Abstract
We show that the multicomponent meson systems can be described by chiral perturbation theory. We chiefly focus on a system of two pion gases at different isospin chemical potential, deriving the general expression of the chiral Lagrangian, the ground state properties and the spectrum of the low-energy excitations. We consider two different kinds of interactions between the two meson gases: one which does not lock the two chiral symmetry groups and one which does lock them. The former is a kind of interaction that has already been discussed in mutlicomponent superfluids. The latter is perhaps more interesting, because seems to be related to an instability. Although the pressure of the system does not show any instability, we find that for sufficiently strong locking, the spectrum of one Bogolyubov mode becomes tachyonic. This unstable branch seems to indicate a transition to an inhomogeneous phase.
Highlights
Cold hadronic matter is an interesting playground for a deep understanding of the properties of the strong interaction
We focus on a system of two pion gases at different isospin chemical potential, deriving the general expression of the chiral Lagrangian, the ground state properties and the spectrum of the low-energy excitations
We have derived the relevant χPT Lagrangian restricting most of the analysis to the global symmetry group given in Eqs. (16) and (17) with Nf 1⁄4 2, corresponding to two fictitious pion gases with different masses and decay constants
Summary
Cold hadronic matter is an interesting playground for a deep understanding of the properties of the strong interaction. We focus on the meson condensed phases, which can be realized in the core of compact stars, see e.g., [11], employing the χPT framework for deriving the relevant low-energy Lagrangian. At the next-to-leading order (NLO) χPT corrections, it is possible to include those interactions that do not lock the two chiral groups This type of interaction is akin to the one typically discussed in ultracold atoms systems and in this case we obtain results similar to those of multicomponent Bose gas, see e.g., [68,69]. In the Appendix B, we discuss the low-energy corrections to the mean-field thermodynamic quantities arising from the vacuum energy of the Bogolyubov modes
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