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Register a new userDynamical Gauge Boson of Hidden Local Symmetry within the Standard Model
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Koichi Yamawaki
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The Standard Model (SM) Higgs Lagrangian is straightforwardly rewritten into the {it scale-invariant} nonlinear sigma model $G/H=[SU(2)_L times SU(2)_R]/SU(2)_{V}simeq O(4)/O(3)$, with the (approximate) scale symmetry realized nonlinearly by the (pseudo) dilaton ($=$ SM Higgs). It is further gauge equivalent to that having the symmetry $O(4)_{rm global}times O(3)_{rm local}$, with $O(3)_{rm local}$ being the Hidden Local Symmetry (HLS). In the large $N$ limit of the scale-invariant version of the Grassmannian model $G/H=O(N)/[O(N-3)times O(3)] $ $simeq O(N)_{rm global}times [O(N-3)times O(3)]_{rm local}$, identical to the SM for $Nrightarrow 4$, we show that the kinetic term of the HLS gauge bosons (SM rho) $rho_mu$ of the $O(3)_{rm local}simeq [SU(2)_V]_{rm local}$ are dynamically generated by the nonperturbative dynamics of the SM itself. The dynamical SM rho stabilizes the skyrmion (SM skyrmion) $X_s$ as a dark matter candidate within the SM: The mass $M_{X_s} ={cal O}(10, {rm GeV})$ consistent with the direct search experiments implies the induced HLS gauge coupling $g_{_{rm HLS}}={cal O}(10^3)$, which realizes the relic abundance, $Omega_{X_s} h^2 ={cal O}(0.1)$. If instead $g_{_{rm HLS}}lesssim 3.5$ ($M_rho lesssim 1.2 $ TeV), the SM rho could be detected with narrow width $lesssim 100 ,{rm GeV}$ at LHC, having all the $a=2$ results of the generic HLS Lagrangian ${cal L}_A+ a {cal L}_V$, i.e., $rho$-universality, KSRF relations and the vector meson dominance, independently of $a$. There exists the second order phase phase transition to the unbroken phase having massless $rho_mu$ and massive $pi$ (no longer NG bosons), both becoming massless free particles just on the transition point (scale-invariant ultraviolet fixed point).The results readily apply to the 2-flavored QCD as well.
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