Dashen's theorem and electromagnetic masses of the mesons

TL;DR

This paper explores the applicability of Dashen's theorem within a chiral field theory framework, showing it extends to axial-vector mesons but not to vector mesons, revealing sector-specific limitations.

Contribution

It generalizes Dashen's theorem to axial-vector mesons using $U(3)_L\times U(3)_R$ chiral theory, highlighting its failure for vector mesons.

Findings

Dashen's theorem applies to pseudoscalar and axial-vector mesons

Fails for vector mesons within the same theoretical framework

Provides insight into meson mass differences and symmetry breaking

Abstract

Employing $U(3)_L\times U(3)_R$ chiral field theory, we find that Dashen's theorem, which holds for pseudoscalar mesons, can be generalized to the sector of axial-vector mesons, however, fails for vector mesons.