Model-independent search strategy for the lepton-flavor-violating heavy Higgs boson decay to $\tau\mu$ at the LHC

In this work we present a model-independent search strategy at the LHC for heavy Higgs bosons decaying into a tau and a muon, $H/A \rightarrow \tau\mu$, showing a plausible tendency to improve the sensitivity obtained by the present experimental limits. This search strategy is performed for the Higgs boson mass range 1-5 TeV and uses as the most relevant kinematical variables, in order to discriminate signal against background, the transverse momenta of the muon and the tau together with the missing transverse energy. We estimate the exclusion limits at 95% C.L. and the significances for evidence and discovery at $\sqrt{s}$ = 14 TeV with $\cal{L}$ = 300 fb$^{-1}$, observing a growth in the sensitivities for high Higgs boson masses. Moreover, since the Higgs boson decay into a $\tau$-lepton pair may mimic our LFV signal, we also study the impact of the ditau channel on the exclusion limits and the significances for evidence and discovery. In particular, the impact on the exclusion limits of LFV heavy Higgs boson decays is significant when the ditau rate begins to compete with the corresponding to the $H/A \rightarrow \tau\mu$ decay.