Meson molecules in strong magnetic fields: non-monotonic evolution of the charged pion and kaon energies

Abstract

In strong magnetic fields, charged quarks occupy the lowest Landau level, leading to an effective dimensional reduction of hadronic dynamics. This dimensional reduction naturally generates a hierarchy of scales, separating fast intra-meson quark dynamics from slow collective meson motion; this motivates a Born-Oppenheimer description of meson-meson systems. Our Born-Oppenheimer analysis shows that the infrared behavior is controlled by the interplay between dimensional reduction and the structure of the meson-meson interaction, leading to three distinct regimes: scattering-dominated, molecular, and compact multiquark states. Charged pseudoscalar mesons such as $π_+$ and $K_+$ provide a particularly interesting realization of this framework, as their lattice spectra at large magnetic fields suggest the emergence of loosely bound states near the boundary between scattering and molecular regimes. Our results suggest that strong magnetic fields provide a useful laboratory for exploring the emergence and classification of hadronic bound states.