Two more hidden scalars around 125 GeV and $h \to \mu\tau$

We show that the $2.4\sigma$ signal of the leptonic flavor violating (LFV) Higgs boson decay $h\to\mu\tau$, as observed by the CMS collaboration recently, can be explained by a certain class of two-Higgs doublet models that allow controllable flavor-changing neutral current with minimal number of free parameters. We postulate that (i) the alignment limit is maintained, which means the lightest neutral scalar ($h$) has identical couplings to that of the Standard Model Higgs boson and (ii) the signal comes from two other neutral scalars, the CP-even $H$ and the CP-odd $A$, almost degenerate with $h$ at 125 GeV. We also show that (i) it is entirely possible that these scalars are hidden, apart from this LFV signal; (ii) the signal strengths of $b\bar{b}$, $\tau^+\tau^-$ and $\gamma\gamma$ around 125 GeV put severe constraints on the parameter space of such models; (iii) the constraint is further enhanced by the non-observation of processes like $\mu\to e\gamma$, and we predict that the branching ratio of $\mu\to e\gamma$ cannot be even an order below the present experimental limit, highlighting the role it plays in forcing $H$ and $A$ to be near-degenerate; (iv) an enhancement in the $\tau^+\tau^-$ production cross-section at around 125 GeV is expected in the gluon fusion channel, and should be observed during the next run of the LHC; (v) the branching ratio in the $e\tau$ channel is enhanced and is expected to be at least about $2\%$. The constrained parameter space and minimum number of free parameters, along with such strong predictions, make this model easily testable and falsifiable.