Thermal behaviors of light scalar resonances at low temperatures

Abstract

We study the thermal properties of the lowest multiplet of the QCD light-flavor scalar resonances, including the $f_0(500)/\sigma$, $K_0^{\ast }(700)/\kappa$, $f_0(980)$ and $a_0(980)$, in the framework of unitarized $U(3)$ chiral perturbation theory. After the successful fits to the meson-meson scattering inputs, such as the phase shifts and inelasticities, we obtain the unknown parameters and further calculate the resonance poles and their residues at zero temperature. By including the finite-temperature effects in the unitarized meson-meson scattering amplitudes, the thermal behaviors of the scalar resonance poles in the complex energy plane are studied. The masses of $\sigma$ and $\kappa$ are found to considerably decrease when increasing the temperatures, while their widths turn out to be still large when the temperatures reach around $200$ MeV. In contrast, both the masses and widths of the $f_0(980)$ and $a_0(980)$ are only slightly changed.

arXiv comment25 pages, 6 figures. To match the published version in PRD. Thermal contributions from the tadpole diagrams are included. A numerical error when searching the thermal poles is corrected. The main conclusions remain unchanged

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