We employ a general two Higgs doublet model to investigate the discovery potential of flavor changing neutral Higgs (FCNH) interactions for a Higgs boson decays into leptons in pp collisions, $pp \to \phi^0 \to \tau^\mp\mu^\pm +X$ from gluon fusion, where $\phi^0$ could be a CP-even scalar ($h^0$, $H^0$) or a CP-odd pseudoscalar ($A^0$).

The light Higgs boson $h^0$ is found to resemble closely the standard Higgs boson at the Large Hadron Collider (LHC).

In the alignment limit of $\cos(\beta-\alpha) \cong 0$, for $h^0$--$H^0$ mixing, FCNH couplings of $h^0$ are naturally suppressed, but such couplings of the heavier Higgs bosons ($H^0, A^0$) are sustained by $\sin(\beta-\alpha) \simeq 1$.

We evaluate physics backgrounds from dominant processes with realistic acceptance cuts and tagging efficiencies.

We find promising results for the LHC with $\sqrt{s} = 14$ TeV, and future pp colliders with $\sqrt{s} = 27$ TeV and 100 TeV.