Complex CKM from spontaneous CP violation without flavor changing neutral current

We analyse the general constraints on unified gauge models with spontaneous CP breaking that satisfy the conditions that (i) CP violation in the quark sector is described by a realistic complex CKM matrix, and (ii) there is no significant flavor changing neutral current effects in the quark sector. We show that the crucial requirement in order to conform to the above conditions is that spontaneous CP breaking occurs at a very high scale by complex vevs of standard model singlet Higgs fields. Two classes of models are found, one consisting of pure Higgs extensions and the other one involving fermionic extensions of the standard model. We give examples of each class and discuss their possible embeddings into higher unified theories. One of the models has the interesting property that spontaneous CP violation is triggered by spontaneous P violation, thereby linking the scale of CP violation to the seesaw scale for neutrino masses.     

Spontaneous CP violating phase as the CKM matrix phase

We propose that the CP violating phase in the CKM mixing matrix is identical to the CP phases responsible for the spontaneous CP violation in the Higgs potential. A multi-Higgs model with Peccei–Quinn (PQ) symmetry is constructed to realize this idea. The CP violating phase does not vanish when all Higgs masses become large. In general, here are flavor changing neutral current (FCNC) interactions mediated by neutral Higgs bosons at the tree level. However, unlike general multi-Higgs models, the FCNC Yukawa couplings are fixed in terms of the quark masses and CKM mixing angles. Implications for meson–anti-meson mixing, including recent data on D–D̄ mixing, and the electric dipole moment (EDM) of the neutron are studied. We find that the neutral Higgs boson masses can be at the order of one hundred GeV. The neutron EDM can be close to the present experimental upper bound.     

Constraint on three-Higgs-doublet model parameters by b → sγ decay considering possibility of the fourth generation in quark sector

Weak radiative B-meson decay has been studied to find plausible constraints on the complex coupling constants that arise from the diagonalization of the charged scalar mixing matrix in Weinberg three-Higgs-doublet model considering possibility of the fourth generation in quark sector. We examined the range of these complex coupling constants taking in to account corrections up to leading QCD logarithms, using evolution of fourth-generation CKM matrix with CP violation phase approximately equal to zero. Range of the mass of fourth generation down-type quark b′ and that of fourth-generation uptype quark t′ have been taken with due consideration of the constraint imposed by the present experimental value of theρ parameter keeping in view the mass difference of the fourth-generation quark doublet.     

The breaking of flavor democracy in the quark sector

The democracy of quark flavors is a well-motivated flavor symmetry,but it must be properly broken in order to explain the observed quark mass spectrum and flavor mixing pattern.We reconstruct the texture of flavor democracy breaking and evaluate its strength in a novel way,by assuming a parallelism between the Q = +2/3 and Q =-1/3 quark sectors and using a nontrivial parametrization of the flavor mixing matrix.Some phenomenological implications of such democratic quark mass matrices,including their variations in the hierarchy basis and their evolution from the electroweak scale to a super-high energy scale,are also discussed.     

A soft origin for CKM-type CP violation

We present a two-Higgs-doublet model, with a Z₃ symmetry, in which CP violation originates solely in a soft (dimension-2) coupling in the scalar potential, and reveals itself solely in the CKM (quark mixing) matrix. In particular, in the mass basis the Yukawa interactions of the neutral scalars are all real. The model has only eleven parameters to fit the six quark masses and the four independent CKM-matrix observables. We find regions of parameter space in which the flavour-changing neutral couplings are so suppressed that they allow the scalars to be no heavier than a few hundred GeV.     

Quark mixing in weak interactions

The status of the quark mixing in weak interaction is reviewed. The 3×3 quark mixing matrix for the three left-handed doublet model is analyzed using various experimental information involving strange, charmed, and b-flavored particles. Its interplay with nonleptonic decays, implication on neutral particle-antiparticle mixing and CP violation in heavy quark systems, and the possible origin of the quark mixing from quark mass matrix are discussed. Finally we briefly review the status of alternative sources for CP violation, and alternative models to the three left-hand quark doublet model.     

THE CP VIOLATION OF SU(7) MODEL

We discuss the CP violation problem of SU(7) models of Grand Unified Theoryincluding four genarations^[1,2]. It is shown that if we properly choose the complex phaseangles in quark mass matrix elements, we are able to obtain the CP violation phaseangle which agrees well with the experimental value. If the Higgs potential is pro-perly choosen we find that the strong CP violation parameter θ is equal to zero atthe tree level.     

Effect on Jarlskog Determinant Above the GUT Scale Within Four Flavor Neutrino Framework

We study the Planck scale effects on Jarlskog determiant in the four flavor framework. On electroweak symmetry breaking, quantum gravitational effects lead to an effective SU(2) × U(1) invariant dimension-5 Lagrangian including neutrino and Higgs forces, which perturbed the neutrino mass term and produce an extra terms in the neutrino mass matrix. We consider that gravitational interaction is independent from flavor and compute the Jarlskog determiant due to Planck scale effects. In the case of leptonic sector, the strentgh of CP violation is measured by Jarlskog determiant. We applied our approach to study Jarlskog determinant in the four flavor neutrino mixing above the GUT scale.

