angular orbital momentum) and $J$ (total angular momentum). We explicitly separate the contribution at zero temperature and the leading order temperature correction. The temperature corrections arise from the temperature dependence of the dilaton parameter (which is the parameter of spontaneous breaking of chiral symmetry related to the pseudoscalar meson decay constant) and the warping of the AdS metric due to temperature. We extend our results to any hadron with integer spin (tetraquarks, dibaryons, etc.). We present numerical analysis for the temperature dependence of meson masses and form factors.