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 quarks and proton decay

In this paper we calculate the hadronic matrix elements of baryon decay operators using a chiral effective lagrangian with quarks, gluons and Goldstone boson fields. We study in detail the cases where the ΔB = 1 operators arise from supersymmetric SU(5) GUT as well as the minimal SU(5) GUT model. In each model the results depend on two parameters. In particular there is a range of values for the two parameters, where the dominant decay modes in the minimal SU(5) GUT are: p → ηe⁺ and n → π^? e⁺.     

New measurement of the η → π 0 γγ branching ratio and the slope parameter for η → 3π 0 decay with the crystal ball

We have measured the quadratic slope parameter α for η → 3π ⁰ decay. Our final result is α=?0.031(4). We have also obtained the branching ratio (BR) for the double radiative decay η → π ⁰ γγ. Our preliminary result is BR(η → π ⁰ γγ=3.2(9)×10^?4. These new measurements were performed using the recent (1998) high-statistics sample of 1.9 × 10⁷ η produced at the AGS at BNL in π ^? p → nη close to threshold. The η decay into neutrals was detected with the Crystal Ball multiphoton spectrometer. Both measurements provide important tests of chiral perturbation theory (χPTh). Our result for α is four times more precise than the present world data and disagrees with current χPTh calculations by about four standard deviations. Our branching ratio for η → π ⁰ γγ is about half the current value and is in agreement with the χPTh predictions.     

On Z → γγ decay and cancellation of axial anomaly in Z → γγ transition amplitude for massive fermions

Z → γγ decay amplitude is considered and proven to be zero due to properties of polarization vectors and Bose statistics. Triangular diagrams for a pseudoscalar → γγ and Z → γγ processes with massive fermions in the loop are explicitely calculated. In the Standard Model axial anomaly vanishes in the sum of these diagrams as Z boson is mixed with one of the Goldstone bosons.     

The direct decay K+ → π+π0γ and its relation to other weak radiative decays

A model for weak nonleptonic transitions, previously shown to explain K₂⁰ → γγ and other weak radiative K-meson decays, is applied here to K⁺ → π⁺π⁰γ. It reproduces correctly the recently determined dominance of the magnetic transitions and allow to make firm predictions for the related K⁺ → π⁺γγ and K₂⁰ → π⁺π^?γ transitions.     

Proton decay in supersymmetric models

We discuss proton decay in supersymmetric theories. We find that it is possible to obtain rates which are comparable with those of standard SU(5). In the presence of a discrete symmetry which occurs in an SU(5) supersymmetric unified model we obtain a definite prediction for the dominant decay mode, i.e. p → K^+?ν_μ and n → K^0?ν_μ.     

Meson properties in an extended non-local NJL model

We consider a non-local version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The non-locality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ^* → π⁰ and ω → π⁰γ^*. The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.     

A measurement of collinear and nearly collinear photon pairs produced by e+e− annihilation at the 3100 MeV resonance

We have measured collinear and nearly collinear photon pairs from e⁺e^? annihilation at total energies covering the resonance at 3100 MeV. The observed cross section is in good agreement with the e⁺e^? → γγ cross section expected from quantum electrodynamics. Upper limits for the decay modes (3100) → γγ, π^Oγ and other modes are derived.     

<Emphasis Type="Italic">η</Emphasis> Physics with the crystal ball detector

The experimental results obtained with the Crystal Ball detector for the physics of η-meson decays are reviewed. The η → 3π ⁰ Dalitz plot slope and the η → π ⁰ γγ decay width are measured with a high accuracy using 3 × 10⁷ η decays. Upper limits on the η → 3γ, η → 2π ⁰ γ, and η → 3π ⁰ γ C-forbidden decays are found. The sensitivity of these upper limits to C violation is estimated. An upper limit on the η → 4π ⁰ C P-forbidden decay is found for the first time and the sensitivity of this value to C P violation is estimated.     

New low-energy theorems for γ →3 π and γγ→3π

New low energy theorems are obtained by relaxing the requirement that the γγ →3 π amplitudes vanish in the neutral soft pion limit. In the framework of a particular model it is shown that the relation eF_3π = F_πf^?2 may have to be generalized to involve also the γγ → 2π amplitudes.     

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.     

