Heavy Higgs boson decays in the alignment limit of the 2HDM
The Standard Model (SM)-like couplings of the observed Higgs boson impose strong constraints on the structure of any extended Higgs sector. We consider the theoretical properties and the phenomenological implications of a generic two Higgs doublet model (2HDM). This model constitutes a simple and attractive extension of the SM that is consistent with the observation of the SM-like Higgs boson and precision electroweak observables, while providing a potential new source of CP-violation. In this paper we focus on the so-called Higgs alignment limit of the generic 2HDM, where the neutral scalar field~$H_1$, with the tree-level couplings of the SM Higgs boson, is a mass eigenstate that is aligned in field space with the direction of the Higgs vacuum expectation value. The properties of the two other heavier neutral Higgs scalars, $H_2$ and $H_3$, in the alignment limit of the 2HDM are also elucidated. It is shown that the couplings of $H_2$ and $H_3$ in the alignment limit are tightly constrained and correlated. For example, in the exact alignment limit at tree level, for bosonic final states $\text{BR}(H_{2,3} \to W^+W^-, ZZ, H_1 Z) = 0$ and $\text{BR}(H^\pm \to W^\pm H_1) = 0$, whereas for fermionic final states $Γ(H_2 \to f\bar f)/Γ(H_3 \to f\bar f) \sim M_2/M_3$ (where $M_α$ is the mass of $H_α$). In some cases, the results of the alignment limit differ depending on whether or not alignment is achieved via the decoupling of heavy scalar states. In particular, in the exact alignment limit without decoupling $\text{BR}(H_{2,3}\to H_1 H_1)=0$, whereas these branching ratios are nonzero in the decoupling regime. Observables that could be used to test the alignment scenario at the LHC are defined and discussed. The couplings of the Higgs bosons away from their exact alignment values are determined to leading order, and some consequences are elucidated.