Isospin symmetry breaking within the HLS Model: A full ( $\rho, \omega, \phi$ ) mixing scheme

Abstract

We study the way isospin symmetry violation can be generated within the Hidden Local Symmetry (HLS) Model. We show that isospin symmetry breaking effects on pseudoscalar mesons naturally induces correspondingly effects within the physics of vector mesons, through kaon loops. In this way, one recovers all features traditionally expected from ρ−ω mixing and one finds support for the Orsay phase modelling of the e + e − → π + π − amplitude. We then examine an effective procedure which generates mixing in the whole ρ, ω, φ sector of the HLS Model. The corresponding model allows us to account for all two body decays of light mesons accessible to the HLS model in modulus and phase, leaving aside the ρ → ππ and K * → Kπ modes only, which raise a specific problem. Comparison with experimental data is performed and covers modulus and phase information ; this represents 26 physics quantities successfully described with very good fit quality within a constrained model which accounts for SU(3) breaking, nonet symmetry breaking in the pseudoscalar sector and, now, isospin symmetry breaking.

The pion form factor within the hidden local symmetry model

“…Their detailed structures and the expression of their couplings depend on the usual HLS parameters g and a, but also on symmetry breaking parameters. These have been fitted several times under various conditions [26,20,23,27], always providing results consistent with each other.…”

“…From a global fit of all radiative and leptonic decays of light meson [26], the best fit value is a = 2.51 ± 0.03. Variants of this model with a mass dependent ω − φ mixing angle [20], or accounting for isospin breaking effects [23] give values consistent with this one at never more than 2 σ.…”

“…It was shown in [23] that this gives rise to an ω contribution to the pion form factor which approximates naturally in the form shown in Eq. (1), precisely.…”

“…When breaking Isospin Symmetry within the HLS Model, charged and neutral kaons carry different masses and this generates a ρ − ω mass-dependent transition term [23]. In this case, the effective piece to be added to the Lagrangian becomes :…”

“…However, the corresponding published data [25] are not available in a usable way for fit ; fortunately, this effect is concentrated in a narrow region around the φ mass, and is invisible in the data to be considered. Nevetheless, one could note that the Orsay phase of the φ meson as well as its branching ratio to ππ are well accounted for within the HLS Model broken in an appropriate way [23].…”