Light scalar ${K}_{0}^{*}\left(700\right)$ meson in vacuum and a hot medium

The ${K}_{0}^{*}\left(700\right)$ meson appears as the lightest strange scalar meson in Particle Data Group (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 antiquark. 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 ${K}_{0}^{*}\left(700\right)$ 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 ${K}_{0}^{*}\left(700\right)$ 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 ${K}_{0}^{*}\left(700\right)$ state at zero temperature. The obtained mass is in accord with the average Breit-Wigner mass value reported by PDG.