Hidden Local Symmetry and Beyond

TL;DR

This paper explores the hidden local symmetry in the Standard Model, proposing the existence of a dynamical gauge boson called the SM rho meson, which could stabilize skyrmions as dark matter candidates.

Contribution

It demonstrates the equivalence of the SM Higgs sector to a nonlinear sigma model with hidden local symmetry and introduces the concept of a dynamical SM rho meson stabilizing dark matter skyrmions.

Findings

The SM Higgs sector can be described by a nonlinear sigma model with hidden local symmetry.

The SM rho meson can acquire a kinetic term from SM dynamics.

Stable skyrmions in the SM may serve as dark matter candidates.

Abstract

Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H= SU(2)_L x SU(2)_R/SU(2)_V with additional symmetry, the nonlinearly realized scale symmetry. Then the SM does have a dynamical gauge boson of the SU(2)_V HLS, "SM rho meson", in addition to the Higgs as a pseudo dilaton as well as the NG bosons to be absorbed into the W and Z. Based on the recent work done with S. Matsuzaki and H. Ohki, I discuss a novel possibility that the SM rho meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call "Dark SM skyrmion (DSMS)".