Pion condensation in ultra-relativistic collisions presents a compelling theoretical phenomenon with significant implications for the dynamics of hadronic matter. Various theoretical frameworks offer insight into the nature of high-temperature Bose-Einstein condensation (BEC). The present study investigates the dissipative behavior of a relativistic pion gas undergoing Bose-Einstein condensation (BEC) in ultra-relativistic heavy-ion collisions. Further, we obtain viscosity ($η$), bulk viscosity ($ζ$), and speed of sound ($c_s$) by employing the Boltzmann transport equation with the relaxation time approximation. Findings show a substantial drop in $η/s$ and $ζ/s$ with the fractional increase in condensation. This effect is becoming more evident in larger systems approaching the thermodynamic limit. Alongside the reduction in viscosities, the speed of sound also decreases with increasing condensation, indicating a softening of the equation of state. The analysis of finite-size effects reveals that larger systems exhibit more pronounced signatures of BEC. These results suggest that pion condensation can influence the hydrodynamic evolution of the hadronic phase in heavy-ion collisions, with consequential implications for interpreting collective flow observables and the underlying equation of state.
We show that the combined effects of a rotation plus a magnetic field can cause charged pion condensation. We suggest that this phenomenon may yield to observable effects in current heavy ion collisions at collider energies, where large magnetism and rotations are expected in off-central collisions.
The intriguing possibility of Bose-Einstein condensation of pions at the LHC is examined with the use of higher order moments of the multiplicity distribution. The scaled variance, skewness and kurtosis are calculated for the pion system. The obtained results show that the normalized kurtosis has a significant increase for the case of the pion condensation.
The possibility of formation of Bose-Einstein Condensation (BEC) is studied in $pp$ collisions at $\sqrt s$ = 7 TeV at the Large Hadron Collider. A thermodynamically consistent non-extensive formulation of the identified hadron transverse momentum distributions is used to estimate the critical temperature required to form BEC of charged pions, which are the most abundant species in a multi-particle production process in hadronic and nuclear collisions. The obtained results have been contrasted with the systems produced in Pb-Pb collisions to have a better understanding. We observe an explicit …
The formation of charged pion condensate under parallel electromagnetic fields is studied within the two-flavor Nambu--Jona-Lasinio model. The technique of Schwinger proper time method is extended to explore the quantity locating in the off-diagonal flavor space, i.e., charged pion. We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find out that it contains a sextic term which possibly induce weakly first order phase transition. Dependence of pion condensation on model parameters is investigated.
The phase diagram of dense quark matter with chiral imbalance is considered with the conditions of electric neutrality and $β$-equilibrium. It has been shown recently that chiral imbalance can generate charged pion condensation in dense quark matter, so it was interesting to verify that this phenomenon takes place in realistic physical scenarios such as electrically neutral matter in $β$-equilibrium, because a window of pion condensation at dense quark matter phase diagram (without chiral imbalance) predicted earlier was closed by the consideration of these conditions at the physical current q…
The indications of a possible pion condensation at the LHC are summarized. The condensation is predicted by the non-equilibrium hadronization model for 2.76 TeV Pb+Pb collisions at the LHC. The model solves the proton/pion puzzle and reproduces the low $p_T$ enhancement of the pion spectra, as well as the spectra of protons and antiprotons, charged kaons, $K^0_S$, $K^*(892)^0$ and $ϕ(1020)$. The obtained parameters allow to estimate the amount of pion condensate on the level of 5\% from the total number of pions at the LHC. The condensate is located at $p_T<250$ MeV.
We investigate the possibility of charged pion condensation in the presence of parallel rotation and magnetic field within the Nambu--Jona-Lasinio model with quarks as the fundamental degrees of freedom. Previous study based on non-interacting Klein-Gordon theory for pions showed that the charged pions will undergo Bose-Einstein condensation under this circumstance [Y. Liu and I. Zahed, Phys. Rev. Lett. ${\bf 120}$, 032001 (2018)]. In this work, we take into account the internal quark structures of charged pions self-consistently through quark polarization loops in an interacting theory, i.e.,…
The Bose-Einstein condensation and the liquid-gas first order phase transition are studied in the interacting pion matter. Two phenomenological models are used: the mean-field model and the hybrid model. Free model parameters are fixed by fitting the lattice QCD data on the pion Bose condensate density at zero temperature. In spite of some minor differences the two model demonstrate an identical qualitative and very close quantitative behavior for the thermodynamic functions and electric charge fluctuations. A peculiar property of the considered models is an intersection of the Bose-Einstein c…
The behavior of pions is studied in systems where their normal leptonic decay is forbidden. When thermal fluctuations are present, a low decay rate is generated, and as a consequence of lepton recombination, the amount of pions remains almost unaltered. Compact stars conditions are favorable for the formation of such intermediate state of charged pions: near condensation and almost stable, leading to a continuum source of anti-neutrinos. In particular, protoneutron stars could be an scenario where this state of matter is relevant.
