Abstract
In this short review we tried to give an outline of investigations of charged pion condensation (PC) in dense baryonic (quark) matter in the framework of effective Nambu–Jona-Lasinio (NJL)-type models. The possibility of charged PC phase in dense quark matter with isospin asymmetry is investigated. First, it is demonstrated that this phase can be realized in the framework of massless NJL model. However, the existence of this phase is enormously fragile to the values of current quark mass and we show that charged PC phase is forbidden in electrically neutral dense quark matter with β -equilibrium when current quark masses are close to their physical value of 5.5 MeV. Nevertheless, then it is shown that in real physical systems there could be conditions promoting the appearance of charged PC phenomenon in dense quark matter; specifically, it was shown that if one takes into consideration the fact that system can have finite size, then a dense charged PC phase can be realized there. It was also demonstrated that the possibility of inhomogeneous pion condensate might allow this phase to appear. In addition, more recently it was revealed that there is another interesting factor that can induce a charged PC phase in dense quark matter even without isospin imbalance. It is a chiral imbalance of the system (non-zero difference between densities of left- and right-handed quarks). These results can be interesting in heavy ion collision experiments, where it is expected to get high baryon densities. It is of interest also in the context of neutron stars, where quark matter might be realized in the core and very high baryon and isospin densities are attained.
Highlights
Great efforts have been made in trying to understand the properties and the phase diagram of strongly interacting matter under high temperatures and/or baryon densities
It is believed that quark matter under such extreme conditions can exist in cores of neutron stars, where baryon density is much higher than the density ρ0 of ordinary nuclear matter, where ρ0 is 0.15 baryon per fm3, or can be formed as a result of a collision of heavy ions [1,2,3,4,5]. (In this case, there are no reasons to speak of protons and neutrons as particles that make up baryonic matter, and it would be more correct to say that we are dealing with dense quark matter.) in reality, within the framework of quantum chromodynamics (QCD), the fundamental theory designed to describe strongly interacting systems, it is rather problematic to get at least some information about the phase structure of dense quark matter
(Though let us note that the s-wave charged pion condensation (PC) is considered highly unlikely to be realized in dense matter [41] but it was argued that p-wave charged PC is possible [42,43,44].) In contrast, as it follows from the above discussion, the possibility of the charged PC phenomenon in dense quark matter, in which baryon density is much higher than ρ0, described in the framework of the effective NJL model remains in question
Summary
Great efforts have been made in trying to understand the properties and the phase diagram of strongly interacting (quark) matter under high temperatures and/or baryon densities (or high values of the baryon chemical potential μ B ). (Though let us note that the s-wave charged PC is considered highly unlikely to be realized in dense matter [41] but it was argued that p-wave charged PC is possible [42,43,44].) In contrast, as it follows from the above discussion, the possibility of the charged PC phenomenon in dense quark matter, in which baryon density is much higher than ρ0 , described in the framework of the effective NJL model remains in question.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
