CMS has reported indications (2.4σ) of the decay of the Higgs boson into µτ . The simplest explanation for such a decay would be a general Two Higgs Doublet Model (2HDM). In this case, one would expect the heavy neutral Higgs bosons, H and A, to also decay in a similar manner. We study two specific models. The first is the type III 2HDM, and the second is a 2HDM, originally proposed by Branco et al., in which all flavor-changing neutral processes are given by the weak mixing matrix. In the latter model, since mixing between the second and third generations in the lepton sector is large, flavor-changing interactions are large. In this model is found that the decays of H and A to µτ can be as high as 60 percent.

We study the custodial Randall-Sundrum model with two Higgs doublets localized in the TeV brane. The scalar potential is CP-conserving and has a softly broken Z 2 symmetry. In the presence of a curvature-scalar mixing term ξ ab RΦ † a Φ b the radion that stabilizes the extra dimension now mixes with the two CP-even neutral scalars h and H. A goodness of fit of the LHC data on the properties of the light Higgs is performed on the parameter space of the type-I and type-II models. LHC direct searches for heavy scalars in different decay channels can help distinguish between the radion and a heavy Higgs. The most important signatures involve the ratio of heavy scalar decays into b quark pairs to those into Z pairs, as well as the decay of the scalar (pseudoscalar) into a Z plus a pseudoscalar (scalar).

The Lee-Wick Standard Model is a highly constrained model which solves the gauge hierarchy problem at the expense of including states with negative norm. It appears to be macroscopically causal and consistent. This model is extended by considering the two-Higgs doublet extension of the Lee-Wick model. Rewriting the Lagrangian using auxiliary fields introduces two additional doublets of Lee-Wick partners. The model is highly constrained, with only one or two additional parameters beyond that of the usual two-Higgs doublet model, and yet there are four doublets. Mass relations are established by diagonalizing the mass matrices and further constraints are established by studying results from B → τ ν, neutral B-meson mixing, and B → Xsγ. The prospects of detecting evidence for this model at the LHC are discussed.

In 2013, Geller, Bar-Shalom and Soni (GBS) proposed a Randall-Sundrum model with a bulk SU(2) doublet. They found that the doublet could both stabilize the extra dimension and break the electroweak symmetry; the radion and the Higgs boson were then one and the same. This alternative to the Goldberger-Wise mechanism contained enhanced Higgs couplings to gluons and photons, but at the time of the GBS paper, these couplings were phenomenologically acceptable. We note that updated results from the LHC rule out the model as presented. One can expand the parameter space by extending the model to include bulk fermions. We do so, and show that for any choice of parameters, the model remains in conflict with LHC data. We then extend the scalar sector to a two Higgs model, and show that the model contains a phenomenologically unacceptable zero mass scalar. This property will likely apply to all extensions to the scalar sector, and thus we conclude that the radion cannot be part of a bulk Higgs doublet. *