It has been shown that the data from the Large Hadron Collider (LHC) does not rule out a chiral sequential fourth generation of fermions that obtain their masses through an identical mechanism as the other three generations. However, this is possible only if the scalar sector of the Standard Model is suitably enhanced, like embedding it in a type-II two-Higgs doublet model. In this article, we try to show that double Higgs production (DHP) can unveil the existence of such a hidden fourth generation in a very efficient way. While the DHP cross-section in the SM is quite small, it is significantly enhanced with a fourth generation. We perform a detailed analysis of the dependence of the DHP cross-section on the model parameters, and show that either a positive signal of DHP is seen in the early next run of the LHC, or the model is ruled out. *

The anomalous magnetic moment of muons has been a long-standing problem in SM. The current deviation of experimental value of the $$(g-2)_{\mu }$$ ( g - 2 ) μ from the standard model prediction is exactly $$4.2\sigma $$ 4.2 σ . Two Higgs Doublet Models can accommodate this discrepancy but such type of model naturally generate flavor changing neutral current(FCNC). To prevent this it was postulated that 2HDM without FCNC required that all fermions of a given charge couple to the same Higgs boson but the rule breaks in Muon Specific Two Higgs Doublet Model where all fermions except muon couple to one Higgs doublet and muon with the other Higgs doublet. The muon specific 2HDM provides an explanation for muon anomaly for extremely large $$\tan \beta $$ tan β with a particular value of $$m_{12}^2$$ m 12 2 . As a result, the parameter space of $$m_{12}^2$$ m 12 2 drastically decreased for the muon anomaly solution. To evade the limitation of this model we have extended this model with a vector like lepton generation which could explain the muon anomaly at low $$\tan \beta $$ tan β value with a heavy pseudo scalar Higgs boson under the shadow of current experimental and theoretical constraints. Moreover, with the help of the cut based analysis and multivariate analysis methods, we have also attempted to shed some light on the potential experimental signature of vector lepton decay to the heavy Higgs boson in the LHC experiment. We have showed that a multivariate analysis can increase the vector like leptons signal significance even in the high VLL mass and low $$\tan \beta $$ tan β region than that of a cut based analysis.

The anomalous magnetic moment of muons has been a long-standing problem in SM. The current deviation of experimental value of the (g − 2) µ from the standard model prediction is exactly 4.2σ. Two Higgs Doublet Models can accommodate this discrepancy but such type of model naturally generate flavor changing neutral current(FCNC). To prevent this it was postulated that 2HDM without FCNC required that all fermions of a given charge couple to the same Higgs boson but the rule breaks in Muon Specific Two Higgs Doublet Model where all fermions except muon couple to one Higgs doublet and muon with the other Higgs doublet. The Muon Specific Two Higgs Doublet model explain muon anomaly with a fine tuning problem of very large tan β value with other parameters. We have found a simple solution of this fine tuning problem by extending this model with a vector like lepton generation which could explain the muon anomaly at low tan β value with a heavy pseudo scalar Higgs boson under the shadow of current experimental and theoretical constraints. Moreover, with the help of the cut based analysis and multivariate analysis methods, we have also attempted to shed some light on the potential experimental signature of vector lepton decay to the heavy Higgs boson in the LHC experiment. We have showed that a multivariate analysis can increase the vector like leptons signal significance by up to an order of magnitude than that of a cut based analysis.