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arXiv · 2602.15410

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

Ziyue Wang
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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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Ziyue Wang. 2026-02-17. pion-rho Mixing as a mechanism for non-monotonic charged pion behavior in magnetic fields. https://arxiv.org/abs/2602.15410

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