On Weinberg's model of CP violation in gauge theories

The consequences of the Weinberg model of CP violation in gauge theories (ref. [1]) are discussed in detail. It is shown (using the valence quark hypothesis) that the contribution of the induced superweak interaction to the experimentally measured quantities η+? and η₀₀ are ≈m_K²/m_π² times larger than that of the direct milliweak decay K₂⁰→2π. The correction to the relation |η+?|/|η₀₀|=1 is also calculated in the model. We estimate the neutron dipole moment $\text{(D}{}_{\mathrm{<mtext>n</mtext>}}\text{??2.8·10}{}^{\mathrm{?25}}\text{e.cm.}\text{)}$ and note that the dipole moments of particles with strange quark constituents should be about three orders of magnitude larger $\text{(}\text{e.g.}\text{D}{}_{\mathrm{\Lambda }}\text{??1.15·10}{}^{\mathrm{?22}}\text{e·}\text{cm}$. The CP violating vertex d?s + gluon is also discussed.All physical quantities appear to depend crucially on the values of quark masses, so that CP violating effects in the models of the type considered may elucidate the nature of quark masses. We argue that the bare (or “mechanical”) values should be used in the calculations and this leads to a considerable difference in the estimates of various effects as compared to those of ref. [1].     

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.     

SU(2) ⊗ U(1) gauge theories of the generalized σ model for π0, η, η' → γγ decays

By embedding the chiral current-mixing gauge theories in the SU(2)_L ? SU(2)_R generalized σ model, it is shown that the correct sign and magnitude for π⁰ → γγ decay, as well as the SU(3) relation of π⁰, η, η' → γγ decays can be obtained within the framework of SU(2) ? U(1) gauge theories of weak and electromagnetic interactions.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

Static hyperon properties in a linearizedSU(3)-Chiral Bag model

We use a linearized Chiral Bag model to describe the strange octet and decuplet baryons. The approach is canonically extended to spontaneously broken chiral SU(3)_L × SU(3)_R, and the corresponding Goldstone Bosons are identified with the pseudoscalar meson octet. We include explicit symmetry breaking corrections both for baryons and mesons. The linearized quark-meson intraction is applied in a self-consistent calculation of the masses and, for Δ, Σ^* and Ξ^*, of the decay widths. Our special interest is in the influence of theK- andη-cloud (in addition to theπ) on hyperon static properties. We show results for radii, masses, decay widths and renormalization constants as obtained by a fit to the experimental hyperon spectra. The effects of theK- andη-mesons are found to be non-negligible, although supressed by symmetry breaking effects. The effective gluon coupling α is reduced in comparison to the SU(2)_L × SU(2)_R case. In addition, we discuss the dependence on the bag constantB. It turns out that the lightest hyperon states, Λ and Σ are well described and stable for B^1/4 < 130 MeV. The heavier strange baryons have stable solutions also for larger values ofB. The bag radii determined at the minimal energies are R₀?1.15 fm for the octet and R₀?1.25 fm for the decuplet baryons.     

Spontaneous CP violation in a Z4 horizontal symmetry model for flavor mixing

The implications of a Z₄ horizontal symmetry model of flavor mixing for CP violation are studied in the framework of minimal SU(2)_L × SU(2)_R × U(1)_{B – L} gauge theory. We show that CP violation in this model arises purely from right-handed currents. We also note that spontaneous breaking of CP symmetry requires a fine tuning of coupling parameters to the level of , which can be avoided by the inclusion of one additional singlet Higgs field, of the kind recently introduced for other purposes.     

Four families of composite quarks and leptons

Four families of composite quarks and leptons, two standard and two non-standard, are found in a unique solution SU(3)_HC × SU(6)_L × SU(6)_R of a restricted 't Hooft anomaly-matching program. Testable predictions emerge, such as prohibition of μ → eγ, zero charge asymmetry in e⁺e^? → τ⁺τ^? in contrast to e⁺e^? → μ⁺μ^?, and a rich new hadron spectrum masses around M_W. A minimal set of spectator fermions contains color-singlet objects with fractional quark-like charges.     

On W±, Z0, γ self-interactions: High energy behaviour and tree unitarity bounds

We analyze the high-energy behaviour of vector boson scattering amplitudes within the framework of a recently suggested lagrangian model based on global weak isospin symmetry broken by electromagnetism. Requiring vanishing of the most strongly (as s²) rising contribution to vector boson scattering amplitudes leads to vector boson self-interactions dependent on a single parameter, for which the anomalous W^± magnetic moment, κ, can be chosen. Tree unitarity is violated at about 2 TeV for arbitrary κ as in the SU(2)_L × U(1)_Y theory for m_H → ∞. The model is well suited for significant tests of the vector boson sector of the SU(2)_L × U(1)_Y electroweak theory in processes such as e⁺e⁻ → W⁺W⁻.     

Quark-lepton symmetry and B − L as the U(1) generator of the electroweak symmetry group

We seek an interpretation of the U(1) part of the electroweak symmetry group in terms of the quantum number B ? L. We show that the electroweak symmetry group, for which U(1) can be interpreted as a local B ? L symmetry, is the left-right symmetry group SU(2)_L × SU(2)_R × U(1)_L+R. The equating of U_L+R(1) to U_B?L(1) should lead to physical consequences which are not shared by standard gauge theory. B ? L may also help to explain the inversion of quark and lepton mass spectra.     

