Exposing the effect of $p$-wave in pion triplet under the strong magnetic field

TL;DR

This paper investigates how strong magnetic fields influence the properties of pion triplet mesons using Dyson-Schwinger equations, revealing significant effects on meson structure and matching lattice QCD results.

Contribution

It introduces a symmetry-preserving coupling formulation to control p-wave effects in mesons without altering quark propagators, aligning model predictions with lattice QCD observations.

Findings

Charged pseudoscalar meson spectra show non-monotonic behavior under magnetic fields.

The model reproduces lattice QCD results for meson properties in magnetic environments.

Strong magnetic fields significantly alter meson internal structure.

Abstract

The static properties, masses and decay constants, of pseudoscalar meson triplet in a strongly magnetized medium are studied through the Dyson-Schwinger equation approach treatment of a contact interaction. Complementary to the usual vector-vector form, a symmetry-preserving formulation of couplings has been proposed in this work, without modifying the quark propagator, to control the strength of the $p$-wave component of Bethe-Salpeter amplitude. It is found that, with the help of flexible auxiliary interaction, our simple model is able to reproduce the observation in the lattice QCD simulation, where the spectra of the charged pseudo-scalar meson shows a non-monotonic behavior as the magnetic field grows. The discovery of this work implies the strong magnetic field affects the inner structure of mesons dramatically.