How to testCP,T, andCPT invariance in the three photon decay of polarized3 S 1 positronium

We investigate whether and how the three photon decay of polarizedj=1 positronium (Ps), in particular³ S ₁ Ps, can be used for tests ofCP, T, andCPT invariance. A general analysis is made in terms of thePs decay matrix. We consider some angular correlations sensitive to possibleCP violation and calculate their expectation values assuming thatCP violation occurs in thePs mass matrix only. Furthermore we discuss some models ofCP violation in the lepton sector and their implications forCP violation inPs mixing and decay. Finally we calculate the contributions due to photon-photon final state interactions to some correlations which are naively, i.e. in the Coulomb approximation,T-andCPT-odd.     

T violation in neutralino decay

We show that in the supersymmetric standard electroweak theory the neutralino decay causesCP violating phenomena. It will be possible to observeT odd asymmetry in the angular distribution if the trilepton decay of theW boson is found. We also discuss the constraint on the magnitude ofCP violation by the electric dipole moment of the neutron.     

Electromagnetic structure of the proton within the CP-violation hypothesis

The so-called non-Rosenbluth behavior of the proton electromagnetic form factors can be explained within the hypothesis of CP violation in electromagnetic processes involving composite systems of strongly interacting particles. It is shown that this hypothesis leads to the appearance of an additional, anapole, form factor of the proton. The proton electromagnetic form factors, including the anapole form factor, are estimated on the basis of experimental data on elastic electron-proton scattering.     

CP symmetry and its violation in fundamental interactions

The concept of discrete symmetries in classical and quantum physics is reviewed. An account is given ofCP violation observed in theK-meson system and of other experiments whereCP symmetry has been tested. The present theoretical ideas onCP violation within the standard model, and problems needing extension of the model are described. Finally, ideas and experimental approaches toCP violation beyond the standard model are reviewed in brief.     

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.     

The strong CP problem revisited

The strong CP-violating θ parameter, the problem of strong CP violation and their status are reviewed. Among all possibilities, two natural solutions to the strong CP puzzle are thoroughly discussed and emphasized: the axion-type mechanism for hard CP violation and the non-Peccei-Quinn scheme for spontaneous CP nonconservation. Basic properties of the axion are derived from the modified Peccei-Quinn symmetry. Astrophysical and cosmological constraints are described for two different types of invisible axions. In nonaxion solutions, CP is spontaneously broken at the grand-unification scale and the CP phase is transmitted down to the low energy sector by quantum effects or by fermion mixing effects. As a by-product, the cosmological baryon asymmetry, which is caused by the same source of CP violation ultimately responsible for the kaon ε parameter, is generated adequately at the one-loop level.     

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.     

Structure of the high temperature gauge ground state and electroweak production of the baryon asymmetry

We investigate the connection of the baryon asymmetry of the universe (BAU) with the Chern-Simons structure of the ground state of gauge theories at high temperatures. We formulate in an explicitly gauge-invariant way the notion of the effective potential for density of the Chern-Simons charge and estimate CP noninvariant corrections to it coming from the nonequilibrium stages of universe expansion. We find that for the case of trivial structure of the ground state the BAU production is only possible if the low-energy CP violation in anomalous reactions δ_ms is larger than 10⁻⁴. We discuss the fate of the CP domain structure of the universe which appears when there is discrete degeneracy of the ground state. The magnitude of BAU could be large only with sufficiently strong high temperature CP violation. So the BAU generation in the framework of standard electroweak theory (where δ_ms∼10⁻¹⁸) takes place only when there is infinite degeneracy. We estimate the Higgs and top masses in the Coleman-Weinberg type of theory.     

Unitarity polygons and CP violation areas and phases in the standard electroweak model

A geometrical interpretation of CP violation in terms of areas of unitarity triangles is presented, in the standard electroweak model with three families of quarks. The extension of the results to the case of four families is investigated. A special case is worked out in detail where it is shown how one determines the CP violating invariant phases and the areas of the CP violation triangles as functions of the moduli of the elements of the quark mixing matrix. For the most general four-family case, which is found to be rather involved, the necessary formulae, for determining the invariant phases and the CP violation areas, are given.     

