pion-rho Mixing as a mechanism for non-monotonic charged pion behavior in magnetic fields

TL;DR

This paper explores how magnetic field-induced pion-rho mixing can explain the non-monotonic behavior of charged pions observed in lattice QCD, using an effective model to demonstrate the mechanism's robustness.

Contribution

It introduces a novel explanation for charged pion behavior in magnetic fields based on $c-0$ mixing, supported by effective action analysis and lattice comparison.

Findings

Level repulsion causes the lowest mixed mode to turn over with increasing magnetic field.

The mechanism reproduces the qualitative trend of lattice results.

Quantitative details depend on the scheme, but the qualitative behavior is robust.

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.