Phenomenology of Higgs bosons in inverse seesaw model with Type-X two Higgs doublet at the LHC

Type-X two Higgs doublet model is known to explain the muon $g-2$ anomaly with a relatively light charged Higgs boson at large $\tan\beta$. The light charged Higgs boson has been searched in the main $\tau \nu$ mode at the colliders. Invoking a scenario of inverse seesaw as the origin of neutrino masses and mixing, the charged Higgs boson can decay additionally to right-handed neutrinos which leads to interesting phenomenology. Considering generic lepton flavour violating signatures at the final states, a $5\sigma$ discovery can be achieved with the early data of LHC, at 14 TeV, for relatively large inverse seesaw Yukawa coupling $Y_N$. The very light pseudoscalar and charged Higgs boson mass reconstruction are performed using the new modes and the results look promising. The inverse seesaw Yukawa coupling is shown to be probed down to $Y_N \sim 0.2$ at HL LHC with 3000 fb$^{-1}$.