Finite isospin chiral perturbation theory in a magnetic field

Abstract

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.

Magnetic vortex lattices in finite isospin chiral perturbation theory

“…In section 3, we summarize the argument for type-II superconductivity in finite isospin χPT with a uniform, external magnetic field that was first present in Ref. [19] and follow that in section 4 with the computation of the magnetic vortex lattice solutions and the corresponding condensation energy (relative to the normal vacuum in an external magnetic field). In subsection 4.1, we argue that neutral pions do not condense within the magnetic vortex lattice near the upper critical field and end with concluding remarks in section 5.…”

“…Previously, in Ref. [19] it was suggested that pions behave like type-II superconductors and the relevant single vortex structures and the critical magnetic field, H c1 , where the transition from superconducting pions to a single pionic vortex, were found. We generalize and improve upon the results by considering possible vortex lattice solutions and the corresponding condensation energy (density), relative to the normal vacuum in the presence of a uniform, external magnetic field.…”

Finite density two color chiral perturbation theory revisited

“…On the other hand, lattice QCD studies at vanishing baryonic density and nonzero isospin density are possible for not too large isospin chemical potentials, see [3][4][5][6][7][8][9]. Moreover, isospin asymmetric matter at nonvanishing magnetic fields cannot be studied using lattice QCD a e-mail: adhika1@stolaf.edu b e-mail: belezn1@stolaf.edu c e-mail: massimo@lngs.infn.it except in a very limited regime [8,10]. As such QCD practitioners have focused their attention on a wide range of variations of QCD including 't Hooft's large N c limit, see [11] for a review and [12,13] for more recent studies with adjoint quarks and two-color QCD with fundamental quarks [12,13].…”

Vortex Solutions in the Abelian Higgs Model with a Neutral Scalar

“…Chiral perturbation theory has three mesons, namely the charged pions π ± and the neutral pion, π 0 . However, in the magnetic vortices that form at moderate external fields only the charged pions (π ± ) condense in the vortex state and the neutral pions are absent in the vortices [17]. This is also true in the context of the linear sigma model [18].…”

“…It can be ignored as long as the electromagnetic energy density associated with the charged superfluids is small compared to the strength of the remaining interactions, see Ref. [17] for a full discussion in the context of chiral perturbation theory. In this paper, we will only consider single vortex solutions and leave the thermodynamic discussion to future work.…”