CP violation studies at Belle

CP-violation in the Standard Model (SM) is described by a single parameter and the pattern of possible CP-violating phenomena is thus extremely constrained. The Belle experiment at the KEK laboratory in Tsukuba (Japan) is testing if this pattern actually occurs by analyzing a sample of about 770 million B-meson decays. CP-violation observed at Belle is consistent with the Cabibbo-Kobayashi-Maskawa (CKM) mechanism, the theory of CP-violation within the SM. We briefly describe how the unitarity triangle allows to probe the CKM theory and review recent measurements of its angles and sides, namely determinations of the CKM angles ? ₁ and ? ₃, and the CKM magnitudes |V _cb | and |V _ub |.     

Searching for signatures of supersymmetry at B-factories

We analyze the predictions for CP asymmetries in B⁰-meson decays within the framework of the supersymmetric standard model (SSM). It is pointed out that owing to sizable new contributions to B_d⁰−B⁰_d and K⁰−K⁰ mixings, the experimentally allowed range for the CP-violating phase δ of the Cabibbo-Kobayashi-Maskawa matrix may be different from the one obtained in the standard model (SM). This has important effects on the allowed values of CP asymmetries in B⁰-meson decays and on their correlations. We calculate the ratio R of the SSM and the SM contributions to the B⁰d–B⁰_d mixing parameter x_d and discuss in detail the ranges of R and S which are consistent with the experimental values of x_d and the CP violation parameter ϵ for K⁰–K⁰ mixing. The CP asymmetries are predicted to have values different from the SM_predictions in sizable regions of parameter space. We also discuss the SSM predictions for B⁰_s–B⁰_s mixing.     

CP violation andZ boson decays

We present a general discussion ofCP-violating effects in the following two and three body decays of theZ boson:Z→l ⁺ l ^?,Z→l ⁺ l ^?γ, wherel=e, μ, τ andZ→2 jets,Z→ 2 jets+γ, andZ→ 3 jets. Experimental observables sensitive toCP violation in these decays are discussed systematically for the case that polarizations of final state particles are not observed. It is shown that the standard model predicts only extremely smallCP-violating effects for the above decays. PossibleCP-violating interactions beyond the standard model are parametrized in terms of aCP-odd effective Lagrangian containing coupling constants proportional to Λ _P ^-1 and Λ _P ^-2 . Here Λ _CP is the mass scale associated with the assumed new interactions. We give estimates of the bounds obtainable for Λ _CP in experiments at LEP1.     

On the addition of vector-like quarks to the standard model

We analyze some of the implications of adding vector-like isosinglet quarks to the standard model and its simplest extension based on the low-energy gauge group SU(3)_c × SU(2) × U(1)^m, which naturally arises in some grand unified theories as well as in some versions of superstring theories. Some of the novel features of this class of models are pointed out: non-unitarity of the Cabibbo-Koyabashi-Maskawa matrix, new CP-violating phases, flavour-changing neutral currents. We derive the CP invariance restrictions on the various quark mass terms and propose a parametrization of the quark mixing matrix which is particularly suitable for models with vector-like quarks. Constraints on these models are derived from rare kaon decays and the value of the K_L − K_S mass difference.     

A new test of CP noninvariance in nonleptonic decay of mesons containing one bottom quark

We show that in six-quark models with a hierarchy of small mixing angles, θ₃ < θ₂ ? 1, and a sizable CP-violating phase δ ～ 1, there is a large difference in the angular distributions, as well as in the rates, when comparing a particular nonleptonic decay mode of a meson containing one bottom quark with the same decay mode of the antiparticle.     

Short-distance CP-violating contributions to the KL→π0e+e− decay

New constributions to the K_L→π⁰e⁺e⁻ amplitude are presented. Short-distance penguin induced diagrams for the s→dγ¹ transition supplement the previously considered electromagnetic penguin. The new CP-violating amplitude corresponds to a new piece of the relevant anomalous dimension matrix. Strong interaction corrections to the new part of the effective hamiltonian are calculated in the leading logarithmic approximation. The role of subleading terms is also discussed.     

