Lightness of Higgs boson and spontaneousCPviolation in the Lee model

Abstract

We proposed a mechanism in which the lightness of Higgs boson and the smallness of charge parity (CP) violation are correlated based on the Lee model, namely, the spontaneous CP-violation two-Higgsdoublet model. In this model, the mass of the lightest Higgs boson m h as well as the quantities K and J are ∝ t β s ξ in the limit t β s ξ → 0 (see text for definitions of t β and ξ), namely, the CP conservation limit. Here, K and J are the measures for CP-violation effects in scalar and Yukawa sectors, respectively. It is a new way to understand why the Higgs boson discovered at the LHC is light. We investigated the important constraints from both high energy LHC data and numerous low energy experiments, especially the measurements of electric dipole moments of electron and neutron as well as the quantities of B meson and kaon. Confronting all data, we found that this model is still viable. It should be emphasized that there is no standard-model limit for this scenario; thus it is always testable for future experiments. In order to pin down the Lee model, it is important to discover the extra neutral and charged Higgs bosons and measure their CP properties and the flavor-changing decays. At the LHC with ffiffi ffi s p ¼ 14 TeV, this scenario is favored if there is significant suppression in the bb decay channel or any vector boson fusion, V þ H production channels. On the contrary, it will be disfavored if the signal strengths are standard-model-like more and more. It can be easily excluded at ð3-5Þσ level with several fb −1 at future e þ e − colliders, via accurately measuring the Higgs boson production cross sections.

Higgs pair production in the CP-violating two-Higgs-doublet model

“…In the allowed mass range of the heavy Higgs bosons, we find the total production cross sections to be σ[pp → h 1 h 1 ] ∼ O(10) − O(100) fb at the LHC 14 TeV runs. They can be as large as ∼ O (10 3 ) fb at the future SppC 100 TeV runs. The discovery of these channels will manifest the structure of the Higgs sector.…”

Higgs boson-μ−τcoupling at high and low energy colliders

“…In the extensions of SM, there may be direct Higgs-µ-τ coupling to explain this hint, for example, in some types of two Higgs doublet models (2HDM) [18], like type III 2HDM [19][20][21][22], 2HDMs with other flavor symmetries [23][24][25], Lee model [26,27], and other models [28][29][30]. It may be also related to other phenomena like the excess in tth searches [31], b → s semi-leptonic decays [24], anomalous magnetic moment (g − 2) for µ [32], LFV τ decays [21,25,[32][33][34], or even the lepton flavored dark matter [35].…”

Spontaneous CP -violation in the simplest little Higgs model and its future collider tests: The scalar sector

“…Following the idea in Refs. [24,32], we should try to measure the tree-level h 2 VV and h 1 h 2 V vertices to confirm CP violation in the scalar sector. For different h 2 masses, we need different future colliders.…”

“…This mechanism was proposed by Lee in 1973 [19] as the first kind of two-Higgs-doublet model [17]. Moreover, the spontaneous CP-violation mechanism is also a possible solution to the strong-CP problem [23], and it may be connected with the lightness of the Higgs boson as well [24]. Besides these models, spontaneous CP violation in the scalar sector can also arise from the composite framework.…”

“…Indirect effects may appear in the electric dipole moments (EDMs) of the electron and neutron [28], modifications in meson mixing parameters [29], or anomalous ZZZ couplings [30], while direct effects may be discovered in hτ þ τ − or htt vertices through measuring the final-state distributions [31]. If another scalar is discovered and we denote the scalars as h 1;2 (h 1 is the SM-like Higgs boson and h 2 is the extra scalar), we can also discover CP violation in the scalar sector through directly measuring tree-level vector-vector-scalar-(VVS) and vector-scalar-scalar-type (VSS) vertices, such as h 2 VV and Vh 1 h 2 vertices, 2 according to the analysis of CP properties [24]. Based on this idea, we recently proposed a model-independent method to measure the CP-violation effects in the scalar sector through e þ e þ → Z Ã → Zh 1 ; Zh 2 ; h 1 h 2 -associated production processes at future e þ e − colliders [32].…”