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.     

Pion pair production in γ-γ collisions at low energy and the born cross section

It is shown that (i) there is a severe constraint on σ(γγ→π⁺π⁻/σ_Born imposed by phenomenological theory and (ii) the low-mass π⁺π⁻ enhancement observed in the reaction γγ→π⁺π⁻ comes from interference between the Born term and the correction term.     

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.     

Search for the radiative decay η→π0γγ in the SND experiment at VEPP-2M

The η→π⁰γγ decay was investigated by the SND detector at VEPP-2M e⁺e⁻ collider in the reaction e⁺e⁻→φ→ηγ. Here we present the results and some details of this study. We report an upper limit (90% c.l.) Br(η→π⁰γγ)<8.4×10⁻⁴ as our final result. Our upper limit does not contradict the earlier measurement by GAMS spectrometer. To facilitate future studies a rather detailed review of the problem is also given.     

A simple chiral Lagrangian approach toK→πππ decays andε′+0−

We analyse theK→πππ decays in the framework of a chiral Lagrangian supplemented by the 1/N expansion (N being the number of colors). The measuredK _L →π⁺π⁰π⁺ Dalitz plot is very well reproduced. Contrary to a recent claim, the Li-Wolfenstein relation between the CP impurities associated with theK→πππ(ε′_+0?) and theK→ππ(ε′) decay amplitudes is rather stable against isospin-breaking effects and higher-order (in the chiral expansion) weak operator corrections. We also predict a branching ratio of 2.1 10^?7 for the CP-conservingK _S →π⁺π⁰π⁺ decay.     

Amplitude analysis ofγγ→ππ from threshold to 1.4 GeV

A new amplitude analysis of results onγγ→π ⁺ π ^? from the Mark II andγγ→π ⁰ π ⁰ from the Crystal Ball experiments is reported. Key constraints from the low energy theorem and from analyticity and unitarity that relateγγ→ππ to other meson scattering reactions are built into the trial forms. Despite these restrictions, the limited angular converge of the experiments means that solutions with quite different proportions ofS wave andD waves of both helicities 0 and 2 are admitted above 1 GeV. This leads to a much wider range of possibilities for the couplings of the braod resonancesf _o(?) andf ₂(1270) than is commonly supposed. The better fits have \(\Gamma _{f_0 } \) in excess of 4 keV and a ratio of \(\Gamma _{f_0 } /\Gamma _{f_2 } \) greater than 2.     

First observation of the KS→π0γγ decay

Using the NA48 detector at the CERN SPS, 31 K_S→π⁰γγ candidates with an estimated background of 13.7±3.2 events have been observed. This first observation leads to a branching ratio of BR(K_S→π⁰γγ)_z>0.2=(4.9±1.6_stat±0.9_syst)×10⁻⁸ in agreement with Chiral Perturbation Theory predictions.     

Lepton and hadron pair production in two-photon reactions

We have measured the production of charged particle pairs in e⁺e^? initiated two-photon reactions. The observed rates and invariant mass spectra agree with expectations from QED if a resonant π⁺π^? production at the f⁰ mass is added. Assuming dominance of the helicity 2 production we obtain the width Γ(f⁰→γγ) = 2.3 ± 0.5 keV.     

Analysis of the low-energy theorem forγp →pπ 0

The derivation of the ‘classical’ low-energy theorem (LET) forγp→pπ ⁰ is re-examined and compared to chiral perturbation theory. Both results are correct and are not contradictory; they differ because different expansions of the same quantity are involved. Possible modifications of the extended partially conserved axial-vector current relation, one of the starting points in the derivation of the LET, are discussed. An alternate, more transparent form of the LET is presented.     

