CP violation conditions in N-Higgs-doublet potentials

Conditions for CP violation in the scalar potential sector of general N-Higgs-doublet models (NHDMs) are analyzed from a group theoretical perspective. For the simplest two-Higgs-doublet model (2HDM) potential, a minimum set of conditions for explicit and spontaneous CP violation is presented. The conditions can be given a clear geometrical interpretation in terms of quantities in the adjoint representation of the basis transformation group for the two doublets. Such conditions depend on CP-odd pseudoscalar invariants. When the potential is CP invariant, the explicit procedure to reach the real CP-basis and the explicit CP transformation can also be obtained. The procedure to find the real basis and the conditions for CP violation are then extended to general NHDM potentials. The analysis becomes more involved and only a formal procedure to reach the real basis is found. Necessary conditions for CP invariance can still be formulated in terms of group invariants: the CP-odd generalized pseudoscalars. The problem can be completely solved for three Higgs-doublets.Comment: RevTeX4 used. Minor modifications, in particular, the parameter counting of $Z$. v3: Eqs.(28)-(31) correcte

Jarlskog-like invariants for theories with scalars and fermions

Within the framework of theories where both scalars and fermions are present, we develop a systematic prescription for the construction of CP-violating quantities that are invariant under basis transformations of those matter fields. In theories with Spontaneous Symmetry Breaking, the analysis involves the vevs' transformation properties under a scalar basis change, with a considerable simplification of the study of CP violation in the scalar sector. These techniques are then applied in detail to the two Higgs-doublet model with quarks. It is shown that there are new invariants involving scalar-fermion interactions, besides those already derived in previous analyses for the fermion-gauge and scalar-gauge sectors.Comment: 12 pages, Latex, no figure

Exact Parametrization of Majorana Neutrino Mass Matrix with Large Mixing

Under the assumption that the neutrinos are Majorana particles we study how the lepton mass matrices can be transformed into the simple form which has the same physical quantities by removing redundant parameters. We propose the exact parametrization of the lepton mass matrices which reflects the small nu_e-nu_mu mixing and the large nu_mu-nu_tau mixing. The relations between the twelve parameters and the physical quantities are shown. Furthermore we calculate the MNS matrix by applying the assumptions used in the quark sector. Finally we also check the validity of these assumptions from the experimental values.Comment: 11 pages, LaTeX, no figure

Flavour Physics and CP Violation in the Standard Model and Beyond

We present the invited lectures given at the Third IDPASC School which took place in Santiago de Compostela in January 2013. The students attending the school had very different backgrounds, some of them were doing their Ph.D. in experimental particle physics, others in theory. As a result, and in order to make the lectures useful for most of the students, we focused on basic topics of broad interest, avoiding the more technical aspects of Flavour Physics and CP Violation. We make a brief review of the Standard Model, paying special attention to the generation of fermion masses and mixing, as well as to CP violation. We describe some of the simplest extensions of the SM, emphasising novel flavour aspects which arise in their framework.Comment: Invited talk at the Third IDPASC School 2013, January 21st - February 2nd 2013, Santiago de Compostela, Galiza, Spain; 36 pages, 8 figures, 2 tables; version with few misprints correcte

Mass matrices and eigenstates for scalars / pseudoscalars; indirect CP violation, mass hierarchies and symmetry breaking

I study indirect CP violation for neutral kaons, and extend it to large values of the CP-violating parameter (taken to be real). I show how and at which condition there can exist a continuous set of basis in which the kinetic and mass terms in the Lagrangian can be diagonalized simultaneously. An ambiguity results for the mass spectrum, which then depends on the basis. In particular, for fixed (positive) (mass)^2 of the CP eigenstates K^0_1, K^0_2, and for certain ranges of values of the CP-violating parameter, a negative (mass)^2 can arise in the CP-violating basis. Under certain conditions, even a small perturbation, by lifting the ambiguity, can strongly alter the pattern of masses. These investigations extend in a natural way to indirect CP violation among a set of Higgs-like doublets. The C-odd commutator [K^0, K^0 bar], or its equivalent for Higgs multiplets, plays an important role. The condition for its vanishing and its consequences are among the main concerns of this work.Comment: LaTeX2e, 35 pages, 10 postscript figures + 1 log

D0−Dˉ0D^0 - \bar D^0 Mixing in the Presence of Isosinglet Quarks

We analyse $\Delta C=2$ transitions in the framework of a minimal extension of the Standard Model where either a $Q=2/3$ or a $Q=-1/3$ isosinglet quark is added to the standard quark spectrum. In the case of a $Q=2/3$ isosinglet quark, it is shown that there is a significant region of parameter space where $D^0 - \bar D^0$ mixing is sufficiently enhanced to be observed at the next round of experiments. On the contrary, in the case of a $Q=-1/3$ isosinglet quark, it is pointed out that obtaining a substancial enhancement of $D^0 - \bar D^0$ mixing, while complying with the experimental constraints on rare kaon decays, requires a contrived choice of parameters.Comment: 10 pages plus four figures. The figures are not included but are available upon reques

Large Neutrino Mixing with Universal Strength of Yukawa Couplings

We analyse, within the framework of universal strength for Yukawa couplings (USY), various structures for the Dirac and Majorana neutrino mass matrices giving rise, through the see-saw mechanism, to a degenerate mass spectrum. A specific USY ansatz is presented for the charged lepton and neutrino effective mass matrix, leading to quasi-degenerate neutrinos and a leptonic mixing matrix which provides a large angle solution for both the atmospheric and solar neutrino problems.Comment: 7 pages, ReVTeX, small comments adde

Quark mixings and flavor changing interactions with singlet quarks

Aspects of the quark mixings and flavor changing interactions are investigated in electroweak models with singlet quarks. The effects on the ordinary quark mixing are determined in terms of the quark masses and the parameters describing the mixing between the ordinary quarks q and the singlet quarks Q (q-Q mixing). Some salient features arise in the flavor changing interactions through the q-Q mixing. The unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix within the ordinary quark sector is violated, and the flavor changing neutral currents (FCNC's) appear both in the gauge and scalar couplings. The flavor changing interactions are calculated appropriately in terms of the q-Q mixing parameters and the quark masses, which really exhibit specific flavor structures. It is found that there are reasonable ranges of the model parameters to reproduce the ordinary quark mass hierarchy and the actual CKM structure even in the presence of q-Q mixing. Some phenomenological effects of the singlet quarks are also discussed. In particular, the scalar FCNC's may be more important in some cases, if the singlet quarks as well as the extra scalar particles from the singlet Higgs fields have masses $\sim$ 100 GeV -- 1 TeV.Comment: 32 pages, 7 figures, added reference

Fundamental CP-violating quantities in a SU(2)⊗ \otimes U(1) model with many Higgs doublets

We consider a SU(2)$\otimes$U(1) gauge theory with many scalar doublets, but without fermions. We devise a systematic method of constructing quantities which are invariant under changes of basis of the scalar fields, but acquire a minus sign under a general CP transformation. Those quantities provide a basis-independent way of checking for the existence of CP violation.Comment: (Latex file, 9 pages). CMU-preprin

Triangular Textures for Quark Mass Matrices

The hierarchical quark masses and small mixing angles are shown to lead to a simple triangular form for the U- and D-type quark mass matrices. In the basis where one of the matrices is diagonal, each matrix element of the other is, to a good approximation, the product of a quark mass and a CKM matrix element. The physical content of a general mass matrix can be easily deciphered in its triangular form. This parameterization could serve as a useful starting point for model building. Examples of mass textures are analyzed using this method.Comment: 10 pages, no figure