     

About the Mixing and CP Violation in Neutrino System

Suppose that the geometrical explanation to the weak CP phase in quark sector is also valid for neutrinos, the mixing and CP violation in neutrino system are discussed. We find that a J_Cp larger than 3 × 10^-3 implies the large-mixing solution for solar neutrino problem. In the case of bi-maximal mixing, we predict relative large CP violation with J_Cp larger than 10^-3 in neutrino system, except the third mixing angle approaching to 0 or π/2 very closely.     

Spontaneous CP violating phase as the phase in PMNS matrix

We study the possibility of identifying the CP violating phases in the PMNS mixing matrix in the lepton sector and also that in the CKM mixing matrix in the quark sector with the phase responsible for the spontaneous CP violation in the Higgs potential, and some implications. Since the phase in the CKM mixing matrix is determined by experimental data, the phase in the lepton sector is also fixed. The mass matrix for neutrinos is constrained, leading to constraints on the Jarlskog CP violating parameter J, and the effective mass 〈m _ββ 〉 for neutrinoless double beta decay. The Yukawa couplings are also constrained. Different ways of identifying the phases have different predictions for \(\mu\to e e\bar{e}\) and \(\tau\to l_{1} l_{2} \bar{l}_{3}\). Future experimental data can be used to distinguish different models.     

Flavor anarchy in a Randall-Sundrum model with 5D minimal flavor violation and a low Kaluza-Klein scale

A variant of a warped extra dimension model is presented. It is based on 5D minimal flavor violation, in which the only sources of flavor breaking are two 5D anarchic Yukawa matrices. These matrices also control the bulk masses, which are responsible for the resulting flavor hierarchy. The theory flows to a next to minimal flavor violation model where flavor violation is dominantly coming from the 3rd generation. Flavor violation is also suppressed by a parameter that dials the violation in the up or down sector. There is therefore a sharp limit in which there is no flavor violation in the down-type quark sector which, remarkably, is consistent with the observed flavor parameters. This is used to eliminate the current Randall-Sundrum flavor and CP problem. Our construction suggests that strong dynamic-based, flavor models may be built based on the same concepts.     

Comments on a Definition of Maximal CP Violation

In the weak basis with diagonalized up quark mass matrix and Hermitian down quark mass matrix, the sequential product of the off dingonal elements M₁₂^dM₂₃^dM₃₁^d is a phase-convention-independent quantity. The idea of using the argument of this product to define maximal CP violation is examined, along with other definitions. The argument in reality is not π/2 allowing experimental and theoretical uncertainties.     

Textured pure phase mass matrices

We study pure phase quark mass matrices with additional texture, starting with symmetric matrices. A variety of textures are consistent with values of masses and flavor mixing matrix elements run to high energy.     

Texture zeros and majorana phases of the neutrino mass matrix

We present the generic formulas to calculate the ratios of neutrino masses and the Majorana phases of CP violation from the neutrino mass matrix with two independent vanishing entries in the flavor basis where the charged lepton mass matrix is diagonal. An order-of-magnitude illustration is given for seven experimentally acceptable textures of the neutrino mass matrix, and some analytical approximations are made for their phenomenological consequences at low energy scales.     

Non-unitary neutrino mixing and CP violation in the minimal inverse seesaw model

We propose a simplified version of the inverse seesaw model, in which only two pairs of the gauge-singlet neutrinos are introduced, to interpret the observed neutrino mass hierarchy and lepton flavor mixing at or below the TeV scale. This “minimal” inverse seesaw scenario (MISS) is technically natural and experimentally testable. In particular, we show that the effective parameters describing the non-unitary neutrino mixing matrix are strongly correlated in the MISS, and thus, their upper bounds can be constrained by current experimental data in a more restrictive way. The Jarlskog invariants of non-unitary CP violation are calculated, and the discovery potential of such new CP-violating effects in the near detector of a neutrino factory is discussed.     

Relation between the neutrino and quark mixing angles and grand unification

We argue that there exists a simple relation between the quark and lepton mixings, which supports the idea of grand unification and probes the underlying robust bimaximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bimaximal, predicting theta(sol)+theta(C)=pi/4, where theta(C) is the Cabibbo angle, theta(atm)+theta(CKM)(23)=pi/4 and theta(MNS)(13) approximately theta(CKM)(13) approximately O(lambda(3)), in perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable of explaining this flavor mixing pattern and inducing the measured quark and lepton masses is outlined.     

夸克质量矩阵与CP对称性破坏

本文给出一类夸克质量矩阵与CP破坏参量的精确解析关系. 有关结果适用于唯象研究不同质量矩阵模型及其CP破坏效应的细微差别.     

What if the mass difference \Delta M_s is around 18 inverse picoseconds?

Present experiments in pursuit of the mass difference in the system have put a lower bound on this quantity of (at 95% C.L.). The same experiments also yield a local minimum in the log-likelihood function around , which is away from being zero. Motivated by these observations, we investigate the consequences of a possible measurement of , in the context of both the standard model and supersymmetric models with minimal flavor violation. We perform a fit of the quark mixing parameters in these theories and estimate the expected ranges of the CP asymmetries in B decays, characterized by and , the interior angles of the CKM-unitarity triangle. Based on this study, we argue that, if indeed turns out to be in its currently-favored range, this would disfavor a large class of supersymmetric models. Indeed, of all the models examined here, the best fit to the data occurs for the standard model. Received: 14 December 2000 / Published online: 23 January 2001