Isospin invariance,CP violation and B−B̄ mixing

With large B⁰−B̄⁰ mixing, the CP asymmetry of certain B decays become nearly maximal. However, the clear identification of relevant B meson decays required for experimental observation of such effects is difficult. We point out that symmetry relations among various B meson decay channels lead to additional constraints which can be useful in extracting CP violating amplitudes. As an example, we consider decay amplitudes to final states containing both a J/ψ and a K_S, whose interference terms provide information on CP violation. We show that these decays are ΔI=0 transitions and obtain isospin relations between the direct terms in the amplitude and experimental results from corresponding decays involving charged kaons.     

Radiative Kaon decays and CP violation in chiral perturbation theory

Chiral perturbation theory is a very useful framework for testing the standard model in processes where long-distance effects are expected to play an essential rôle. We analyze the rare K decays K⁰→γℓ⁺ℓ⁻, K⁺→π⁺γ3 and K_L→π⁰ℓ⁺ℓ⁻ in the effective chiral formulation of the standard model. These processes, like the decays K⁰→γγ, K⁺→π⁺ℓ⁺ℓ⁻, K_S→π⁰ℓ⁺ℓ⁻ and K⁰→π⁰γγ discussed in previous work, have the property that the corresponding amplitudes vanish to lowest order in chiral perturbation theory. Precise predictions for decay rates and spectra are made in terms of a few coupling constants not restricted by softly broken chiral symmetry alone. Special consideration is given to various possible tests of CP noninvariance in these decays, in particular to effects due to intrinsic CP violation in the amplitudes. We find that chiral perturbation theory correlates different CP-violating observables such as the charge asymmetries in K^±→π^±γγ and K^±→π^±ℓ⁺ℓ⁻, the one-photon exchange contribution to K_L→π⁰e⁺e⁻ and the transverse polarization in K_L →π⁰μ⁺μ⁻. Detailed numerical results are shown.     

First evidence for direct CP violation

The double ratio R of the relative decay rates of the short- and long-lived neutral kaons into two charged and two neutral pions was measured to be 0.980±0.004±0.005. The deviation of R from the CP violation in the transition of the CP-odd K₂ into two pions with ϵ′/ϵ=(3.3 ± 1.1)×10⁻³.     

Leading logarithms of heavy quark masses in processes with light and heavy quarks

The matrix elements of operators containing both heavy quark (Q) and light quark (q) fields can contain large logarithms of the type ln(m_Q²/μ²), where μ is a typical QCD mass scale and m_Q is the heavy quark mass. We outline a method for summing leading logarithms of this type. We apply it to the decay constant f_M of a low lying pseudoscalar meson M with Q̄q flavor quantum numbers and predict the ratios of decay constants for mesons with different heavy flavors. We also apply it to a matrix element of a four-quark operator which is relevant for B⁰−B̄⁰ mixing.     

Cabibbo angle,CP violation and quark masses

By adding suitable discrete flavor symmetries to SU(2)_L ? SU(2)_R ? U(1) left-right symmetric gauge models of weak and electromagnetic interactions, we are able to express all the mixing angles between the quark flavors (u, d, s,c) in terms of the quark masses. This enables us to compute the Cabibbo angle and the CP violating phases using plausible values for the quark masses. The CP violating K ar 2π decay amplitude η_+? (and η₀₀ in the model is then given purely in terms of the parity violating parameter of the model (m_WL⁺/m_WR⁺)².     

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.     

Predictions of the CKM model for CP asymmetries in B decay

We discuss present-day uncertainties for the value of the CP-violating phase δ in the CKM matrix and point out how a knowledge of m_t and/or x_s could substantially reduce this uncertainty. A model-independent measurement of δ is, in principle, possible by studying certain CP-violating asymmetries, involving B⁰ mesons decaying into CP-conjugate hadronic final states. There exist three different classes of these asymmetries and we give estimates for their values, based on our present knowledge of the CKM matrix. Some comments on the experimental requirements for detecting these asymmetries are also presented.     

From a new smell to a new flavour −BdBd mixing,CP violation and new physics

Using the preliminary data on B_dB̄_d mixing from ARGUS, and the standard model with three families, we infer a lower bound on the top quark mass of 50–70 GeV; also, B_sB̄_s mixing has to be close to maximal. We discuss how the prospects for observing CP violation in B⁰ decays are enhanced and sketch alternative scenarios for new physics.     