Neutrino properties from high-energy astrophysical neutrinos

It is shown how high-energy neutrino beams from very distant sources can be utilized to learn about some properties of neutrinos such as lifetimes. Furthermore, even mixing elements such as U_e3 and the CP-violating phase in the neutrino mixing matrix can be measured in principle. Pseudo-Dirac mass differences as small as 10^?18 eV² can be probed as well.     

General analysis of CP-violation in polarized $b \rightarrow d \ell^ + \ell^-$ decay

The CP-violating asymmetries in the decay, when one of the leptons is polarized, is investigated using the most general form of the effective Hamiltonian. The sensitivity of the CP-violating asymmetries to the new Wilson coefficients is studied.Received: 23 August 2003, Published online: 4 November 2003     

Challenges for extended technicolour theories

We develop the dialectic between extended technicolour theories and phenomenological constraints on rare processes. The natural suppression of flavour-changing neutral currents and CP-violating processes which can occur in models with elementary scalars is not a general feature of naïve extended technicolour (ETC) models. We study the extent to which naïve ETC estimates must in fact be suppressed in order to be compatible with the phenomenology of such rare processes. We emphasize the potential significance of the exchanges of neutral flavour-changing bosons and find that the strongest constraints arise from considering the combination of the D₁⁰-D₂⁰ and K₁⁰-K₂⁰ systems. CP-violating effects in ETC models must be severely suppressed if they are to be compatible with the observational facts. We point to several rare processes whose further experimental study is of particular concern to ETC theories.     

A model of flavor mixing

A model of quark mass matrices is presented where flavor mixings can be expanded in powers of small parameters. These parameters characterize the observed quark mass pattern. The weak mixing matrix has a very simple form. The correlation of the weak mixing angles and CP-violating phases with the main features of the quark spectrum may be easily studied. An upper bound is predicted on the top-quark mass, m_t^p⩽45 GeV, and a rate for the b→u transition close to its experimental limit.     

Probing ZWW couplings through Z0→Wff′

We investigated the possibility of probing the ZWW couplings through the rare decay mode Z⁰→Wff′ of Z⁰. Neglecting masses of the fermions, we computed the combined polarization density matrix of Z and W as a function of the most general ZWW couplings. Integrations over phase space are carried out and the diagonal matrix elements are expressed as quadratic forms of the seven independent couplings. We found that several charge symmetrix polarization channels are particularly sensitive to the CP-violating coupling f₆, which is proportional to the weak magnetic quadrupole moment.     

Charmless decays B \to{\mathrm{PP}}, {\mathrm{PV}}, and the effects of new strong and electroweak penguins in topcolor-assisted technicolor model

Based on the low energy effective Hamiltonian with generalized factorization, we calculate the new physics contributions to the branching ratios and CP-violating asymmetries of the two-body charmless hadronic decays from the new strong and electroweak penguin diagrams in the topcolor-assisted technicolor (TC2) model. The top-pion penguins dominate the new physics corrections, and both new gluonic and electroweak penguins contribute effectively to most decay modes. For tree-dominated decay modes , etc. the new physics corrections are less than 10%. For decays , etc. the new physics enhancements can be rather large (from to ) and are insensitive to the variations of and within reasonable ranges. For the decays and is strongly dependent: varying from to in the range of –. The new physics corrections to the CP-violating asymmetries vary greatly for different B decay channels. For five measured CP asymmetries of the decays, is only about 20% and will be masked by large theoretical uncertainties. The new physics enhancements to interesting decays are significant in size (), insensitive to the variations of the input parameters and hence lead to a plausible interpretation for the unexpectedly large decay rates. The TC2 model predictions for branching ratios and CP-violating asymmteries of all fifty-seven decay modes are consistent with the available data within one or two standard deviations. Received: 18 August 2000 / Revised version: 22 October 2000 / Published online: 5 February 2001     

CP violation and strong phases from penguins in B±→PP and B±→VP decays

We calculate direct CP-violating rate asymmetries in chargedB→PP andB→VP decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order α _s from absorptive parts of one-loop matrix elements of the next-to-leading logarithm corrected effective Hamiltonian. CPT constraints are maintained. Based on this model, we find that partial rate asymmetries between charge conjugateB ^± decays can be as high as 20% for certain channels with branching ratios in the 10^?6 range. Because the $c\bar c$ threshold lies so close to the physical momentum scale, the asymmetries depend sensitively on the model assumptions used to evaluate the imaginary parts of the matrix elements, in particular, on the internal momentum transfer. The charge asymmetries of partial rates would provide unambiguous evidence for direct CP violation.     

