Speaker
Description
One of remarkable features in the expected structure of the QCD phase diagram is the existence of QCD critical point (CP), which is the end point of the phase boundary of the first-order between the hadronic phase and the QGP phase. At the CP, the phase transition becomes second order, and thus there should be gapless and long-life modes called the soft modes, which govern the low-energy dynamics. Thus revealing the precise nature of the soft modes has a decisive importance for understanding the dynamical properties of the system around the CP.
In this talk, we shall report on an intensive investigation [1] of the soft mode at the QCD CP on the basis of the functional renormalization group (FRG) method in the local potential approximation. We calculate the spectral function as a function of the energy and momentum in the scalar and pseudo-scalar channels in the quark-meson model on the basis of the recent development[2]. At finite baryon chemical potential with a finite quark mass, the baryon-number fluctuation is coupled to the scalar channel and the spectral function in the sigma channel has a support not only in the time-like and but also in the space-like regions, which correspond to the mesonic and the particle-hole phonon excitations, respectively. We find that the energy of the peak position of the latter becomes vanishingly small with the height being enhanced as the system approaches the QCD CP, which is a manifestation of the fact that the phonon mode is the soft mode associated with the second-order transition at the CP, as was suggested by some authors[3,4]. We also extract the dispersion curves of the mesonic and the phonon modes, which leads to a novel and striking finding that the dispersion curve of the would-be sigma mesonic mode crosses the light-cone into the space-like region, and then eventually merge into the phonon mode as the system approaches further close to the CP. This suggests that the sigma-mesonic mode also becomes soft at the CP, in contrast to the pionic mode. We also discuss implications of the results on the type of possible inhomogeneous phases at higher densities and experiments, and theoretical elaboration to incorporate higher-derivative effects.
[1] T. Yokota, T. Kunihiro and K. Morita, arXiv:1603.02147.
[2] R. A. Tripolt, L. von Smekal and J. Wambach, Phys. Rev. D 90, no. 7, 074031 (2014).
[3] H. Fujii and M. Ohtani, Phys. Rev. D 70, 014016 (2004).
[4] D. T. Son and M. A. Stephanov, Phys. Rev. D 70, 056001 (2004).
