Unruh thermalization, gluon condensation, and freeze-out

The deconfinement transition and the hadronization mechanism at high energy are related to the quark-antiquark string breaking, and the corresponding temperature depends on the string tension $\sigma$. In the Unruh scheme of hadron production, it turns out $T=\sqrt{\sigma /2\pi }$, with $\sigma \simeq {\epsilon }^{\mathrm{vac}}$, the vacuum energy density. In heavy ion collisions at lower energy, i.e., large baryonchemical potential, ${\mu }_B$, the dynamics is dominated by Fermi statistics and baryon repulsion. However, one can still consider ${\epsilon }^{\mathrm{vac}}$ as the relevant physical scale, and its evaluation as a function of the baryon density, in a nuclear matter approach, gives dynamical information on the ${\mu }_B$ dependence of the hadronization temperature and on the value of the critical end point in the $T-{\mu }_B$ plane.

Figure 1

Freeze-out curve in the statistical hadronization model compared with the criteria discussed in the text. The green squares without error bars are the QCD lattice simulation data.

Figure 2

$T$ as a function of $\mu$ in the black-hole analogy based on Eq. (7).

Figure 3

Extrapolation of the number density as a function of ${\mu }_S={\mu }_B-m$; the green line refers to the nuclear matter results [55, 56].

Figure 4

Extrapolation of the binding density per nucleon as a function of ${\mu }_S={\mu }_B-m$ [55, 56].

Figure 5

Freeze-out curve for $T(0)=150\mathrm{MeV}$, ${\epsilon }^{\mathrm{vac}}({\mu }_B^0{)}^{1/4}=260\mathrm{MeV}$ and ${\mu }_B^0=200$, 400 MeV (blue points, black points). The green line gives the constant value for ${\mu }_B<{\mu }_B^0$.

Figure 6

Fit of the freeze-out curve which gives ${\mu }_B^0\simeq 0.353\mathrm{GeV}$ and ${\epsilon }^{\mathrm{vac}}({\mu }_B^0{)}^{1/4}=184\mathrm{Mev}$.