# Quark Matter 2018

13-19 May 2018
Venice, Italy
Europe/Zurich timezone
The organisers warmly thank all participants for such a lively QM2018! See you in China in 2019!

## Tachyonic instability of the scalar mode prior to the QCD critical point based on the functional renormalization-group method in the two-flavor case

15 May 2018, 17:00
2h 40m
First floor and third floor (Palazzo del Casinò)

### First floor and third floor

#### Palazzo del Casinò

Poster Phase diagram and search for the critical point

### Speaker

Takeru Yokota (Kyoto University, Japan)

### Description

We investigate spectral properties of the collective excitations around the QCD critical point (CP) by applying the functional renormalization-group (FRG) method to the two-flavor quark-meson model with current quark mass $m_q$ being varied. The nature of the CP such as the soft modes is known to be affected by the value of $m_q$: We first determine the whole phase structure in the three-dimensional space $(T, μ, m_q)$ consisting of temperature $T$, quark chemical potential $\mu$ and $m_q$, with the tricritical point, $\mathrm{O}(4)$ and $\mathrm{Z}_2$ critical lines being located; they altogether make a winglike shape quite reminiscent of those known in the condensed matters with a tricritical point. We then calculate the spectral functions in the scalar and pseudoscalar channel around the critical points. We find that the sigma mesonic mode becomes tachyonic with a superluminal velocity at finite momenta before the system reaches the $\mathrm{Z}_2$ point from the lower density, even for $m_q$ smaller than the physical value. One of the possible implications of the appearance of such a tachyonic mode at finite momenta is that the assumed equilibrium state with a uniform chiral condensate is unstable toward a state with an inhomogeneous $\sigma$ condensate. No such anomalous behavior is found in the pseudoscalar channel. We find that the $\sigma$-to-$2\sigma$ coupling due to finite $m_q$ plays an essential role for the drastic modification of the spectral function.

Content type Theory Presenter name already specified

### Primary authors

Takeru Yokota (Kyoto University, Japan) Teiji Kunihiro (Kyoto University) Kenji Morita (Kyoto University)

### Presentation Materials

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