Speaker
Description
The restoration of the $SU(2)$ chiral symmetry is believed to occur at high temperatures, i.e., in the early universe. We generalize the $N/D$ dispersive method to finite-temperature scenarios to study the properties of the $\sigma$ meson observed in pion-pion scattering. The thermal $\sigma$ pole trajectory is obtained with cross-channel effects incorporated. The results predict a transition of the $\sigma$ particle into a bound state at high temperatures, along with the emergence of a novel subthreshold resonance pole.
Also, we uncover for the first time vacuum instabilities of the $O(N)$ model at large $m_\pi$ and high temperatures. Specifically, the phenomenologically favored vacuum describing $\pi$-$\sigma$ physics will move across the branch point of the effective potential and turn into a saddle point. Additionally, the effective coupling constant is defined and generalized to cases with nonzero pion masses and finite temperatures, demonstrating a strict correspondence between its sign (positive or negative) and the double-branch structure of the effective potential.
The $N/D$-modified $O(N)$ linear $\sigma$ model, in the light of dispersion relations and thermal field theory, not only deepens our understanding of the $\sigma$ particle at high temperatures which could be verified only in the early universe. Moreover, it may also serve as a valuable theoretical laboratory when studying the nonperturbative dynamics in QCD and the nonequilibrium dynamics of the cosmological phase transitions.
| Other topic / keywords: | QCD phase structure at high temperature, sigma meson transition in the early universe |
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