Composite Gauge Bosons and "Low Energy Theorems" of Hidden Local Symmetries

Abstract

We show that the vector mesons (ρ, ω, K*, \BarK*, φ) are dynamical gauge bosons of the hidden local symmetry in the U(3)L×U(3)R/U(3)V nonlinear sigma model. General proof is given of the gauge equivalence between a nonlinear sigma model based on the manifold G/H and a “linear” model with Gglobal×Hlocal symmetry, where the latter generally contains arbitrary parameter. Under the assumption that the gauge bonsons of the hidden local symmetry Hlocal develop the kinetic term, we derive “low energy theorems” corresponding to the hidden local symmetry, one of which turns out to be the successful KSRF relation, gρ=2gρππfπ, in the case G/H=U(3)L×U(3)R/U(3)V. Here, the electromagnetic interaction is introduced in a characteristic way, which via Higgs mechanism of the hidden local symmetry and, when the above arbitrary parameter is chosen so as to ensure the universality of vector meson couplings, it satisfies another form of the KSRF relation, mρ2=2g2ρππfπ2, and its U(3) versions. The same parameter also yields “vector meson dominance” of the electromagnetic form factor of the pseudoscalar mesons.