In a scenario with two almost mass degenerate heavy sterile Majorana neutrinos with a mass $sim 1$ GeV, we present the semileptonic decay widths of heavy charged pseudoscalars such as $B$ mesons, either lepton-number-violating ($B^{pm} to mu^{pm} e^{
pm} pi^{mp}$), or lepton-number-conserving ($B^{pm} to mu^{pm} e^{mp} pi^{pm}$), mediated by such on-shell neutrinos. It had been explained in the literature that such decays may be eventually detected, and that they can present even detectable CP violation effects. In this work we point out that, in addition, such decays may present detectable effects of heavy neutrino oscillation, allowing us to extract the oscillation length and thus the heavy neutrino mass difference $Delta M_N$, as well as a CP-violating Majorana phase.
We examined the influence of additional scalar doublet on the parameter space of the Standard Model supplemented with a generation of new vector like leptons. In particular we identified the viable regions of parameter space by inspecting various con
straints especially electroweak precision (S, T and U) parameters. We demonstrated that the additional scalar assists in alleviating the tension of electroweak precision constraints and thus permitting larger Yukawa mixing and mass splittings among vector like species. We also compared and contrasted the regions of parameter space pertaining to the latest LHC Higgs to diphoton channel results in this scenario with vector like leptons in single Higgs doublet and pure two Higgs doublet model case.
