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We investigate the implications of a minimal $SU(2)$ gauge symmetry extensionof the standard model at the LHC. To achieve the spontaneous symmetry breaking,a heavy Higgs doublet of the $SU(2)$ is introduced. To obtain an anomaly freemodel and the decays of new charged gauge bosons, we include a vector-likequark doublet. We also employ a real scalar boson to dictate the heavy Higgsproduction via the gluon-gluon fusion processes. It is found that the new gaugecoupling and the masses of new gauge bosons can be strictly bounded by theelectroweak $\rho$-parameter and dilepton resonance experiments at the LHC. Itis found that due to the new charged gauge boson enhancement, the crosssections for a heavy scalar boson to diphoton channel measured by ATLAS and CMScan be easily satisfied when the values of Yukawa couplings are properly taken.Furthermore, by adopting event simulation, we find that the significance of$pp\to (\gamma \gamma)_H+{\rm jet}$, where the diphoton is from the heavy Higgsdecay, can be over $4\sigma$ when the luminosity is above 60 fb$^{-1}$.

Phenomenology of an $SU(2)_1 \times SU(2)_2 \times U(1)_Y$ model at the LHC