Proving Rho Meson Is a Dynamical Gauge Boson of Hidden Local Symmetry

Abstract

The rho meson has long been successfully identified with a dynamical gauge boson of Hidden Local Symmetry (HLS) (Formula presented.) in the non-linear sigma model (Formula presented.) gauge equivalent to the model having the symmetry (Formula presented.), with (Formula presented.). However, under a hitherto unproven assumption that its kinetic term is dynamically generated, together with an ad hoc choice of the auxiliary field parameter “ (Formula presented.) ”, we prove this assumption, thereby solving the long-standing mystery. The rho meson kinetic term is generated simply by the large N limit of the Grassmannian model (Formula presented.) gauge equivalent to (Formula presented.), extrapolated to (Formula presented.), (Formula presented.), with all the phenomenologically successful “ (Formula presented.) results”, i.e., (Formula presented.) -universality, KSRF relation, and the Vector Meson Dominance, realized independently of the parameter “a”. This in turn establishes validity of the large N dynamics at the quantitative level directly by the experiments. The relevant cutoff reads (Formula presented.) for (Formula presented.), which is regarded as a matching scale of the HLS as a “magnetic dual” to QCD. Skyrmion is stabilized by such a dynamically generated rho meson without recourse to the underlying QCD, a further signal of the duality. The unbroken phase with a massless rho meson may be realized as a novel chiral-restored hadronic phase in the hot/dense QCD.