QCD at finite isospin density: chiral perturbation theory confronts lattice data

Abstract

We consider the thermodynamics of three-flavor QCD in the pion-condensed phase at nonzero isospin chemical potential (${\mu }_I$) and vanishing temperature using chiral perturbation theory in the isospin limit. The transition from the vacuum phase to a superfluid phase with a Bose-Einstein condensate of charged pions is shown to be second order and takes place at ${\mu }_I=m_{\pi }$. We calculate the pressure, isospin density, and energy density to next-to-leading order in the low-energy expansion. Our results are compared with recent high-precision lattice simulations as well as previously obtained results in two-flavor chiral perturbation theory. The agreement between the lattice results and the predictions from three-flavor chiral perturbation theory is very good for ${\mu }_I<200$ MeV. For larger values of ${\mu }_I$, the agreement between lattice data and the two-flavor predictions is surprisingly good and better than with the three-flavor predictions. Finally, in the limit $m_s\gg m_u=m_d$, we show that the three-flavor observables reduce to the two-flavor observables with renormalized parameters. The disagreement between the results for two-flavor and three-flavor $\chi$PT can largely be explained by the differences in the measured low-energy constants.

arXiv comment8 pages and 4 figs. v2: Expanded discussion, in particular the matching between two- and three flavor couplings for large strange-quark masses. Matches published version

References in corpus (44)

• Color superconductivity in dense quark matter
• The phase diagram of dense QCD
• From hadrons to quarks in neutron stars: a review
• QCD at finite isospin density
• Cold Quark Matter
• Lattice QCD at finite isospin density at zero and finite temperature
• Functional integrals for QCD at nonzero chemical potential and zero density
• Pion Superfluidity and Meson Properties at Finite Isospin Density
• Mesonic low-energy constants
• Renormalization of chiral perturbation theory to order p^6
• QCD-like Theories at Finite Baryon and Isospin Density
• QCD phase diagram for nonzero isospin-asymmetry
• Numerical Study of Dense Adjoint Matter in Two Color QCD
• Flavor-Mixing Effects on the QCD Phase Diagram at non-vanishing Isospin Chemical Potential: One or Two Phase Transitions?
• NNNLO pressure of cold quark matter: leading logarithm
• BEC-BCS Crossover in the Nambu--Jona-Lasinio Model of QCD
• Isospin Chemical Potential and the QCD Phase Diagram at Nonzero Temperature and Baryon Chemical Potential
• QCD at small non-zero quark chemical potentials
• Quenched lattice QCD at finite isospin density and related theories
• A calculation of the QCD phase diagram at finite temperature, and baryon and isospin chemical potentials
• Thermal Pions at Finite Isospin Chemical Potential
• Fluctuations in the quark-meson model for QCD with isospin chemical potential
• Towards the phase diagram of dense two-color matter
• Pion condensation in electrically neutral cold matter with finite baryon density
• Pion condensation in quark matter with finite baryon density
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Meson condensation
• Scrutinizing the pion condensed phase
• Phase Structure of Nambu-Jona-Lasinio Model at Finite Isospin Density
• Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential
• Pion Condensation in Baryonic Matter: from Sarma Phase to Larkin-Ovchinnikov-Fudde-Ferrell Phase
• The fate of pion condensation in quark matter: from the chiral limit to the physical pion mass
• Pion condensation and phase diagram in the Polyakov-loop quark-meson model
• Thermodynamics of (2+1)-flavor strongly interacting matter at nonzero isospin
• QCD phase diagram at finite baryon and isospin chemical potentials in Polyakov loop extended quark meson model with vector interaction
• Quark mass and isospin dependence of the deconfining critical temperature
• Two-flavor chiral perturbation theory at nonzero isospin: Pion condensation at zero temperature
• Cold QCD at finite isospin density: confronting effective models with recent lattice data
• Equation of state of imbalanced cold matter from chiral perturbation theory
• Deconfinement Transition at High Isospin Chemical Potential and Low Temperature
• Thermodynamics and susceptibilities of isospin imbalanced QCD matter
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• 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

Cited by in corpus (26)

• Meson condensation
• Pion condensation in the early Universe at nonvanishing lepton flavor asymmetry and its gravitational wave signatures
• Two-flavor chiral perturbation theory at nonzero isospin: Pion condensation at zero temperature
• QCD constraints on isospin-dense matter and the nuclear equation of state
• Sound velocity peak and conformality in isospin QCD
• Pion crystals hosting topologically stable baryons
• High-Energy Phase Diagrams with Charge and Isospin Axes under Heavy-Ion Collision and Stellar Conditions
• Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature
• Pion and kaon condensation at zero temperature in three-flavor $\chi$PT at nonzero isospin and strange chemical potentials at next-to-leading order
• QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case
• Competition of chiral soliton lattice and Abrikosov vortex lattice in QCD with isospin chemical potential
• Quark and pion condensates at finite isospin density in chiral perturbation theory
• Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory
• Critical point and Bose-Einstein condensation in pion matter
• On the origin of the peak of the sound velocity for isospin imbalanced strongly interacting matter
• Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models
• Pion superfluid phase transition under external magnetic field including inverse magnetic catalysis effect
• Gluon Propagators in $2+1$ Lattice QCD with Nonzero Isospin Chemical Potential
• Pion stars embedded in neutrino clouds
• On the effective lagrangian at nonzero isospin chemical potential
• Magnetic field effect on pion superfluid
• Speed of sound peak in isospin QCD: a natural prediction of the Medium Separation Scheme
• Phase diagram of interacting pion matter and isospin charge fluctuations
• Multicomponent superfluidity in two-color QCD at finite density at next-to-leading order
• QCD at high temperature and density: selected highlights
• Light mesons around critical end points in $T-{\mu }_B-{\mu }_I-eB$ space