Light charged Higgs boson scenario in 3-Higgs doublet models

The constraints from the measurements of the $B\to X_s\gamma$ decay rate on the parameter space of 3-Higgs Doublet Models (3HDMs), where all the doublets have non-zero vacuum expectation values, are studied at the next-to-leading order in QCD. In order to naturally avoid the presence of flavour changing neutral currents at the tree level, we impose two softly-broken discrete $Z_2$ symmetries. This gives rise to five independent types of 3HDMs that differ in their Yukawa couplings. We show that in all these 3HDMs (including the case of type-II-like Yukawa interactions) both masses of the two charged Higgs bosons $m_{H_1^\pm}$ and $m_{H_2^\pm}$ can be smaller than the top mass $m_t$ while complying with the constraints from $B\to X_s\gamma$. As an interesting phenomenological consequence, the branching ratios of the charged Higgs bosons decay into the $cb$ final states can be as large as $80\%$ when their masses are taken to be below $m_t$ in two of the five 3HDMs (named as Type-Y and Type-Z). This light charged Higgs boson scenario provides a hallmark 3HDM signature that cannot be realised in $Z_2$ symmetric 2-Higgs doublet models. We find that in the Type-Y and Type-Z 3HDMs the scenario with $90\,{\rm GeV}< m_{H^\pm_1}^{}\,, m_{H^\pm_2}^{}<m_t$ is ruled out by the direct searches at the LHC, but in the Type-Y 3HDM $80~\text{GeV}<m_{H_1^\pm}^{}<90~\text{GeV}$ and $90~\text{GeV}<m_{H_2^\pm}^{}<m_t$ is allowed by $B\to X_s\gamma$ and direct searches at LEP2, Tevatron and LHC due to the reduced sensitivity of these searches to the degenerate case $m_{H_1^\pm}\approx m_{W^\pm}$. The cases where only one or both charged Higgs bosons are above the top quark mass are also naturally allowed in the both Type-Y and Type-Z 3HDMs.