Fluctuations in the quark-meson model for QCD with isospin chemical potential

Abstract

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and isospin chemical potentials, ${\mu }_B$ and ${\mu }_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite ${\mu }_B=3\mu$ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the (${\mu }_I,\mu$)-plane of this phase diagram is strongly constrained by the "Silver Blaze problem." In particular, the onset of pion condensation must occur at ${\mu }_I=m_{\pi }/2$, independent of $\mu$ as long as $\mu +{\mu }_I$ stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.

10 pages, 11 figures; matches published version

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Cited by in corpus (12)

• Inhomogeneous chiral condensates
• Magnetic structure of isospin-asymmetric QCD matter in neutron stars
• Towards quantitative precision in the chiral crossover: masses and fluctuation scales
• Universal Aspects of QCD-like Theories
• Flow equations for spectral functions at finite external momenta
• QCD Equation of State at Finite Chemical Potentials for Relativistic Nuclear Collisions
• Continuum Goldstone spectrum of two-color QCD at finite density with staggered quarks
• Consistent parameter fixing in the quark-meson model with vacuum fluctuations
• Sarma phase in relativistic and non-relativistic systems
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Spectral Functions from the Functional Renormalization Group
• Spectral functions from the functional renormalization group at finite temperature and density