2023/10/14 by Yamawaki, Koichi
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)
paper · doi:10.48550/arxiv.2310.09487
The rho meson has long been successfully identified with a dynamical gauge boson of the Hidden Local Symmetry (HLS) H\rm local in the nonlinear sigma model G/H gauge equivalent to the model having the symmetry G\rm global× H\rm local, with G= [SU(2)L × SU(2)R]≃ O(4), H=SU(2)V≃ O(3), however under a hitherto unproven assumption that its kinetic term is dynamically generated, together with an ad hoc choice of the auxiliary field parameter "a=2". 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 G/H=O(N)/[O(N-3)× O(3)] gauge equivalent to O(N)\rm global× [O(N-3)× O(3)]\rm local, extrapolated to N=4, O(4)\rm global× O(3)\rm local, with all the phenomenologically successful "a=2 results" i.e., ρ-universality, KSRF relation and the Vector Meson Dominance, realized \it independently of the parameter "a". This in turn establishes validity of the large N dynamics at quantitative level directly by the experiments. The relevant cutoff reads Λ≃ 4 πFπ for N=4, 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, further signal of the duality. The unbroken phase with massless rho meson may be realized as a novel chiral restored hadronic phase in hot/dense QCD.