We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an SU (2) doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global SU (2) transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.

We present a background model for dark matter searches using an array of NaI(Tl) crystals in the COSINE-100 experiment that is located in the Yangyang underground laboratory. The model includes background contributions from both internal and external sources, including cosmogenic radionuclides and surface $$^{210}$$ 210 Pb contamination. To build the model in the low energy region, with a threshold of 1 keV, we used a depth profile of $$^{210}$$ 210 Pb contamination in the surface of the NaI(Tl) crystals determined in a comparison between measured and simulated spectra. We also considered the effect of the energy scale errors propagated from the statistical uncertainties and the nonlinear detector response at low energies. The 1.7 years COSINE-100 data taken between October 21, 2016 and July 18, 2018 were used for this analysis. Our Monte Carlo simulation provides a non-Gaussian peak around 50 keV originating from beta decays of bulk $$^{210}$$ 210 Pb in a good agreement with the measured background. This model estimates that the activities of bulk $$^{210}$$ 210 Pb and $$^{3}$$ 3 H are dominating the background rate that amounts to an average level of $$2.85\pm 0.15$$ 2.85 ± 0.15  counts/day/keV/kg in the energy region of (1–6) keV, using COSINE-100 data with a total exposure of 97.7 kg$$\cdot $$ · years.

At large Nc, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking-namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally non-zero but whose spatial averages all vanish. We show that this is not possible unless all chirally-invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a non-linear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters which cannot be spatially uniform. Next we show that the no-go theorem applies to large Nc QCD in any phase which has a non-zero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally-restored phase, the field configuration can be reduced to that of a nonlinear sigma model. It is also shown that this no-go theorem is fully consistent with the vanishing of the spatial average of the chiral condensate 1 2 Tr(U) (as happens in "half-skyrmion" configurations). This is because the chiral condensate is only one of an infinite set of chiral order parameters, some of which must be non-zero. It is also shown that while an approximation of a unit cell of a Skyrme crystal as a hypersphere does lead to a phase which is chirally restored (in the average sense), this is an artifact of the approximation.

In many models in condensed matter and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different ways of consistently regularizing and renormalizing quantum fluctuations, focusing on momentum cutoff, symmetric energy cutoff, and dimensional regularization. We apply these techniques calculating the vacuum energy in the Nambu-Jona-Lasinio model in 1 þ 1 dimensions in the large-N c limit and in the 3 þ 1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.

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In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at nextto-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state. We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2+1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in χPT.

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the µI -T plane where µI is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At T = 0, the onset of pion condensation is at µI = 1 2 mπ in accordance with exact results. The phase transition to a Bosecondensed phase is of second order for all values of µI and in the O(2) universality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of µI these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken O(2) symmetry. We compare our results with recent lattice simulations and find overall good agreement.1 Or their Polyakov-loop extended versions (PNJL and PQM).

The phase diagram of finite isospin, zero temperature QCD with the pions coupled to photons in a uniform external magnetic field is explored in the low field, small isospin density regime for which chiral perturbation theory is a valid description. For realistic pion masses, the system behaves as a type-II superconductor: a uniform superconducting state is formed at low-enough magnetic fields, a vortex state for intermediate magnetic fields and finally a normal state for large magnetic fields. In each these phases (including the vortex phase), the π 0 remains uncondensed just as in the zero-external field problem. The critical magnetic field where the phase transition from the uniform superconducting state to a vortex state occurs was found numerically.