Charged pseudoscalar mesons in a strong magnetic field under the Weinberg model

Recent lattice QCD simulations have further validated their earlier unusual findings: The lowest energies of charged pseudoscalar mesons $\pi^\pm$ and $K^\pm$ decrease at stronger magnetic field, though quasiparticle approximation assumes an increasing feature. We address this long-standing puzzle by employing the chiral effective Weinberg model, in which pseudoscalar and vector mesons exhibit intrinsic mutual couplings. Under this framework, charged pseudoscalar mesons deviate from pure quasiparticle behavior due to their interactions with neutral pseudoscalar and charged vector mesons. By incorporating the modifications induced by neutral pseudoscalar-charged vector loops, we demonstrate that the lowest energies of $\pi^\pm$ and $K^\pm$ indeed decrease at stronger magnetic field in both the lowest- and full-Landau-level calculations. However, instabilities emerge under a fixed mesonic coupling constant, and appear unavoidable when attempting to reproduce the observed peak structures. In contrast to the quark-antiquark meson description in models such as the NJL model, our results support the conjecture that a charged pseudoscalar meson could effectively form a molecular bound state of a neutral pseudoscalar meson and a charged vector meson in the strong magnetic field regime.