The interpretation of quark ($q$)- antiquark ($bar q$) pairs production and the sequential string breaking as tunneling through the event horizon of colour confinement leads to a thermal hadronic spectrum with a universal Unruh temperature, $T simeq
165$ Mev,related to the quark acceleration, $a$, by $T=a/2pi$. The resulting temperature depends on the quark mass and then on the content of the produced hadrons, causing a deviation from full equilibrium and hence a suppression of strange particle production in elementary collisions. In nucleus-nucleus collisions, where the quark density is much bigger, one has to introduce an average temperature (acceleration) which dilutes the quark mass effect and the strangeness suppression almost disappears.
In this article we study chiral symmetry breaking for quark matter in a magnetic background, $bm B$, at finite temperature and quark chemical potential, $mu$, making use of the Ginzburg-Landau effective action formalism. As a microscopic model to com
pute the effective action we use the renormalized quark-meson model. Our main goal is to study the evolution of the critical endpoint, ${cal CP}$, as a function of the magnetic field strength, and investigate on the realization of inverse magnetic catalysis at finite chemical potential. We find that the phase transition at zero chemical potential is always of the second order; for small and intermediate values of $bm B$, ${cal CP}$ moves towards small $mu$, while for larger $bm B$ it moves towards moderately larger values of $mu$. Our results are in agreement with the inverse magnetic catalysis scenario at finite chemical potential and not too large values of the magnetic field, while at larger $bm B$ direct magnetic catalysis sets in.
We calculate the speed of sound $c_s$ in an ideal gas of resonances whose mass spectrum is assumed to have the Hagedorn form $rho(m) sim m^{-a}exp{bm}$, which leads to singular behavior at the critical temperature $T_c = 1/b$. With $a = 4$ the pressu
re and the energy density remain finite at $T_c$, while the specific heat diverges there. As a function of the temperature the corresponding speed of sound initially increases similarly to that of an ideal pion gas until near $T_c$ where the resonance effects dominate causing $c_s$ to vanish as $(T_c - T)^{1/4}$. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around $T_c$, the actual critical behavior in these models is no longer present.
We explore the relevance of confinement in quark matter models for the possible quark core of neutron stars. For the quark phase, we adopt the equation of state (EoS) derived with the Field Correlator Method, extended to the zero temperature limit. F
or the hadronic phase, we use the microscopic Brueckner-Hartree-Fock many-body theory. We find that the currently adopted value of the gluon condensate $G_2 simeq 0.006-0.007 rm {GeV^4}$, which gives a critical temperature $T_c simeq 170 rm MeV$, produces maximum masses which are only marginally consistent with the observational limit, while larger masses are possible if the gluon condensate is increased.
The thermal multihadron production observed in different high energy collisions poses two basic problems: (1) why do even elementary collisions with comparatively few secondaries (e+e- annihilation) show thermal behaviour, and 2) why is there in such
interactions a suppression of strange particle production? We show that the recently proposed mechanism of thermal hadron production through Hawking-Unruh radiation can naturally account for both. The event horizon of colour confinement leads to thermal behaviour, but the resulting temperature depends on the strange quark content of the produced hadrons, causing a deviation from full equilibrium and hence a suppression of strange particle production. We apply the resulting formalism to multihadron production in e+e- annihilation over a wide energy range and make a comprehensive analysis of the data in the conventional statistical hadronization model and the modified Hawking-Unruh formulation. We show that this formulation provides a very good description of the measured hadronic abundances, fully determined in terms of the string tension and the bare strange quark mass; it contains no adjustable parameters.
The recently suggested interpretation of the universal hadronic freeze-out temperature T_f ~ 170 Mev - found for all high energy scattering processes that produce hadrons: e+ e-, p p, p anti-p, pi p, etc. and N N (heavy-ion collisions) - as a Unruh t
emperature triggers here the search for the gravitational black-hole that in its near-horizon approximation better simulates this hadronic phenomenon. To identify such a black-hole we begin our gravity-gauge theory phenomenologies matching by asking the question: which black-hole behind that Rindler horizon could reproduce the experimental behavior of T_f (sqrt{s}) in N N, where sqrt{s} is the collision energy. Provided certain natural assumptions hold, we show that the exact string black-hole turns out to be the best candidate (as it fits the available data on T_f (sqrt{s})) and that its limiting case, the Witten black-hole, is the unique candidate to explain the constant T_f for all elementary scattering processes at large energy. We also are able to propose an effective description of the screening of the hadronic string tension sigma(mu_b) due to the baryon density effects on T_f.