CP-violation effect in neutralino pair production in e+ −e− annihilation and the electric dipole moment of the electron

It is shown that in the supersymmetric extensions of the standard electroweak theory, the threshold behaviour of the cross section of production of two different neutralinos in e⁺ −e⁻ annihilation may be sensitive to the violation of CP invariance by the neutral gaugino-higgsino mass term. The corresponding CP violation effect may be substantial quite far from the threshold. A relation (although rather indirect) between the form of the behaviour of this section in the threshold region and the value of the electric dipole moment of the electron may exist.     

On the strong-CP problem in models with several Higgs multiplets and supersymmetry

We point out that the strong-CP problem becomes even more pressing in the context of weak models where CP violation originates in the Higgs sector. θ renormalization is numerically too large at the one-loop level and even divergent at the two-loop level. When supersymmetry (SUSY) is introduced, many more possible sources for CP violation open up. θ renormalization could stay finite in perturbation theory, however, we find that the one-loop result turns out to be too large by orders of magnitude unless SUSY fields like gauginos and higgsinos are highly degenerate in mass or SUSY breaking proceeds in a very special way, or a Peccei-Quinn symmetry holds leading to superlight axions.     

Allowance for <Emphasis Type="Italic">CP</Emphasis> violation in the exponential parametrization of neutrino mixing

An exponential form of the Pontecorvo–Maki–Nakagawa–Sakatamixingmatrix for neutrinos is discussed. This form makes it possible to separate the contributions of purely rotational components of the mixing matrix and elements that are responsible for CP violation. The logarithm of the mixing matrix and exact values for each parameter of the exponential neutrino mixing matrix are found on the basis of the most recent experimental data on neutrino mixing. The parameters of the real rotational part in the exponential representation of the mixing matrix and the parameters of its imaginary part, which is responsible for CP violation, are evaluated. The hypothesis of complementarity of quark and neutrino mixing is confirmed. Factorization in the form of the product of rotations about the real and imaginary axes is demonstrated.     

Violation of CP invariance in the two-doublet higgs sector of the MSSM

Problems of substantiation and investigation of CP violation in models with the extended Higgs sector are discussed. The general form of the effective two-doublet Higgs potential with complex parameters whose CP invariance is violated both explicitly and spontaneously is considered. For the special case of the two-doublet Higgs sector of the minimum supersymmetric model in which the CP invariance of the effective potential is violated by the interaction of Higgs fields with third generation scalar quarks, the physical states of Higgs bosons, their masses and interaction constants are obtained. The basic phenomenological scenarios and predictions for investigation of the properties of the Higgs sector are considered.     

Can the quark mass matrix be real?

We study the possibility of solving the strong CP problem in a theory where CP is broken spontaneously and the quark mass matrix, M_ij, not just its determinant, remains real to one part in 10⁸. We find that it is difficult to build natural models consistent with the known CP violation phenomenology. We find that such models require new fermions and possess a hierarchy problem. We present an SO(10) example which succeeds at the one-loop level, however, two-loop effects will introduce phases into M_ij.     

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.     

Spontaneous breakdown of CP symmetry,cabbibo angle in nuclear and hypernuclear physics

Following a suggestion of Salam and Strathdee that CP violation disappears and the Cabbibo angle vanishes at high magnetic fields we infer that no CP (or T) violation should be observed in nuclear beta decays and that stable hypernuclei are in principle possible.     

Can CP violation be observed in heavy-ion collisions?

We demonstrate that, at least at present, there is no convincing way to detect CP violation in heavy-ion collisions.     

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.     

CP violation and the EPR experiment

We dispute a recent claim that CP violation permits faster-than-light signals in EPR-style experiments.     

Spontaneous CP violation in left-right symmetric gauge theories

Motivated by arguments in favour of spontaneous CP violation, we investigate the general conditions imposed by P and CP invariance on the Yukawa couplings in SU(2)_L × SU(2)_R × U(1) gauge theories. A complete discussion of these constraints is presented for two minimal Higgs sectors. In addition to the standard case of manifest CP invariance, we find two phenomenologically interesting models where the P and CP transformations are non-aligned in flavour and Higgs spaces. To a certain extent, P and CP invariance may be responsible for the existence of horizontal symmetries. An intimate connection between CP violation and the general flavour problem emerges.