S-wave pion-nucleon interactions in the linear sigma model, and in Manohar-Georgi and Gasser-Sainio-Svarc models with finite number of terms in Lagrangians, as well as in a general phenomenological approach are reviewed. Subtleties associated with the current algebra theorems and field redefinitions are discussed. In the first and third models most likely the s-wave pion condensation in the isospin-symmetric matter does not occur at least up to high densities, whereas within the second model it may appear already at moderate densities. In the phenomenological approach two parameterizations of …
We studied thermal evolution of isolated neutron stars (NSs) including the pion condensation core, with an emphasis on the stiffness of equation of state (EOS). Many temperature observations can be explained by the minimal cooling scenario which excludes the fast neutrino cooling process. However, several NSs are cold enough to require it. The most crucial problem for NS cooling theory is whether the nucleon direct Urca (DU) process is open. The DU process is forbidden if the nucleon symmetry energy is significantly low. Hence, another fast cooling process is required in such an EOS. As the ca…
We analyse in detail the possibility of Bose-Einstein condensation of pions produced in heavy-ion collisions at the beam energy $\sqrt{s_{\rm NN}}$ = 2.76 TeV. Our approach is based on the chemical non-equilibrium thermal model of hadron production which has been generalised to include separately the contribution from the local zero-momentum state. In order to study both the hadronic multiplicities and the transverse-momentum spectra, we use the Cracow freeze-out model which parameterises the flow and space-time geometry of the system at freeze-out in a very economic way. Our analysis indicate…
We revisit the suggestion that charged rho-mesons undergo Bose-Einstein condensation in isospin-rich nuclear matter. Using a simple version of the Nambu-Jona-Lasinio (NJL) model, we conclude that rho-meson condensation is either avoided or postponed to isospin chemical potentials much higher than the rho-meson mass as a consequence of the repulsive interaction with the preformed pion condensate. In order to support our numerical results, we work out a linear sigma model for pions and rho-mesons, showing that the two models lead to similar patterns of medium dependence of meson masses. As a byp…
Finite isospin chemical potential $μ_I$ and temperature $T$ have been introduced in the framework of soft-wall AdS/QCD model. By self-consistently solve the equation of motion, we obtain the phase boundary of pion condensation phase, across which the system undergoes a phase transition between pion condensation phase and normal phase. Comparing the free energy of solutions with and without pion condensation, we find that the phase transition is of first order type both at large $μ_I$ and small $μ_I$. Qualitatively, the behavior at large $μ_I$ is in agreement with the lattice simulation in Phys…
In this work pion and kaon condensation in the framework of chiral perturbation theory is studied. I consider a system at vanishing temperature with nonzero isospin chemical potential and strangeness chemical potential; meson masses and mixing in the normal phase, the pion condensation phase and the kaon condensation phase are described. There are differences with previous works, but the results presented here are supported by both theory group analysis and by direct calculations. Some pion decay channels in the normal and the pion condensation phases are studied, finding a nonmonotonic behavi…
We study the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant $I_2=\vec{E}\cdot{\vec B}$. We show that the presence of $I_2$ can induce neutral pion ($π^0$) condensation in the QCD vacuum through the electromagnetic triangle anomaly. Within the frameworks of chiral perturbation theory at leading small-momenta expansion as well as the Nambu--Jona-Lasinio model at leading $1/N_c$ expansion, we quantify the dependence of the $π^0$ condensate on $I_2$. The stability of the $π^0$-condensed vacuum against the Schwinger charged pair producti…
The relaxation times over which dissipative fluxes restore their steady state values have been evaluated for a pion gas using the 14-moment method. The effect of the medium has been implemented through a temperature dependent pi-pi cross-section in the collision integral which is obtained by including one-loop self-energies in the propagators of the exchanged rho and sigma mesons. To account for chemical freeze out in heavy ion collisions, a temperature dependent pion chemical potential has been introduced in the distribution function. The temperature dependence of the relaxation times for she…