Lepton number nonconservation in supersymmetric theories

We consider a class of supersymmetric models lepton number nonconservation due to mixing of scalar leptons. It is shown that a range of parameters exists such that the processes μ→eγ, μ→eγγ, μ→3e, μ⁺ e ^?→μ^? e ⁺ are strongly suppressed, whereas the decay \(\mu \to e\tilde \gamma \tilde \gamma \) can proceed with a rate \(BR(\mu \to e\tilde \gamma \tilde \gamma ) \lesssim 0.01\) . The signatures of such decay can be the production of right-handed electrons with the energy aroundm _μ/3 and modification of the energy spectrum of the electrons in that region as compared with the standard model prediction.     

Isospin symmetry violating effects and scattering length extraction from kaon decays

The isospin symmetry breaking effects in the charged kaons decays to two or three pions are considered. In semileptonic decay K ^± → π ⁺ π ^?e^± ν (called K _e4) these effects turn out to be crucial for correct extraction of ππ scattering lengths. Taking in account electromagnetic interaction between the pions in the final state and isospin symmetry breaking due to different masses of charged and neutral pions allows to adjust the values of scattering lengths obtained from experimental data on K _e4 decay and predictions of Chiral Perturbation Theory (ChPT). Final state interactions of pions in the decay K ^± → π ^± π ⁰ π ⁰ leading to the anomaly (cusp) in the π ⁰ π ⁰ invariant mass distribution in the vicinity of charged pions’ threshold are discussed and recent results of accounting of the electromagnetic interaction among charged pions leading to π ⁺ π ^? bound states (pioniumatom) just under the charged pions’ threshold are presented.     

Dynamics of f 0(980)-resonance production in the reaction γγ → π + π −

The results of the experiment performed by the Belle Collaboration and aimed at observing the f ₀(980) resonance in the reaction γγ → π ⁺ π ^? are analyzed. It is indicated that these results suggest the presence of mechanisms in this reaction that lead to a strong distortion of the f ₀(980)-resonance line shape in relation to the line shape expected for a solitary Breit-Wigner resonance. It is shown that the K ⁺ K ^?-loop mechanism of f ₀(980) coupling to the γγ system and the destructive interference between the background and f ₀(980)-resonance contributions in the region of the π ⁺ π ^? invariant mass below the K ⁺ K ^? threshold are the main factors responsible for the formation of a specific (stepwise) f ₀(980)-resonance line shape in the cross section for the reaction γγ → π ⁺ π ^?.     

Observation of ω → π0μ+μ− decay

The results of studying the mass spectrum of μ⁺μ^?γγ systems produced in π^?p collisions at 25 and 33 GeV/c presented. The wide-aperture magnetic spectrometer with a hodoscope γ-detector was used to identify muon pairs and photons. There is a clear peak in the mass spectrum which corresponds to the decay ω → π⁰μ⁺μ^? previously not observed. The branching ratio for the decay is estimated to be 9 × 10^?5 with a systematic error of 50%.     

Isospin violation in τ → 3πντ

Isospin violating signals in the τ^? → (3π)^?ν_τ decay mode are discussed. For the τ^? → π^?π^?π⁺ν_τ decay mode, isospin violation arises from the vector current contribution in the τ^? → ωπ^?ν_τ decay with the subsequent isospin violating ω decay into π⁺π^?. We demonstrate that such effects may be observed in presently available data through the measurement of the interference effects of these vector current contributions with the dominating axial vector current,i. e. through a measurement of the structure functionsW _F, WG, WH andW _I. In the case of the τ^? → π⁰π⁰π^?ν_τ decay mode, a vector current contribution is generated by ηπ⁰ mixing in the decay chain τ^? → η?^?ν_τ → π⁰π⁰π^?ν_τ. We find that this effect is rather small, the magnitude of the associated interference terms being too low for present statistics.     

Study of process e + e − → π+π−π0π0 at energies √s < 1 GeV with the spherical neutral detector

The cross section for the process e ⁺ e ^? → π⁺π^?π⁰π⁰ has been measured in an experiment with a spherical neutral detector, with the cross section at energies √s < 920 MeV having been measured for the first time. The model of vector dominance describes well the data obtained if the ρ, ρ′, and ρ″ resonances are taken into account. The probability of the decay ρ → π⁺π^?π⁰π⁰ is B(ρ → π⁺π^?π⁰π⁰) = (1.60 ± 0.74 ± 0.18) × 10^?5. The upper limit for the decay ω → π⁺π^?π⁰π⁰ has been improved by two orders of magnitude compared to previous measurements and is B(ω → π⁺π^?π⁰π⁰) < 2 × 10^?4 at a 90% confidence level.