In the NJL model with exact phase-space diagonalization, magnetic catalysis of the chiral condensate quenches the tachyonic instability of the spin-aligned rho+ by driving the 2M threshold above the Zeeman-lowered mass, preventing condensation.
pion-rho Mixing as a mechanism for non-monotonic charged pion behavior in magnetic fields
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abstract
We investigate whether magnetic field induced $\pi-\rho$ mixing can explain the non-monotonic behavior of the charged pion reported in lattice QCD. Using a near-pole effective action derived from the SU(2)$_f$ Nambu--Jona-Lasinio model, we show that the lowest Landau level charged pion mixes with the longitudinally polarized charged rho meson, which shares the same quantum numbers in a magnetic background. The resulting level repulsion is strongly amplified by the suppression of the rho wave-function renormalization near the pole. As a consequence, the lowest mixed mode develops a turnover as the magnetic field increases, reproducing the qualitative trend seen on the lattice. Comparison with the direct determinant solution of the Landau-projected kernel shows that the mechanism is robust, although the quantitative location of the maximum remains scheme dependent. These results support $\pi-\rho$ mixing as an important candidate mechanism for charged meson spectra in strong magnetic fields.
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In the Weinberg model, neutral pseudoscalar-charged vector meson loops cause the lowest energies of charged pseudoscalars to decrease with increasing magnetic field strength, supporting a molecular bound-state interpretation despite model instabilities.
Neutral mesons conserve continuous transverse momenta in magnetic fields while charged mesons exhibit quantized transverse dynamics, with high-spin charged mesons stabilized by cancellation of internal zero-point energy against orbital Zeeman energy.
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Mass spectra of charged mesons and the quenching of vector meson condensation via exact phase-space diagonalization
In the NJL model with exact phase-space diagonalization, magnetic catalysis of the chiral condensate quenches the tachyonic instability of the spin-aligned rho+ by driving the 2M threshold above the Zeeman-lowered mass, preventing condensation.
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Charged pseudoscalar mesons in a strong magnetic field under the Weinberg model
In the Weinberg model, neutral pseudoscalar-charged vector meson loops cause the lowest energies of charged pseudoscalars to decrease with increasing magnetic field strength, supporting a molecular bound-state interpretation despite model instabilities.
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Delineating neutral and charged mesons in magnetic fields
Neutral mesons conserve continuous transverse momenta in magnetic fields while charged mesons exhibit quantized transverse dynamics, with high-spin charged mesons stabilized by cancellation of internal zero-point energy against orbital Zeeman energy.