H\to hh in the Mirror Model at the CERN Large Hadron Collider

The Higgs sector may play an important role in detecting the mirror particles, which can be the candidates of the dark matter and appear as missing energy in the detectors at the LHC. In this paper we worked out the Higgs boson spectrum and the Higgs couplings for the symmetric vacuum, namely $v_1=v_2=v$, in the mirror model, and investigated the constraints from electro-weak precision observable (EWPO). Our study showed that the EWPO has already constrained the Higgs boson sector severely. We then explored the Higgs boson phenomenology, and focused on the scenario that the heavier Higgs boson $H$ can decay into a pair of lighter Higgs boson $h$. We proposed to study the invisible decay of the Higgs boson via the pair production of them, in which one Higgs boson decays into bottom quarks and the other decays invisibly. Our detail simulation for signals and backgrounds showed that the observation of signal can reach $5\sigma$ significance for $m_H=260$ GeV and $m_h=115$ GeV with $10 fb^{-1}$integrated luminosity at the LHC. Moreover the possible method to further suppress dominant $Zb\bar{b}$ background was discussed. We also simulated the signals and backgrounds for $H \to h h \to 4b$. Our results showed that it is very difficult to isolate the signals from huge QCD continuum backgrounds.