CP violation with beautiful baryons

CP violation can be studied in modes of charmed or bottom baryons when a decay process is compared with its charge-conjugated partner. It can show up as a rate asymmetry and in a study of other decay parameters. Neither tagging nor time-dependences are required to observeCP violation with modes of baryons, in contrast to the conventionalB ⁰ modes. Numerous modes of bottom baryons have the potential to show largeCP-violating effects within the Standard Model. Those effects can be substantial for modes with aD ⁰, which is seen in a final state that can also be fed from a \(\bar D^0 \) . For instance, a comparison of theΛ _b→Λ _CP ⁰ with the \(\bar \Lambda _b \to \bar \Lambda D_{CP}^0 \) process can show sizeableCP violation. HereD _CP ^o denotesCP eigenstates ofD ⁰, which occur at a few percent. Six related processes, such asΛ _b→ΛD ⁰, \(\Lambda _b \to \Lambda \bar D^0 \) ,Λ _b→Λ _CP ⁰ , and their charge-conjugated counterparts, can extract ?, which is the most problematic angle of the unitarity triangle and which is conventionally probed with theB _s→ρ⁰ K _S asymmetry. HereD ⁰ andD ^?0 are identified by their charged kaon or lepton. We predictB(Λ _b→ΛD ⁰)～10^?5, thusB(Λ _b→Λ _CP ⁰ )～10^?7. Under favourable circumstances,CP violation can occur at the few tens of percent level. Thus 10²–10³ Λ _b→Λ _CP ⁰ decays start probing ?. Tables list many additional modes with typical branching ratios at the 10^?5–10^?6 level, with large detection efficiencies (in contrast to theD _CP ⁰ ), and with potentially largeCP-violating effects, such as Ξ _b ⁰ →ΛΨ, Λ?, ΛK^*0; Ξ _b ^? →ΛK^(*)?, Ξ^?K_s, Ξ^?K^*0, Ω _b ^? →Ξ^?φ, Ξ^?ρ⁰, ΛK^(*)?, ΩK_s, Ω^?K^*0.     

Spontaneous CP violation in the left-right model and the kaon system

A left-right model with spontaneous CP breakdown, consistent with the particle physics phenomenology, is presented. Constraints on free parameters of the model: mass of the new righthanded gauge boson M₂ and ratio r of the two vacuum expectation valuesof the bidoublet, are found from the measurement of ϵ in the kaon system. For most of the parameter space, M₂ is restricted to be below 10 TeV Higher masses can be achieved only by fine tuning of Kobayashi-Maskawa matrix elements, quark masses, r and the phase α which is the unique source of CP violation in the model. Large number of combinations of signs of quark masses, which are observables of the model, are found to be not allowed since they contradict with data. The range of ϵ'/ϵ the model predicts is around 10⁻⁴ in magnitude.     

CP,T and CPT Invariance in Neutral Kaon Decays

A brief survey of the phenomenology (with emphasis on its present status) of CP, T and CPT invariance in neutral kaon decays is given. Existing limits on the invariances of the mass matrix of the K⁰−K̄⁰ system are stated. Also included are our new results and also those of DASS and KABIR for limits on these invariances for the decay amplitudes, obtained by using existing data, and the available information on the total mass matrix. The CPT invariant part of amplitudes for decay to the I = 0 and I = 2, ππ channels is T (and CP) invariant, in the Eberhard phase convention, to about 0.4% and about 4% respectively; the corresponding T invariant part of these amplitudes is CPT (and CP) invariant to about 1% and about 5% respectively. A limit similar to this last one (5%) was already obtained in the literature by making a further approximation. The CP, T and CPT invariant part of the averaged ΔS = − ΔQ amplitude in K₁₃ decay is found to be less than about 5% of the corresponding ΔS = ΔQ amplitude; the T invariant part of the difference of the averaged ΔS = ΔQ and the averaged ΔS = − ΔQ amplitudes is CPT (and CP) invariant to about 1%. A limit similar to this one (1%) was also obtained in the literature by making a further assumption about the mass matrix. These amplitude limits are expected to have about one significant figure accuracy. Due to large experimental errors, the amplitude limits on the other non-invariance parameters for the above channels are not very good. Difficulties in deriving corresponding parameters for the 3π channel are noted. In certain respects, CPT invariance has been verified experimentally to a poorer accuracy than CP invariance and T invariance.     

Gauge theoretical realization of the superweak model of CP violation

It is pointed out that the presence in a gauge theory of vector bosons or left-over Higgs bosons with a weak interaction strength of the order of10^?11G_E and which have CPviolating couplings to the strangeness-changing neutral current, will lead to the superweak model of CP violation. An example of such a theory, based on the gauge group SU (2) ?U(1), is given.     

