Scrutinizing the pion condensed phase

Abstract

When the isospin chemical potential exceeds the pion mass, charged pions condense in the zero-momentum state forming a superfluid. Chiral perturbation theory provides a very powerful tool for studying this phase. However, the formalism that is usually employed in this context does not clarify various aspects of the condensation mechanism and makes the identification of the soft modes problematic. We re-examine the pion condensed phase using different approaches within the chiral perturbation theory framework. As a first step, we perform a low-density expansion of the chiral Lagrangian valid close to the onset of the Bose-Einstein condensation. We obtain an effective theory that can be mapped to a Gross-Pitaevskii Lagrangian in which, remarkably, all the coefficients depend on the isospin chemical potential. The low-density expansion becomes unreliable deep in the pion condensed phase. For this reason, we develop an alternative field expansion deriving a low-energy Lagrangian analog to that of quantum magnets. By integrating out the "radial" fluctuations we obtain a soft Lagrangian in terms of the Nambu-Goldstone bosons arising from the breaking of the pion number symmetry. Finally, we test the robustness of the second-order transition between the normal and the pion condensed phase when next-to-leading-order chiral corrections are included. We determine the range of parameters for turning the second-order phase transition into a first-order one, finding that the currently accepted values of these corrections are unlikely to change the order of the phase transition.

12 pages, 2 figures; improved Sec.4; added Appendix B

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• On Profiles of Boson Stars with Self-Interactions
• Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL${}_2$ model
• Isospin asymmetry in holographic baryonic matter
• Insights on the peak in the speed of sound of ultradense matter
• Pion crystals hosting topologically stable baryons
• Chiral density wave versus pion condensation at finite density
• Thermodynamics and susceptibilities of isospin imbalanced QCD matter
• High-Energy Phase Diagrams with Charge and Isospin Axes under Heavy-Ion Collision and Stellar Conditions
• The dual properties of chiral and isospin asymmetric dense quark matter formed of two-color quarks
• Hot QCD at finite isospin density: confronting SU(3) Nambu-Jona-Lasinio model with recent lattice data
• Rotation induced charged pion condensation in a strong magnetic field: A Nambu--Jona-Lasino model study
• Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature
• QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case
• Pion and kaon condensation at zero temperature in three-flavor $\chi$PT at nonzero isospin and strange chemical potentials at next-to-leading order
• Multicomponent meson superfluids in chiral perturbation theory
• Influence of chiral asymmetry on phase structure of the two-color quark matter
• Condensation of interacting scalar bosons at finite temperatures
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Speed of Sound for Hadronic and Quark Phases in a Magnetic Field
• Finite Density Two Color Chiral Perturbation Theory Revisited
• QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model
• Phase Transition in Interacting Boson System at Finite Temperatures
• Pion condensation in a soft-wall AdS/QCD model
• The contributions of the vector-channel at finite isospin chemical potential with the self-consistent mean field approximation
• Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models
• On the origin of the peak of the sound velocity for isospin imbalanced strongly interacting matter
• Thermodynamic properties of interacting bosons with zero chemical potential
• Pion stars embedded in neutrino clouds
• QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation
• On the effective lagrangian at nonzero isospin chemical potential
• Superfluid dark stars
• Phonon modes of magnetic vortex lattices in finite isospin chiral perturbation theory
• Chiral symmetry breaking and pion condensation in the early universe
• Non-relativistic Boson Stars as N-Body Quantum Systems
• Multicomponent superfluidity in two-color QCD at finite density at next-to-leading order
• Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter