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 $mu_B=3mu$ 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

Chiral mirror-baryon-meson model and nuclear matter beyond mean-field approximation

“…In the quark-meson-diquark model for two-color QCD or the quark-meson model for QCD at finite isospin density one verifies at mean-field level that the RPA-pole masses agree with the onset of Bose-Einstein condensation of diquarks or charged pions, respectively, as they must. In contrast, one then deduces that especially the pion curvature mass can deviate from this by up to 30% [46,47]. Beyond mean-field, pole masses in present truncations for two-point functions are typically considerably closer to such onsets than curvature masses as well.…”

“…It is known from the quark-meson model where they change the mean-field chiral transition into a transition to bound quark matter [57]. The same effect turns the relativistic analogue of a Chandrasekhar-Clogston transition inside the pion condensation phase at finite isospin chemical potential, as observed at mean-field with ∆s > 0, into a first-order transition to a stable Sarma phase with ∆s < 0, when mesonic fluctuations are included [47,58]. This would be analogous to a partially polarized phase in ultracold Fermi gases at unitarity.…”

Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop

“…3 Moreover, since the SU(2) A symmetry is broken by the magnetic field, as explained above, the effective potential is therefore a function of these two invariants. This is similar to the case of two-color QCD with a baryon chemical potential [35] or three-color QCD with an isospin chemical potential [36]. In the LPA, the effective action then takes the form…”

Magnetic structure of isospin-asymmetric QCD matter in neutron stars

“…The isospin density has been shown to change the nature of the chiral transition in 8-flavor QCD [34]. The structure of the − phase diagram has been studied in various model frameworks as well [35][36][37][38]. A possible critical endpoint at nonzero isospin densities and magnetic fields was also discussed in Refs.…”