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<p>The QCD phase transitions are explored at finite isospin density and in a magnetic field within an extended two-flavor Nambu–Jona-Lasinio model. By using the Ginzburg–Landau approximation, we analyze the transitions from the normal chiral-symmetry-breaking phase to pion superfluidity or rho superconductivity. To avoid the spurious divergence at large isospin chemical potential, we employ the Landau representation rather than the proper-time representation of the fermion propagator in a constant magnetic field. For the Landau representation, the same cutoff on the Landau energies, rather than on the Landau-level indices, must be used to regularize the sums over Landau levels. Then, the Ginzburg–Landau coefficients for pion and rho mesons are derived both analytically and numerically within the random-phase approximation. The results show that pion superfluidity is favored for a weak magnetic field while rho superconductivity is favored for a strong magnetic field as the isospin chemical potential increases, in line with the magnetic enhancement (reduction) of the lowest energy of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pi ^+\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>π</mi> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\rho ^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ρ</mi> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>) meson. The emergence of a rho-superconducting phase at strong magnetic field and finite isospin density implies a nontrivial interplay between QCD and QED.</p>

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QCD phase transitions at finite isospin density and magnetic field

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Chu-Jun Ke,
  • Gao-Qing Cao

摘要

The QCD phase transitions are explored at finite isospin density and in a magnetic field within an extended two-flavor Nambu–Jona-Lasinio model. By using the Ginzburg–Landau approximation, we analyze the transitions from the normal chiral-symmetry-breaking phase to pion superfluidity or rho superconductivity. To avoid the spurious divergence at large isospin chemical potential, we employ the Landau representation rather than the proper-time representation of the fermion propagator in a constant magnetic field. For the Landau representation, the same cutoff on the Landau energies, rather than on the Landau-level indices, must be used to regularize the sums over Landau levels. Then, the Ginzburg–Landau coefficients for pion and rho mesons are derived both analytically and numerically within the random-phase approximation. The results show that pion superfluidity is favored for a weak magnetic field while rho superconductivity is favored for a strong magnetic field as the isospin chemical potential increases, in line with the magnetic enhancement (reduction) of the lowest energy of the \(\pi ^+\) π + ( \(\rho ^{+}\) ρ + ) meson. The emergence of a rho-superconducting phase at strong magnetic field and finite isospin density implies a nontrivial interplay between QCD and QED.