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

TL;DR

This paper uses the functional renormalization group to analyze the phase diagram of the two-flavor quark-meson model at finite baryon and isospin chemical potentials, emphasizing the importance of mesonic fluctuations and the Silver Blaze problem.

Contribution

It introduces a detailed FRG analysis of the quark-meson model considering both chemical potentials, highlighting the role of mesonic fluctuations and pion mass calculations beyond mean field.

Findings

Pion condensation onset at μ_I = m_π/2, independent of μ, under certain conditions.

Finite μ_B adds complexity to the phase diagram compared to two-color QCD.

Consistent pion mass computation is crucial for preserving the Silver Blaze property.

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.