Bohr's complementarity relation and the violation of CP symmetry in the neutral kaon system

We test Bohr's complementary relation, for single and bipartite neutral kaons. They present a system that is oscillating, decaying and breaks the CP symmetry. We discuss the effect of the CP violation and moreover show that the quantity that complements the single partite information for bipartite kaons is an entanglement measure. Which is independent of CP violation, while nonlocality is sensitive to CP violation.     

Testing non-standard CP violation in neutrino propagation

Non-standard physics which can be described by effective four fermion interactions may be an additional source of CP violation in the neutrino propagation. We discuss the detectability of such a CP violation at a neutrino factory. We assume the current baseline setup of the international design study of a neutrino factory (IDS-NF) for the simulation. We find that the CP violation from certain non-standard interactions is, in principle, detectable significantly below their current bounds – even if there is no CP violation in the standard oscillation framework. Therefore, a new physics effect might be mis-interpreted as the canonical Dirac CP violation, and a possibly even more exciting effect might be missed.     

The exponential parameterization of the neutrino mixing matrix as an SU(3) group element and an account for new experimental data

The exponential form of the Pontecorvo–Maki–Nakagawa–Sakata mixing matrix for neutrinos is considered in the context of the fundamental representation of the SU(3) group. The logarithm of the mixing matrix is obtained. Based on the most recent experimental data on neutrino mixing, the exact values of the entries of the exponential matrix are calculated. The exact values for its real and imaginary parts are determined, respectively, in charge of the mixing without CP violation and of the pure CP violation effect. The hypothesis of complementarity for quarks and neutrinos is confirmed. The factorization of the exponential mixing matrix, which allows the separation of the mixing and of the CP violation itself in the form of the product of rotations around the real and imaginary axes, is demonstrated.     

CP violation in a multi higgs doublet model

We study CP violation in a multi-Higgs doublet model based on aS ₃×Z ₃ horizontal symmetry. We consider two mechanisms for CP violation in this model: a) CP violation due to complex Yukawa couplings; and b) CP violation due to scalarpseudoscalar mixings. We find that the predictions for ε′/ε, CP violation in B decays and the electric dipole moments of neutron and electron are different between these two mechanisms. These predictions are also dramatically different from the minimal Standard Model predictions.     

CP violation in a multi higgs doublet model

We study CP violation in a multi-Higgs doublet model based on aS ₃×Z ₃ horizontal symmetry. We consider two mechanisms for CP violation in this model: a) CP violation due to complex Yukawa couplings; and b) CP violation due to scalarpseudoscalar mixings. We find that the predictions for ε′/ε, CP violation in B decays and the electric dipole moments of neutron and electron are different between these two mechanisms. These predictions are also dramatically different from the minimal Standard Model predictions.     

A parameterization of electro-weak mass matrices for quarks

We discuss quark flavor mixing and CP violation using a 10 parameter quark mass matrix in the electro-weak basis. The matrix handles the high mass of the top quark, 174±16 GeV, and contains two CP violating phases. We show that this scheme favors minimal CP violation by a single phase factor and leads to maximal CP violation in the standard parameterization of the quark flavor mixing matrix.     

CP,T and fundamental interactions

We discuss the importance of the CP (simultaneous particle–antiparticle and left–right permutation) and T (time reversal) symmetries in the context of fundamental interactions. We show that they may provide clues to go beyond the 4-D gauge interactions. We insist on the fact that T violation is not associated to a degradation (like in entropy), but simply characterised by different trajectories.     

Higgs and neutrino sector,EDM and ε<Subscript>K</Subscript> in a spontaneously CP and R-parity breaking supersymmetric model

We construct an extension of the supersymmetric standard model where both CP symmetry and R-parity are spontaneously broken. We study the electroweak symmetry breaking sector of the model and find minima consistent with the experimental bounds on Higgs boson masses. Neutrino masses and mixing angles are generated through both seesaw and bilinear R-parity violation. We show that the hierarchical mass pattern is obtained, and mixings are consistent with measured values. Due to the spontaneous CP and R-parity violation, the neutrino sector is CP violating, and we calculate the corresponding phase. We further restrict the parameter space to agree with the limits on the electric dipole moment of the neutron. Finally, we study the CP violation parameter ε_K in the kaon system and show that we obtain results consistent with the experimental value.     

在中微子振荡中的CP破坏

讨论了中微子味混合与中微子振荡的理论,定量地研究了在中微子振荡中的CP破坏效应.在一类超对称模型中,计算了真空中中微子振荡几率和 CP破坏效应.     

