Diagnosing CP properties of the 2HDM

We have investigated a Two-Higgs-Doublet Model (2HDM), focusing on CP violation. Various scenarios with spontaneous and explicit breaking of CP have been considered. Some features of CP violation related to a choice of the basis for the two Higgs doublets have been discussed and clarified. Regions in the physical parameter space corresponding to spontaneous and explicit CP violation have been located and discussed. The possibility to determine parameters of the scalar potential with no reference to Yukawa couplings has been considered and an unavoidable ambiguity has been found. The issue of disentangling spontaneous and explicit CP violation has been investigated.Comment: 32 pages, 5 figures. Minor changes. Version to appear in JHE

Measuring CP violation in Two-Higgs-Doublet models in light of the LHC Higgs data

In Two-Higgs-Doublet models, the conditions for CP violation can be expressed in terms of invariants under U(2) rotations among the two SU(2) Higgs doublet fields. In order to design a strategy for measuring the invariants we express them in terms of observables, i.e., masses and couplings of scalar bosons. We find amplitudes directly sensitive to the invariants. Observation of the Standard-Model-like Higgs boson at the LHC severely constrains the models. In particular, in the model with Z_2 symmetry imposed on dimension-4 terms (in order to eliminate tree-level flavour-changing neutral currents), CP violation is strongly suppressed. On the other hand, the most general Two-Higgs-Doublet model (without Z_2 symmetry) would still allow for CP violation to be present in the model, without being in conflict with the LHC data. Consequently, also flavour-changing neutral currents would in general be expected. We briefly sketch a strategy for measuring the remaining CP violation.Comment: 26 pages, 7 figures. Version published in JHE

Testing the presence of CP violation in the 2HDM

We review CP properties of the Two-Higgs-Doublet model. In particular, we show that spontaneous CP violation occurs in the parameter space on the border between regions allowing explicit CP violation and those where there is another minimum, deeper than the one corresponding to v=246 GeV. We discuss weak-basis invariants which describe CP violation and express them through measurable quantities like coupling constants and masses. Also, we discuss how CP violation is constrained by the LHC Higgs data. Finally, we identify effective operators that could be adopted to measure CP-invariants.Comment: 9 pages, Proceedings of the Corfu Summer Institute 2014 "School and Workshops on Elementary Particle Physics and Gravity", 3-21 September 2014 Corfu, Greece. v2: References adde

A Simple Method to detect spontaneous CP Violation in multi-Higgs models

For models with several Higgs doublets we present an alternative method to the one proposed by Branco, Gerard and Grimus, in 1984, to check whether or not CP is spontaneously violated in the Higgs potential. The previous method is powerful and rigorous. It requires the identification of a matrix $U$ corresponding to a symmetry of the Lagrangian and verifying a simple relation involving the vacuum expectation values. The nonexistence of such a matrix signals spontaneous CP violation. However, as the number of Higgs doublets increases, finding such a matrix $U$ may not be straightforward and it may turn out to be easier to analyse the potential by going to the so-called Higgs basis. The transformation to the Higgs basis is straightforward once the vacuum expectation values are known. The method proposed in this work is also powerful and rigorous and can be particularly useful to analyse models with more than two Higgs doublets and with continuous symmetries.Comment: 9 pages, no figures. v2: minor changes, matching JHEP versio

Update on the CP-Violating Inert-Doublet Model

We have updated a recently proposed extension of the Inert Doublet Model. The extension amounts to the addition of an extra non-inert scalar doublet. The model thus offers a possibility of CP violation in the scalar sector and a candidate for the Dark Matter. The recent XENON100 direct-detection experiment excludes a considerable range of medium-low dark-matter masses, leaving only as viable very low masses of order 5-10 GeV, as well as the regions from \sim 60 to \sim 110 GeV, and above \sim 530 GeV. For favorable parameter regions one may observe related long-lived charged particles produced at the LHC.Comment: Contribution to PoS Proceedings, The XXth International Workshop High Energy Physics and Quantum Field Theory, September 24 - October 1, 2011, Sochi, Russi

Spontaneous symmetry breaking in the S3S_3-symmetric scalar sector

We present a detailed study of the vacua of the $S_3$-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability.Comment: 37 pages. v2: Minor changes in the references, matches published version. v3: Table 6 corrected: two additional cases conserve CP. Related discussion adapted. Version consistent with JHEP Erratu

Symmetries and Mass Degeneracies in the Scalar Sector

We explore some aspects of models with two and three SU(2) scalar doublets that lead to mass degeneracies among some of the physical scalars. In Higgs sectors with two scalar doublets, the exact degeneracy of scalar masses, without an artificial fine-tuning of the scalar potential parameters, is possible only in the case of the inert doublet model (IDM), where the scalar potential respects a global U(1) symmetry that is not broken by the vacuum. In the case of three doublets, we introduce and analyze the replicated inert doublet model, which possesses two inert doublets of scalars. We then generalize this model to obtain a scalar potential, first proposed by Ivanov and Silva, with a CP4 symmetry that guarantees the existence of pairwise degenerate scalar states among two pairs of neutral scalars and two pairs of charged scalars. Here, CP4 is a generalized CP symmetry with the property that $({\rm CP}4)^n$ is the identity operator only for integer $n$ values that are multiples of 4. The form of the CP4-symmetric scalar potential is simplest when expressed in the Higgs basis, where the neutral scalar field vacuum expectation value resides entirely in one of the scalar doublet fields. The symmetries of the model permit a term in the scalar potential with a complex coefficient that cannot be removed by any redefinition of the scalar fields within the class of Higgs bases (in which case, we say that no real Higgs basis exists). A striking feature of the CP4-symmetric model is that it preserves CP even in the absence of a real Higgs basis, as illustrated by the cancellation of the contributions to the CP violating form factors of the effective ZZZ and ZWW vertices.Comment: 52 pages, 2 figures, second revised version with new material, as published by JHE

Implications of symmetries in the scalar sector

Symmetries play a very important r\^ole in Particle Physics. In extended scalar sectors, the existence of symmetries may permit the models to comply with the experimental constraints in a natural way, and at the same time reduce the number of free parameters. There is a strong interplay among internal symmetries of the scalar potential, its CP properties and mass degeneracies of the physical scalars. Some of these aspects were discussed in this talk.Comment: 8 pages, to be published in the Proceedings of DISCRETE2018: 6th Symposium on Prospects in the Physics of Discrete Symmetries, 26-30 Nov 2018. Vienna, Austri

Spontaneous symmetry breaking in three-Higgs-doublet S3S_3-symmetric models

The talk summarises work done by the authors consisting of a detailed study of the possible vacua in models with three Higgs doublets with $S_3$ symmetry and without explicit CP violation. Different vacua require special regions of the parameter space which were analysed in our work. We establish the possibility of spontaneous CP violation in this framework and we also show which complex vacua conserve CP. In our work we discussed constraints from vacuum stability. The results presented here are relevant for model building.Comment: 11 pages, no figures. Prepared for the proceedings of DISCRETE2016: the Fifth Symposium on Prospects in the Physics of Discrete Symmetries, 28 November-3 December 2016, University of Warsaw, Poland, to appear in the Journal of Physics: Conference Series (JPCS