Tachyonic instability of the scalar mode prior to QCD critical point based on Functional renormalization-group method

Understand

We establish and elucidate the physical meaning of the appearance of an acausal mode in the sigma mesonic channel, found in the previous work by the present authors, when the system approaches the $\mathrm{Z}_{2}$ critical point.

• The functional renormalization group method is applied to the two--flavor quark--meson model with varying current quark mass $m_q$ even away from the physical value at which the pion mass is reproduced.
• We first determine the whole phase structure in the three-dimensional space $(T, \mu, m_q)$ 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 wing-like shape quite reminiscent of those known in the condensed matters with a tricritical point.
• We then calculate the spectral functions $\rho_{\sigma, \pi}(\omega, p)$ in the scalar and pseudoscalar channel around the critical points.