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.     

Neutrino Mass Hierarchy and CP Violation in Long Baseline Neutrino Experiment

We discuss the CP violation in long base line neutrino oscillation experiments. The direct measurement of CP violation is the difference of transitions probability between CP conjugate channels. The sign of Δ ₃₁ is not yet determined, we assume two mass hierarchy conditions, normal (Δ ₃₁>0) and inverted (Δ ₃₁<0). In this paper, we study the CP violation and neutrino mass hierarchy effect in vacuum and matter for long baseline BNL experiments. By an appropriate chose of experimental parameter, neutrino energy and traveled distance. We find that, in matter normal mass hierarchy en-chanced maximum CP violation over their invert mass hierarchy value by 12 %.     

VARIETIES OF CP VIOLATION IN NEUTRAL B MESON DECAYS

We discuss various CP violation effects of neutral B mesons within the framework of the standard model.We classify 28 hadronic two-body decay channels of neutral B mesons into four classes,each of them has different CP violation effects, that is,CP violation due to phase dif- ference between mixing elements M₁₂ and Г₁₂; due to that between mixing elements and decay amplitudes; due to CP phase in the pure particle decay amplitudes and the interplay of these sources .Cascade decays of these channels are also discussed where copious interference is taken into account .Results are given in re- phasing invariants of the K-M matrix .It is shown that CP violation effects might be large(tHe largest,10^-1,but the CP asymmetry event branching cross section is small,at the order or approximate 10^-5±1/2.     

CP violation in the general two-Higgs-doublet model: a geometric view

We discuss the CP properties of the potential in the general two-Higgs-doublet model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these invariant functions, parametrising the gauge orbits of the Higgs fields, is isomorphic to the forward light cone and its interior. CP transformations are shown to correspond to reflections in the space of the gauge invariant functions. We consider CP transformations where no mixing of the Higgs doublets is taken into account as well as the general case where the Higgs basis is not fixed. We present basis independent conditions for explicit CP violation which may be checked easily for any THDM potential. Conditions for spontaneous CP violation, that is CP violation through the vacuum expectation values of the Higgs fields, are also derived in a basis independent way.     

The discovery of CP violation in B-meson decays

We present the KEK B-factory project, which discovered CP violation in B-meson decays and proved that the Kobayashi-Maskawa theory correctly explains CP violation in meson decays.(Communicated by Toshimitsu YAMAZAKI, M.J.A.).     

Isospin amplitudes and CP violation in (B \to K \pi) decays

We present a simple isospin invariant parametrization for decay amplitudes which consistently includes CP violation and (quasi-elastic) hadronic final state interactions. We find that the observed decays do not lead to a significant bound on the angle of the unitarity triangle. On the other hand, we claim that a sizeable CP violation asymmetry in rates is by no means excluded. Received: 9 June 1998 / Published online: 8 September 1998     

CP violation: the past, the present and the future

We have just entered a period during which we expect considerable progress toward understanding CP violation. Here we review what we have learnt so far, and what is to be expected in the near future. To do this we cover the foundation of CP violation at a level which can be understood by physicists who are not working in this field.     

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.     

Are CP Violating Effects in the Standard Model Really Tiny?

We derive an effective action of the bosonic sector of the Standard Model by integrating out the fermionic degrees of freedom in the worldline approach. The CP violation due to the complex phase in the CKM matrix gives rise to CP-violating operators in the effective action. We calculate the prefactor of the appropriate next-to-leading order operators and give general estimates of CP violation in the bosonic sector of the Standard Model. In particular, we show that the effective CP violation for weak gauge fields is not suppressed by the Yukawa couplings of the light quarks and is much larger than the bound given by the Jarlskog determinant.     

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.     

Direct CP violation in B(s)→J/ψP(V)

In the framework of factorization, we study direct CP violation in the decays of B_(s)→J/ψP(V) (P(V) refer to the pseudoscalar (vector) meson). The CP violation depends strongly on Cabibbo-Kobayashi- Maskawa (CKM) matrix elements and the effective parameter, N_c. The recent experimental data for the branching ratios of B_(s)→J/ψP(V) are accurate enough and we can give a strong constraint on the range of N_c. We nd that the CP violating asymmetry is consistent with the available experiment values for the b→d transition, and a little smaller than the b→s transition. We also predict the CP violation of other decay channels for B_(s)→J/ψP(V). We expect our results can give valuable guidance for experiments.