After the first predictions in seventies that in dense nuclear matter, for example, in neutron stars there could be pion condensation phenomenon, it was shown that at least s-wave pion condensation is unlikely to occur in such a medium in different approaches including NJL model consideration with neutrality and $β$-equilibrium condition. Then it has been found a condition that can promote this phenomenon in dense baryonic matter, it is chiral imbalance, so now it is interesting if this generation can survive rather strict requirement of electric neutrality and $β$-equilibrium. Here in this pa…
We study the asymmetric nuclear matter using a holographic QCD model by introducing a baryonic charge in the infrared boundary. We first show that, in the normal hadron phase, the predicted values of the symmetry energy and it's slope parameter are comparable with the empirical values. We find that the phase transition from the normal phase to the pion condensation phase is delayed compared with the pure mesonic matter: The critical chemical potential is larger than the pion mass which is obtained for the pure mesonic matter. We also show that, in the pion condensation phase, the pion contribu…
We analyze various aspects of pion and kaon condensation in the framework of chiral perturbation theory. Considering a system at vanishing temperature and varying the isospin chemical potential and the strange quark chemical potential we reproduce known results about the phase transition to the pion condensation phase and to the kaon condensation phase. However, we obtain mesonic mixings and masses in the condensed phases that are in disagreement with the results reported in previous works. Our findings are obtained both by a theory group analysis and by direct calculation by means of the same…
We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the $μ_I$--$T$ plane where $μ_I$ is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At $T=0$, the onset of pion condensation is at $μ_I={1\over2}m_π$ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of $μ_I$ and in the $O(2)$ universality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends…
Dilepton Production as a Probe of Pion Condensation in Hot and Dense QCD Matter
University of Wrocław（弗罗茨瓦夫大学）；West University of Timişoara（蒂米什瓦拉西大学）；Aliah University（阿利亚大学）；Polish Academy of Sciences PAN（波兰科学院）；Hiroshima University（广岛大学）
Signatures from pion condensation and lepton flavor asymmetries in the cosmological gravitational wave background
Instituto de Física, Universidade de São Paulo（圣保罗大学物理研究所）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）；Institut für Theoretische Physik, J. W. Goethe Universität（歌德大学理论物理研究所）
The phase structure of dense quark matter in the two color case has been investigated with nonzero baryon $μ_B$, isospin $μ_I$ and chiral isospin $μ_{I5}$ chemical potentials. %in the framework of Nambu--Jona-Lasinio model with quark-antiquark and quark-quark interaction channels. It has been shown in the mean-field approximation that there exist three dualities, one of them between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case. The other two dual symmetries between the phase with condensation of charged pions and the phase wi…
The Chiral Soliton Lattice (CSL) is a state with a periodic array of topological solitons that spontaneously breaks parity and translational symmetries. Such a state is known to appear in chiral magnets. We show that CSL also appears as a ground state of quantum chromodynamics at nonzero chemical potential in a magnetic field. By analyzing the fluctuations of the CSL, we furthermore demonstrate that in strong but achievable magnetic fields, charged pions undergo Bose-Einstein condensation. Our results, based on a systematic low-energy effective theory, are model-independent and fully analytic.
The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature $T$, baryon chemical potential $μ_B$, and isospin chemical potential $μ_I$. The parameters of the model are determined by matching the meson and quark masses, as well as the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. In this paper, we study the possibility of different phases at zero temperature. In particular, we investigate the competition between an inhomogeneous chiral condensate and a pion condensat…
We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study 1) the possibility of inhomogeneous chiral condensates and its competition with a homogeneous pion condensate in the $μ$--$μ_I$ plane at $T=0$ and 2) the phase diagram in the $μ_I$--$T$ plane. In the $μ$--$μ_I$ plane, we find that an inhomogeneous chiral condensate only exists for pion masses lower that 37.1 MeV and does not coexist with a homogeneous pion condensate. In the $μ_I$--$T$ plane, we find that the phase transition to a Bose-condensed phase is of second order for all value…
The density of the Bose-Einstein condensate for non-interacting pions in a cubic box, at given temperature and (average) total pion density, is calculaated for three sets of boundary conditions. The densities are much larger than predicted from thermodynamics and depend significantly on the choice of the boundary conditions, even for volumes as large as $6.4\cdot 10$fm$^3$.
