Light scalar K₀^(*)(700) meson in vacuum and a hot medium

The $K_{0}^{*}(700)$ meson appears as the lightest strange scalar meson in PDG. Although there were a lot of experimental and theoretical efforts to establish this particle and determine its properties and nature, it still needs confirmation in an experiment and its internal quark-gluon organization needs to be clarified. In this connection, we study some spectroscopic properties of this state in a hot medium as well as a vacuum by modeling it as a usual meson of a quark and an aniquark. In particular, we investigate its mass and coupling or decay constant in terms of the temperature of a hot medium by including the medium effects by the fermionic and gluonic parts of the energy momentum tensor as well as the temperature-dependent continuum threshold, quark, gluon and mixed condensates. We observe that the mass of $K_{0}^{*}(700)$ remains unchanged up to $T \simeq 0.6 ~ T_c$ with $ T_c $ being the critical temperature, but it starts to diminish after this point and approaches zero near to the critical temperature referring to the melting of the meson. The coupling of $K_{0}^{*}(700)$ is also sensitive to $ T $ at higher temperatures. It starts to grow rapidly after $T \simeq 0.85 ~ T_c$. We turn off the medium effects and calculate the mass and coupling of the $K_{0}^{*}(700)$ state at zero temperature. The obtained mass is in accord with the average Breit-Wigner mass value reported by PDG.