Abstract
We show that the $\sigma/f_0(500)$ state with finite-temperature $T$ corrections to its spectral properties included, plays an essential role for the description of the scalar susceptibility $\chi_S$, signaling chiral symmetry restoration. First, we use the $O(4)$ Linear Sigma Model as a testbed to derive the connection between $\chi_S$ and the $\sigma$ propagator and to check the validity and reliability of the approach where $\chi_S$ is saturated by the $\sigma/f_0(500)$ inverse self-energy, which we calculate at finite $T$ to one loop. A more accurate phenomenological description is achieved by considering the saturation approach as given by the thermal $f_0(500)$ state generated in Unitarized Chiral Perturbation Theory. Such approach allows to describe fairly well recent lattice data within the uncertainty range given by the UChPT parameters. Finally, we compare the UChPT saturated description with one based on the Hadron Resonance Gas, for which the hadron mass dependences are extracted from recent theoretical analysis. Several fits to lattice data are performed, which confirm the validity of the thermal $f_0(500)$ saturated approach and hence the importance of that thermal state for chiral symmetry restoration.
Highlights
Chiral symmetry restoration and its nature are surely among the key problems for our present understanding of the QCD phase diagram
We use the Oð4Þ linear sigma model as a test bed to derive the connection between χS and the σ propagator and to check the validity and reliability of the approach where χS is saturated by the σ=f0ð500Þ inverse self-energy, which we calculate at finite T to one loop
A more accurate phenomenological description is achieved by considering the saturation approach as given by the thermal f0ð500Þ state generated in unitarized chiral perturbation theory (UChPT)
Summary
Chiral symmetry restoration and its nature are surely among the key problems for our present understanding of the QCD phase diagram. II, in which we will focus the discussion on the Oð4Þ linear sigma model (LSM) as an example of a theory including explicitly the σ degree of freedom, in which the connection between the scalar susceptibility and the σ self-energy will be analyzed, and on unitarized ChPT (UChPT), which provides a more accurate description of the f0ð500Þ state at T 1⁄4 0 without the need of such a state in the Lagrangian In both cases, we will see that the saturated approach provides a description closer to lattice data, the UChPT approach reproducing the expected crossover peak unlike the LSM one. The present analysis will confirm the importance of considering thermal (or generally in-medium) interactions to describe certain hadron gas observables and the relevance in particular of the f0ð500Þ thermal sate, opening up interesting possibilities for future theoretical and lattice studies. Within UChPT, we will consider a saturated approach in terms of the thermal f0ð500Þ generated as a pole in ππ scattering
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