Pseudoscalar mesons in hot, dense matter

Phase transitions in hot and dense matter, and the in-medium behavior of pseudoscalar mesons (${\pi }^{\pm }$, ${\pi }^0$, $K^{\pm }$, $K^0$, ${\overline{K}}^0$, $\eta$, and ${\eta }^{\prime }$), are investigated, in the framework of the three flavor Nambu-Jona-Lasinio model, including the ’t Hooft interaction, which breaks the $U_A\left(1\right)$ symmetry. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in quark matter with different degrees of strangeness, and finite temperature and density. At $T=0$, the role of strange valence quarks in the medium is discussed, in connection with the phase transition and the mesonic behavior. It is found that the appearance of strange quarks, above certain densities, leads to meaningful changes in different observables, especially in matter with $\beta$ equilibrium. The behavior of mesons in the $T\text{‐}\rho$ plane is analyzed in connection with possible signatures of restoration of symmetries.

Figure 1

Temperature dependence of the pion (solid line), kaon (dotted line), $\eta$ (dashed line), and ${\eta }^{\prime }$ (short-dashed line) masses. The curves $2M_u$ and $M_u+M_s$ (dot-dashed line) show the temperature dependence of the quark thresholds. The respective Mott temperatures are $T_{M\pi }\simeq T_{MK}=212\mathrm{MeV}$ and $T_{M\eta }=180\mathrm{MeV}$.

Figure 2

Energy per baryon number (a) and pressure (b) as a function of density. Solid line: $T=0$, dashed line: $T=56\mathrm{MeV}$.

Figure 3

Energy per baryon number for all types of quark matter considered at $T=0$.

Figure 4

Constituent quark masses $M_u$, $M_d$, $M_s$ and chemical potentials ${\mu }_u$, ${\mu }_d$, ${\mu }_e$ as functions of density at $T=0$. Left panel: without $\beta$ equilibrium ($M_u=M_d$ in Cases II and III). Right panel: with $\beta$ equilibrium.

Figure 5

Combined effects of temperature $\left(T\right)$ and density $({\rho }_n∕{\rho }_0)$ in neutron matter in $\beta$ equilibrium: (a) pressure, (b) $M_u$, and (c) $M_s$.

Figure 6

Pion masses as functions of density without (left panel) and with (right panel) $\beta$ equilibrium at $T=0$.

Figure 7

Kaon and antikaon masses as functions of density at $T=0$: Case I (a) and (c), and with $\beta$ equilibrium (b) and (d). ${\omega }^{\prime }$ is the lower limit of the Dirac sea continuum; ${\omega }_{\mathit{\text{up}}}$, ${\omega }_{\mathit{\text{low}}}$ are the limits of the Fermi sea continuum.

Figure 8

Density dependence of meson-quark coupling constants for $T=0$: Case I (a) and (c), and with $\beta$ equilibrium (b) and (c).

Figure 9

Kaon and antikaon masses (left panel) and meson-quark coupling constants (right panel) as functions of density for Cases II and III at $T=0$. In Case II $K^0$, ${\overline{K}}^0$, and ${\overline{K}}_S^0$ are degenerated with $K^{+}$, $K^{-}$, and $K_S^{-}$, respectively. In Case III all kaons are degenerated (dash-dot-dot line).

Figure 10

$\eta$ and ${\eta }^{\prime }$ masses as functions of density without (left panel) and with (right panel) $\beta$ equilibrium at $T=0$. ${\omega }_u$, ${\omega }_d$ are the limits of the Dirac continua.

Figure 11

Pion masses as functions of temperature and density.

Figure 12

Kaon masses as functions of temperature and density.