Novel picture of the soft modes at the QCD critical point based on the FRG method

TL;DR

This paper uses the functional renormalization group to study the soft modes at the QCD critical point, revealing the softening of the sigma-mesonic and hydrodynamic modes and their merging near the critical point.

Contribution

It provides a novel analysis of the soft modes at the QCD critical point using the FRG method, highlighting the behavior of mesonic and phonon modes.

Findings

The peak of the particle-hole mode in the sigma channel vanishes near the CP.

The sigma-mesonic mode's dispersion crosses into the space-like region and merges with the phonon mode.

The sigma-mesonic mode and hydrodynamic mode form a combined soft mode at the CP.

Abstract

We investigate the soft mode at the QCD critical point (CP) on the basis of the functional renormalization group. We calculate the spectral functions in the meson channels in the two-flavor quark--meson model. Our result shows that the energy of the peak position of the particle--hole mode in the sigma channel becomes vanishingly small as the system approaches the QCD CP, which is a manifestation of the softening of the phonon mode. We also extract the dispersion curves of the mesonic and the phonon mode, a hydrodynamic mode which leads to a finding that the dispersion curve of the sigma-mesonic mode crosses the light-cone into the space-like momentum region, and then eventually merges into the phonon mode as the system approaches further close to the CP. This may suggest that the sigma-mesonic mode forms the soft mode together with the hydrodynamic mode at the CP.