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 at colliders

The prospects of experimental detection ofCP violation ate ⁺ e ^? and\(pp/p\bar p\) colliders are reviewed. After a general discussion on the quantities which can measureCP violation and on the implications of theCPT theorem, various possibilities of measuringCP violation arising outside the standard model are taken up.CP violation in leptonic processes, especially polarization effects ine ⁺ e ^?→l ⁺ l ^? are discussed next.CP violation in\(t\overline t \) andW ⁺ W ^? production and decay is also described.     

Fourth-generation signatures in D0-;D̄0 mixing and rare D decays

We study the effects of a fourth generation on D⁰-D̄⁰ mixing and the rare decays D⁰→μ⁺μ⁻, D→ℓ⁺ℓ ⁻X (where X is nonstrange), D→πℓ⁺ℓ⁻ and D→ϱγ (orωγ). D⁰-D̄⁰ mixing can be as large as the experimental limit of 0.5%. The fourth generation can enhance the branching ratios for the rare decays by several orders of magnitude: it can be as large as 10⁻⁹ for the decays D⁰→μ⁺μ⁻, D→ℓ⁺ℓ⁻X and D→πℓ⁺ℓ⁻. The long-distance contribution to the radiative decays is estimated to be ∼ 10⁻⁸ and is shown to be dominant in the three-generation model. The fourth generation can bring this branching ratio up to ∼ 10⁻⁶.     

K 0 → \bar K^0 and B 0 → \bar B^0 transitions in the minimal supersymmetric standard model involving explicit CP violation in the Higgs sector

Mixing in the systems of neutral K ⁰ and B ⁰ mesons is considered within the minimal supersymmetric standard model (MSSM) containing a type-II Yukawa sector and featuring an explicitCP violation in the Higgs potential. In the case of a strong mixing of CP-even and CP-odd states, the model admits the presence of a light charged Higgs boson. Basic mixing parameters are calculated. These include the mass difference Δm _LS between neutral kaons and the parameter ε, which characterizes the amount of an indirect CP violation (that is, that which arises owing to an ultraweak mixing of CP-invariant and CP-noninvariant components). In the limit of the low-energy one-loop approximation, it is shown that, for the K ⁰ mesons, the contribution of nonstandard-physics effects to the mass splitting of the neutral kaons and an indirect CP violation are very small and are weakly dependent on the mass of the charged Higgs boson. Under certain conditions, the nonstandard contributions for the B ⁰- $ \bar B_d^0 $ and B ⁰- $ \bar B_s^0 $ systems may become somewhat more substantial, which constrains the MSSM parameter space.     

Inclusive cross sections in the central region and the supercritical pomeron

Using the double-Regge formalism and a supercritical pomeron with α_P(0)=1+Δ, we analyse the energy dependence of inclusive cross sections for negatively charged particles (c⁻) and K_s⁰ at CM rapidity y=0 in the CERN PS-Sp̄pS collider energy range. The values of Δ(c⁻)=0.170±0.008 and Δ(K_s⁰)=0.167±0.024 are found to be very close to each other and compatible with estimates of Δ derived from the total cross sections.     

Classical CP N−1 crystal

Two-dimensional Euclidean CP ^N?1 ffields are conformal-transformed into fields with periodic spatial (crystal-like) structures, both at zero temperature and at finite temperature. Specific solutions of the crystal-like CP ^N?1 model are discussed     

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 |.     

Fermion Mass and Mixing in a Simple Extension of the Standard Model Based on T7 Flavor Symmetry

We build a simple Standard Model extension based on T₇ flavor symmetry which accommodates lepton mass, mixing with non-zero θ₁₃, and CP violation phase. The lepton mixing matrix is obtained from three triplets and one singlet under T₇ symmetry, and the charged-lepton mass is derived through the spontaneous symmetry breaking by just one T₇ triplet (φ), while neutrinos get small masses from one SU(2) _L doublet and two SU(2)_L singlets in which one is in 1 and the two others are in 3 and 3* under T₇, respectively. There exist viable parameters of the model that predict the effective Majorana neutrino mass with values m_β ≃ 10⁻² eV and 4.95 × 10⁻² eV as well as a lightest neutrino mass m_light ≃ 4.97 × 10⁻³ eV and 1.61 × 10⁻³ eV for the normal and inverted neutrino mass hierarchies, respectively. The model also gives a remarkable prediction of Dirac CP violation δ_CP ≃ 303.3° in the normal hierarchy and δ_CP ≃ 56.69° in the inverted hierarchy which is still missing in the neutrino mixing matrix. The quark mixing angles of the model are closed to the experimental data, whereas the obtained values for the quark masses are consistent with with the experimental data at the tree level.