Multi-Higgs models with CP symmetries of increasingly high order

When building CP-symmetric models beyond the Standard Model, one can impose CP-symmetry of higher order. This means that one needs to apply the CP-transformation more than two times to get the identity transformation, but still the model is perfectly CP-conserving. A multi-Higgs-doublet model based on CP-symmetry of order 4, dubbed CP4, was recently proposed and its phenomenology is being explored. Here, we show that the construction does not stop at CP4. We build examples of renormalizable multi-Higgs-doublet potentials which are symmetric under CP8 or CP16, without leading to any accidental symmetry. If the vacuum conserves CP-symmetry of order 2k, then the neutral scalars become CP-eigenstates, which are characterized not by CP-parities but by CP-charges defined modulo 2k. One or more lightest states can be the dark matter candidates, which are protected against decay not by the internal symmetry but by the exotic CP. We briefly discuss their mass spectra and interaction patterns for CP8 and CP16.Comment: 13 pages; v2: extra comments and references; v3: extra clarifications, matches published versio

Beyond basis invariants

Physical observables cannot depend on the basis one chooses to describe fields. Therefore, all physically relevant properties of a model are, in principle, expressible in terms of basis-invariant combinations of the parameters. However, in many cases it becomes prohibitively difficult to establish key physical features exclusively in terms of basis invariants. Here, we advocate an alternative route in such cases: the formulation of basis-invariant statements in terms of basis-covariant objects. We give several examples where the basis-covariant path is superior to the traditional approach in terms of basis invariants. In particular, this includes the formulation of necessary and sufficient basis-invariant conditions for various physically distinct forms of CP conservation in two- and three-Higgs-doublet models.Comment: 20 pages, no figure

CP4 miracle: shaping Yukawa sector with CP symmetry of order four

We explore the phenomenology of a unique three-Higgs-doublet model based on the single CP symmetry of order 4 (CP4) without any accidental symmetries. The CP4 symmetry is imposed on the scalar potential and Yukawa interactions, strongly shaping both sectors of the model and leading to a very characteristic phenomenology. The scalar sector is analyzed in detail, and in the Yukawa sector we list all possible CP4-symmetric structures which do not run into immediate conflict with experiment, namely, do not lead to massless or mass-degenerate quarks nor to insufficient mixing or CP-violation in the CKM matrix. We show that the parameter space of the model, although very constrained by CP4, is large enough to comply with the electroweak precision data and the LHC results for the 125 GeV Higgs boson phenomenology, as well as to perfectly reproduce all fermion masses, mixing, and CP violation. Despite the presence of flavor changing neutral currents mediated by heavy Higgs scalars, we find through a parameter space scan many points which accurately reproduce the kaon CP-violating parameter $\epsilon_K$ as well as oscillation parameters in K and $B_{(s)}$ mesons. Thus, CP4 offers a novel minimalistic framework for building models with very few assumptions, sufficient predictive power, and rich phenomenology yet to be explored.Comment: 39 pages, 8 figures, 1 table; v2: expanded discussion, extra references, matches published versio

Dark matter from CP symmetry of order 4: evolution in the asymmetric regime

Multi-Higgs models equipped with global symmetries produce scalar dark matter (DM) candidates stabilized by the unbroken symmetry. It is remarkable that a conserved CP symmetry can also stabilize DM candidates, provided it is a CP symmetry of order higher than two. CP4 3HDM, the three-Higgs-doublet model with CP symmetry of order 4, is the simplest example of this kind. It contains two mass-degenerate scalar DM candidates $\varphi$ and $\bar\varphi$, each of them being a CP4 eigenstate and, therefore, its own antiparticle. A novel phenomenological feature of this model is the presence of $\varphi\varphi \leftrightarrow \bar\varphi\bar\varphi$ conversion process, which conserves CP. It offers a rare example of DM models in which self-interaction in the dark sector can significantly affect cosmological and astrophysical observables. Here, we explore the thermal evolution of these DM species in the asymmetric regime. We assume that a mechanism external to CP4 3HDM produces an initial imbalance of the densities of $\varphi$ and $\bar\varphi$. As the Universe cools down, we track the evolution of the asymmetry through different stages, and determine how the final asymmetry depends on the interplay between the conversion and annihilation $\varphi\bar\varphi \to$ SM and on the initial conditions. We begin with the analytic treatment of Boltzmann equations, present a detailed qualitative description of the process, and then corroborate it with numerical results obtained using a dedicated computer code. Finally, we check if the model can produce an observable indirect detection signal.Comment: 17 pages, 4 figure

Symmetries for the 4HDM: extensions of cyclic groups

Multi-Higgs models equipped with global symmetry groups, either exact or softly broken, offer a rich framework for constructions beyond the Standard Model and lead to remarkable phenomenological consequences. Knowing all the symmetry options within each class of models can guide its phenomenological exploration, as confirmed by the vast literature on the two- and three-Higgs-doublet models. Here, we begin a systematic study of finite non-abelian symmetry groups which can be imposed on the scalar sector of the four-Higgs-doublet model (4HDM) without leading to accidental symmetries. In this work, we derive the full list of such non-abelian groups available in the 4HDM that can be constructed as extensions of cyclic groups by their automorphism groups. This list is remarkably restricted but it contains cases which have not been previously studied. Since the methods we develop may prove useful for other classes of models, we present them in a pedagogical manner.Comment: v2: 36 pages, 2 tables, additional clarifications, matches the published versio

Inclusive One Jet Production With Multiple Interactions in the Regge Limit of pQCD

DIS on a two nucleon system in the regge limit is considered. In this framework a review is given of a pQCD approach for the computation of the corrections to the inclusive one jet production cross section at finite number of colors and discuss the general results.Comment: 4 pages, latex, aicproc format, Contribution to the proceedings of "Diffraction 2008", 9-14 Sep. 2008, La Londe-les-Maures, Franc

Frustrated symmetries in multi-Higgs-doublet models

Within multi-Higgs-doublet models, one can impose symmetries on the Higgs potential, either discrete or continuous, that mix several doublets. In two-Higgs-doublet model any such symmetry can be conserved or spontaneously violated after the electroweak symmetry breaking (EWSB), depending on the coefficients of the potential. With more than two doublets, there exist symmetries which are always spontaneously violated after EWSB. We discuss the origin of this phenomenon and show its similarity to geometric frustration in condensed-matter physics.Comment: 7 pages, no figure