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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 allowcontrollable flavor-changing neutral current with minimal number of freeparameters. We postulate that (i) the alignment limit is maintained, whichmeans the lightest neutral scalar ($h$) has identical couplings to that of theStandard Model Higgs boson and (ii) the signal comes from two other neutralscalars, the CP-even $H$ and the CP-odd $A$, almost degenerate with $h$ at 125GeV. We also show that (i) it is entirely possible that these scalars arehidden, 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 theparameter space of such models; (iii) the constraint is further enhanced by thenon-observation of processes like $\mu\to e\gamma$, and we predict that thebranching ratio of $\mu\to e\gamma$ cannot be even an order below the presentexperimental limit, highlighting the role it plays in forcing $H$ and $A$ to benear-degenerate; (iv) an enhancement in the $\tau^+\tau^-$ productioncross-section at around 125 GeV is expected in the gluon fusion channel, andshould be observed during the next run of the LHC; (v) the branching ratio inthe $e\tau$ channel is enhanced and is expected to be at least about $2\%$. Theconstrained parameter space and minimum number of free parameters, along withsuch strong predictions, make this model easily testable and falsifiable.

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