Visions: The coming revolutions in particle physics

We study the branching ratio, CP-violating asymmetry, forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the exclusive decay B → Kτ⁺τ⁻ in the two Higgs doublet model with tree level flavor changing neutral currents (model III). We analyse the dependencies of these quantities on the neutral Higgs boson contributions and the CP parameter sinθ in the model III. We observe that to determine the neutral Higgs boson effects, the measurements of the forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the decay B → Kτ⁺τ⁻ are promising.     

<Emphasis Type="Italic">CP</Emphasis> violation due to multi-Froggatt–Nielsen fields

We study how to incorporate CP violation in the Froggatt–Nielsen (FN) mechanism. To this end, we introduce non-renormalizable interactions with a flavor democratic structure to the fermion mass generation sector. It is found that at least two iso-singlet scalar fields with a discrete symmetry imposed are necessary to generate CP violation due to the appearance of the relative phase between their vacuum expectation values. In the simplest model, the ratios of quark masses and the Cabibbo–Kobayashi–Maskawa (CKM) matrix including the CP violating phase are determined by the CKM element |V_us| and the ratio of two vacuum expectation values of FN fields, R=|R|e^iα (a magnitude and a phase). It is demonstrated how the angles φ_i (i=1,...,3) of the unitarity triangle and the CKM off-diagonal elements |V_ub| and |V_cb| are predicted as a function of |V_us|, |R| and α. Although the predicted value of the CP violating phase does not agree with the experimental data within the simplest model, the basic idea of our scenario would be promising if one wants to construct a more realistic model of flavor and CP violation. PACS 11.30.Er; 12.60.-i     

Spontaneous CP violation in extended technicolor models with horizontal U(2)L ⊗ U(2)R flavor symmetries (I)

The Eichten, Lane, Preskill mechanism for CP violation in extended technicolor (ETC) models is examined in models with “horizontal” U(2)_L ? U(2)_R flavor symmetries. We identify a class of chiral perturbations which generate spontaneous CP violation when the vacuum alignment is determined by Dashen's theorem, and show that, in general, a discrete symmetry must be invoked to avoid strong CP non-conservation. CP-violating phases appearing in the electroweak and broken ETC interactions may be naturally suppressed by ratios of ETC vector boson masses.     

Compatibility of the K+n and K−n total cross section measurements,KL0-KS0 regeneration amplitude on hydrogen and CP-violating parameter |η+−|

It is shown that the K⁺n- and K^?n total cross section differenceis and the K_L⁰-K_S⁰ transmission regeneration amplitude measurements at high energies are in good agreement with the CP-violating parameter value |ν_+? = (2.30±0.03) × 10^?3.     

Nonconservation of muon number and CP noninvariance

Based upon a possible quark-lepton symmetry, we suggest that the conservation of muon number may be violated by a matrix element of the order of the Fermi constant times the CP-violating parameter times the squared electric charge. We urge a renewed experimental search for the decay μ^± → e^±e⁺e^? with a branching ratio of about 4 × 10^?9.     

Neutrino mixing and leptonic CP phase in neutrino oscillations

Oscillations of the Dirac neutrinos of three generations in vacuum are considered with allowance made for the effect of the CP-violating leptonic phase (analogue of the quark CP phase) in the lepton mixing matrix. The general formulas for the probabilities of neutrino transition from one sort to another in oscillations are obtained as functions of three mixing angles and the CP phase. It is found that the leptonic CP phase can, in principle, be reconstructed by measuring the oscillation-averaged probabilities of neutrino transition from one sort to another. The manifestation of the CP phase as a deviation of the probabilities of direct processes from those of inverse processes is an effect that is practically unobservable as yet.     

CP-violating correlations in the reactione + e −»hadrons

We investigateCP-violating observables involving jets in the processe ⁺ e ^–»hadrons. These observables are sensitive to sources ofCP-violation beyond the standard model. We use an effective Lagrangian approach to parametrize possible newCP-violating interactions. Bounds on electric and weak diple moments of leptons and quarks are discussed.