Higgs boson decays and production in the left-right twin Higgs model

The left-right twin Higgs model predicts one neutral Higgs boson $\phi_{0}$ and it acquires mass $m_{\phi_{0}}\sim \mu_{r}$ with the $\mu$ term, which can be lighter than half the SM-like Higgs boson mass in a portion of parameter space. Thus, the SM-like Higgs boson $h$ can dominantly decay into a pair of light neutral Higgs bosons especially when $m_{h}$ is below the $WW$ threshold. First, we examine the branching ratios of the SM-like Higgs boson decays and find that the new decay mode $h\rightarrow \phi_{0}\phi_{0}$ is dominant for the case of $m_{h}>2m_{\phi_{0}}$. Then we study the production via gluon fusion followed by the decay into two photons or two weak gauge bosons and found that the production rate can be significantly suppressed for some part of parameter space. Finally, we comparatively study the process $\gamma\gamma\rightarrow h \rightarrow b\bar{b}$ at ILC in the cases of $m_{h}>2m_{\phi_{0}}$ and $m_{h}<2m_{\phi_{0}}$, respectively. We find that these predictions can significantly deviated from the SM predictions, e.g., the gluon-gluon fusion channel, in the cases of $m_{h}>2m_{\phi_{0}}$ and $m_{h}<2m_{\phi_{0}}$, can be suppressed by about 80% and 45%, respectively. Therefor, it is possible to probe the left-right twin Higgs model via these Higgs boson production processes at the LHC experiment or in the future ILC experiment.