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We discuss how one can identify CP violation (and conservation) in multi-Higgs-doublet potentials. After a brief review of CP violation in the 2HDM, we refer to the fact that for NHDM with $N geq 3$ the well known methods useful in the case $N = 2$ have not been generalized in order to provide a set of well defined necessary and sufficient conditions for CP conservation. We then present a simple method, proposed by the authors, to be used in such cases. Two non-trivial examples based on an $S_3$-symmetric three-doublet model are analyzed by means of this new method.
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We consider the phenomenological implications of charged scalar extensions of the SM Higgs sector in addition to EFT couplings of this new state to SM matter. We perform a detailed investigation of modifications of loop-induced decays of the 125 GeV Higgs boson, which receives corrections from the propagating charged scalars alongside one-loop EFT operator insertions and demonstrate that the interplay of $Hto gammagamma$ and $Hto Zgamma$ decays can be used to clarify the additional states phenomenology in case a discovery is made in the future. In parallel, EFT interactions of the charged Higgs can lead to a decreased sensitivity to the virtual presence of charged Higgs states, which can significantly weaken the constraints that are naively expected from the precisely measured $Hto gammagamma$ branching ratio. Again $Hto Zgamma$ measurements provide complementary sensitivity that can be exploited in the future.
The proper renormalization of mixing angles in quantum field theories is a long-standing problem. It is relevant for the renormalization of the quark mixing matrix in the Standard Model and for various mixing scenarios in theories beyond. In this contribution we specifically consider theories with extended scalar sectors. We describe renormalization schemes for mixing angles based on combinations of observables or symmetry requirements such as rigid or background-field gauge invariance and compare their properties to previous approaches such as $bar{MS}$ schemes. We formulate specific renormalization conditions for the mixing angles in the Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model and calculate electroweak corrections to Higgs-boson decays via W- or Z-boson pairs within these models for a selection of (new and old) renormalization schemes.
We determine the complete set of independent gauge and gauge-Higgs CP-odd effective operators for the generic case of a dynamical Higgs, up to four derivatives in the chiral expansion. The relation with the linear basis of dimension six CP-odd operators is clarified. Phenomenological applications include bounds inferred from electric dipole moment limits, and from present and future collider data on triple gauge coupling measurements and Higgs signals.
The prospects for a muon collider operated as a Higgs factory are reviewed. The large muon mass means that the s-channel Higgs production mechanism is available, and simultaneously suppresses bremsstrahlung so that the beam energy spread can be kept to the MeV level required to exploit this. Thus this is the only machine which can make a direct scan over the Higgs resonance, and make an extraordinary mass measurement. Further possibilities such as a scan of the H and A of supersymmetry and CP violation are also mentioned.
CP-violation in the Higgs sector remains a possible source of the baryon asymmetry of the universe. Recent differential measurements of signed angular distributions in Higgs boson production provide a general experimental probe of the CP structure of Higgs boson interactions. We interpret these measurements using the Standard Model Effective Field Theory and show that they do not distinguish the various CP-violating operators that couple the Higgs and gauge fields. However, the constraints can be sharpened by measuring additional CP-sensitive observables and exploiting phase-space-dependent effects. Using these observables, we demonstrate that perturbatively meaningful constraints on CP-violating operators can be obtained at the LHC with luminosities of ${cal{O}}$(100/fb). Our results provide a roadmap to a global Higgs boson coupling analysis that includes CP-violating effects.
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