Abstract
In this work, we self-consistently explore the possibility of charged pion superfluidity and cosmic trajectories in early Universe under the framework of Polyakov-Nambu--Jona-Lasinio model. By taking the badly constrained lepton flavor asymmetries $l_{\rm e}$ and $l_\mu$ as free parameters, the upper boundaries of pion superfluidity phase are consistently found to be around the pseudocritical temperature at zero chemical potentials. So the results greatly support the choice of $T=0.16~{\rm GeV}$ as the upper boundary of pion superfluidity in the previous lattice QCD study. Take $l_{\rm e}+l_\mu=-0.2$ as an example, we demonstrate the features of pion condensation and the associated cosmic trajectories with the evolution of early Universe. While the trajectory of electric chemical potential reacts strongly at both the lower and upper boundaries of reentrant pion superfluidity, the trajectories of other chemical potentials only respond strongly at the upper boundary.
Highlights
As we know, the field of high energy nuclear physics (HENP) initiated with the search of quark-gluon plasma (QGP) phase [1] for quantum chromodynamics (QCD) matter, and the QGP phase was expected to be realized through relativistic heavy ion collisions (HICs) [2,3]
We obtain the upper boundaries of pion superfluidity to be consistently T ∼ 0.21 GeV, which is much larger than Tpc, a well-known drawback of the PNJL model [32]
The upper boundaries are almost the corresponding pseudocritical temperatures at zero chemical potentials, which supports the setting of the upper boundary around Tpc in Ref. [22]
Summary
The field of high energy nuclear physics (HENP) initiated with the search of quark-gluon plasma (QGP) phase [1] for quantum chromodynamics (QCD) matter, and the QGP phase was expected to be realized through relativistic heavy ion collisions (HICs) [2,3]. In the QCD epoch, the baryon and lepton number Uð1Þ symmetries were already violated, and the tracing back of the observations in the present Universe constrains the corresponding number densities as nB=s 1⁄4 8.6 à 10−11 [23] and jnl=sj < 0.012 [24] with s the entropy density Under these and electric neutrality constraints, the cosmic trajectories of several chemical potentials were explored by combining the hadron resonance gas model, lattice QCD, and the free quark gas model [25]. [22], the temperature effect on mπÆðμQ; TÞ, the order parameter of their effective mass model, was only taken into account through the ideal gas part This might be the reason why the lattice QCD inspired model could not predict the upper phase boundary.
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