Where is the origin of CP violations?

If experimentally b → c is more suppressed than b → u, the Kobayashi-Maskawa mechanism of CP violation may not work. In the SU (2) × U(1) × S₃ model, which gives all elements of the KM matrix naturally by the quark masses, this is the case and CP violations originate mainly from the Yukawa sector.     

Polarization amplitudes fore + e − →W + W − ande + e − →ZZ

The main purpose of this work is to study the three weak boson vertex. We give explicit formulae for all polarization amplitudes of the processese ⁺ e ^? →W ⁺ W ^? ande ⁺ e ^? →ZZ, with arbitrary couplings between the various intermediate vector bosons. Using these expressions we discuss possible signatures ofC, P andT violation in the three vector boson coupling, as well as the effects of anomalous magnetic dipole and electric quadrupole moments ofW ^±. The amplitudes for the above processes in any SU(2) × U(1) and SU(2)_L × SU(2)_R × U(1) gauge theory are also given, while the special case of the Weinberg-Salam model is studied in detail.     

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.     

Grand unified model with a stable proton and no axion problem

We present a grand unified model of the strong, electromagnetic and weak interactions based on a local SU(8)_L×SU(8)_R gauge theory which possesses a global U(8)_L × U(8)_R invariance. We break the symmetry down to the standard SU(3)_C × SU(2)_L × U(1) model, with the proton remaining stable and the left-handed neutrinos obliged to remain massless. A novel feature of our model is the simultaneous absence of both strong CP violations and of axions.     

Relations between SU(2)- and SU(3)-LECs in chiral perturbation theory

Chiral perturbation theory in the two-flavour sector allows one to analyse Green functions in QCD in the limit where the strange quark mass is considered to be large in comparison to the external momenta and to the light quark masses m _u and m _d . In this framework, the low-energy constants of SU(2) _R × SU(2) _L depend on the value of the heavy quark masses. For the coupling constants which occur at order p ² and p ⁴ in the chiral expansion, we worked out in [1] the dependence on the strange quark mass at two-loop accuracy, and provided in [2] analogous relations for some of the couplings c _i which are relevant at order p ₆. This talk comments on the methods used, and illustrates implications of the results obtained.     

SU(6)W and πN→ϱN revisited

We point out that the intersection of the Berkeley-SLAC and Saclay signs of πN→?N resonant amplitudes are consistent with ?-broken SU(6)_W if both the 70, L^P = 1^?and 56, L^P = 2⁺ multiplets choose anti-SU(6)_W solutions. The symmetry scheme still fails in that the πN→πΔ relative signs require an SU(6)_W-like solution for the 56, L^P = 2⁺. This failure however now rests on a single incorrect sign prediction among all N? and Δπ amplitudes.     

The price of natural flavour conservation in neutral weak interactions

The natural conservation of flavours to O(G_F²) in neutral weak interactions severely constrains choices of gauge groups as well as their fermion representations. In the absence of exactly conserved quantum numbers other than charge, and of |ΔQ| ? 2 charged currents, essentially the only weak and electromagnetic gauge groups whose neutral interactions naturally conserve all flavours are SU(2)_L ? U(1) and SU(2)_L ? [U(1)]². The plausible extensions of these gauge groups to grand unified models including the strong interactions are based on SU(5) and SO(10) respectively. Making the SU(5) model completely natural, including in the Higgs sector, gives the prediction $\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{/m}{}_{\mathrm{<mtext>e</mtext>}}\text{? m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{\mu }}\text{? m}{}_{\mathrm{<mtext>b</mtext>}}\text{/m}{}_{\mathrm{\tau }}\text{? 2605}$ where τ is the probable new heavy lepton and b is the conjectured third flavour of charge $\text{?1}\text{3}\text{quark}$. The SO(10) model contains a potential SU(2)_L ? SU(2)_R ? U(1) weak and electromagnetic gauge group, and has a complicated Higgs structure which does not naturally conserve quark flavours.     

Radiative corrections to quark-lepton mass matrices in superstring-inspired models

We examine if quark-lepton mass matrices are modified by generation changing currents in superstring-inspired models. It is shown that sufficiently large corrections to the quark mass matrices can be derived in an SU(3)_C × SU(2)_L × SU(2)_R × U(1)_L × U(1)_R model with δ ⩾ 2 and an SU(3)_C × SU(2)_L × U(1)_L × U(1)_R model. Consistency with other experiments are investigated by means of renormalization group equations.     

Parity violating effects in dilepton production using polarized targets

Parity violating effects in PP → μ⁺μ^?X and $\text{P}\text{P}\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{X}$ with the polarized targets have been calculated in the parton picture. The weak neutral currents used are based on an SU(2)_L × SU(2)_R × U(1) model. The result for the Weinbergy-Salam model occurs as a special case.     

Natural suppression of strong P and T non-invariance

In gauge theories with spontaneously broken left-right symmetry, strong P and T non-invariant effects can also be made to vanish naturally in the tree approximation without introducing massless quarks or axions. In a four-flavor SU(2)_L × SU(2)_R × U(1)_L+R model with manifest left-right symmetry, we show that strong CP noninvariance is absent up to the one-loop level and weak CP-violation is of superweak type. Extension to the case of six quarks gives a left-right symmetric generalization of the Kobayashi-Maskawa model without axions.