Vector Meson Masses from Hidden Local Symmetry in Constant Magnetic Field

TL;DR

This paper investigates how vector meson masses respond to constant magnetic fields using the hidden local symmetry model, revealing mass modifications, mixing effects, and potential massless states, with implications for lattice QCD tests.

Contribution

It extends the HLS model to include magnetic field effects on vector mesons up to O(p^4), uncovering anomalous magnetic interactions and significant meson mixing phenomena.

Findings

Charged rho meson tends to become massless at O(p^4).

Neutral mesons exhibit magnetic-dependent mixing.

Omega meson mass is significantly enhanced in magnetic fields.

Abstract

We discuss the magnetic responses of vector meson masses based on the hidden local symmetry (HLS) model in constant magnetic field, described by the lightest two-flavor system including the pion, rho and omega mesons in the spectrum. The effective masses influenced under the magnetic field are evaluated in a way of the derivative/chiral expansion established in the HLS model. At the leading order O(p^2) the g-factor of the charged rho meson is fixed to be 2, implying that the rho meson at this order is treated just like a point-like spin-1 particle. Beyond the leading order, one finds anomalous magnetic interactions of the charged rho meson, involving the anomalous magnetic moment, which give corrections to the effective mass. It is then suggested that up to O(p^4) the charged rho meson tends to become massless. Of interest is that nontrivial magnetic-dependence of neutral mesons emerges to give rise to the significant mixing among neutral mesons. Consequently, it leads to the dramatic enhancement of the omega meson mass, which is testable in future lattice simulations. Corrections from terms beyond O(p^4) are also addressed.