Saturation of counterterms by resonances inK →πe + e − decays

The decaysK ⁺→π ⁺ e ⁺ e ^?,K _S→π ⁰ e ⁺ e ^? andK _L→π ⁰ e ⁺ e ^? are reinvestigated within the framework of chiral perturbation theory. The counterterms induced by strong, electromagnetic and weak interactions are determined assuming the resonance exchange. The weak deformation model, the factorization model and the largeN _c limit are used to create a weak Lagrangian. It is found that the results of the first two approaches depend on theH ₁ coupling, defined in the effective chiral Lagrangian of theO(p ⁴) order. The set of parameters used in the extended Nambu and Jona-Lasinio model can accommodeteK ⁺→π ⁺ e ⁺ e ^? decay rate within the factorization approach. The CP violatingK _L→π ⁰ e ⁺ e ^? decay rate is discussed.     

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.     

K→ππγ and chiral perturbation theory

Weak radiative decaysK _L,S →π⁺π^?γ andK ⁺→π⁺π⁰γ are reexamined. The electromagnetic form factors and long-distance contributions to the direct photon emission are evaluated using the higher order effective chiral Lagrangian. We find that (1) the naive soft-pion theorem cannot be applied to the magnetic-type transition amplitude, (2) the shortdistance contribution toK _L →π⁺π^?γ is comparable to or even bigger than the long-distance one, (3) the ΔI=1/2 enhancement persists in the decayK ⁺→π⁺π⁰γ, (4) to the order of 1/Λ _χ ² (Λ _χ being the chiral-symmetry breaking scale) the direct photon emission amplitude does not receive a contribution from penguin operators, and (5) the 1/N _c expansion improves the discrepancy between theory and experiment.     

First observation of γγ → ωω

The reaction γγ → 2π⁺ 2π⁻ 2π⁰ has been studied using the ARGUS detector at the e⁺e⁻ storage ring DORIS II at DESY. Production of ω mesons is observed and, in particular, the reaction γγ → ωω is seen for the first time. The cross section for γγ → ωω has an enhancement at ∼ 1.9 GeV/c² of about 10 nb. The cross sections for γγ → 2π⁺ 2π⁻ 2π⁰ and γγ → ωπ⁺ π⁻ π⁰ are also given.     

π−p → γγn at threshold

We discuss perturbation theory estimates (in a pseudoscalar-coupled pion-nucleon theory) for near threshold π^?p → γγn, both from atomic L = 0 and L = 1 orbits. The comparison of various contributing amplitudes (including the Δ resonance contributions) is discussed so as to ascertain which ones dominate, at least in c.m. transverse gauge. A detailed calculation (at threshold) gives a predicted total branching ratio of 2γ to 1γ rates as 1.31 × 10^?4, and also exhibits the γ-γ angular distribution. Significant differences from previous literature are elucidated.     

Situation around thea 0(980) meson after the experimentγγ→a 0→π 0 η

Based on the four-quark interpretation of the scalara ₀(980) meson a model for theγγ→a ₀→π ⁰ η reaction amplitude is constructed which describes well the experimental data. The ideas about the nature of thea ₀(980) meson which appeared after the Crystal Ball measurement of the two-photon production of thea ₀ meson are discussed briefly.     

Where are the missing V0V0′ in γγ reactions?

The measured cross sections ofγγ→V⁰V^0′ are inconsistent with the measurements of the γγ total hadronic cross section above 2 GeV. Higher cross sections for γγ→ϱ⁰ϱ⁰ or additional V⁰V^0′ final states are needed to solve this inconsistency.     

Pion pair production in photon-photon collisions at spear

We report a measurement of the cross section for the process γγ→π⁺π^? at invariant masses 500 MeV/c² < m_ππ<2000 MeV/c². A value for the radiative width of the f(1270) tensor meson Γ_f→γγ = 3.6 ± 0.3 ± 0.5 KeV (helicity λ = 2) has been obtained from a fit to the observed ππ mass spectrum.     

Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from symmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay π⁰ → γγ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay a → γγ in a supersymmetric composite model might be suppressed with the same mechanism that works for π⁰ → γγ in SQCD.