Fermiophobic light Higgs boson in the type-I two-Higgs-doublet model

The null results in the new physics searches at the LHC do not exclude an intermediate-mass new particle if it is fermiophobic. Type-I in the two-Higgs-doublet model accommodates a fermiophobic light Higgs boson $h_{\rm f}$ if $\alpha=\pi/2$. The heavier $CP$-even Higgs boson explains the observed Higgs boson at a mass of 125 GeV. We first obtain the still-valid parameter space satisfying the theoretical requirements, flavor-changing neutral currents in $B$ physics, the cutoff scale above 1 TeV, Higgs precision data, and the direct collider search bounds at high energy colliders. We also study the high energy scale behavior via the analysis of the renormalization group equations. An important result is that the fermiophobic type-I can maintain the stability of the scalar potential all the way up to the Planck scale if $m_{h_{\rm f}}$ is larger than half the observed Higgs boson mass. Since the parameter space is severely curtailed, especially for the high cutoff scale, the signal rates in the multi-photon states of new Higgs bosons at the LHC are well predicted. We suggest the processes of $4\gamma+VV'$ ($V^{(\prime)}=Z, W^\pm$) as the golden discovery channels for the model since they enjoy an almost background-free environment and substantial selection efficiencies for four photons.