Π0 Decay Research Articles

A Khuri-Treiman model of η→3π and K→3π decays

A Khuri-Treiman model of η→3π and K→3π decays

Spin-zero pole dominance in the weak and electromagnetic interactions of the K-meson

The assumption of π, η and σ dominance of the weak and electromagnetic decays of the K-meson is examined using the hard-meson current algebra amplitudes for the strong-interaction factors. The K → 3π decay spectrum, the KL0 → 2γ decay and the KL0-KS0 mass difference are calculated and compared with experiment.

Secondary electrons and photons in the upper atmosphere

We present a theoretical and experimental study of the production and propagation of atmospheric secondary negatrons, positrons, and photons moving in the vertical direction. The one-dimensional transport equations have been solved numerically to obtain energy spectra and intensity versus depth for energies as low as 4 Mev and for atmospheric depths up to 400 g/cm2. The calculations are performed for the solar modulation level of 1968 and geomagnetic cutoff values of zero and 4.5 Gv. We also present experimental data on negatrons and positrons in the energy range from 6.5 to 200 Mev obtained from balloon observations near Ft. Churchill, Canada, in 1968. The comparisons with measurements confirm the calculated energy spectra and intensity versus depth. The spectral shapes of secondary negatrons and positrons are found to be very dependent upon the atmospheric depth. In the high atmosphere, the photon spectrum below ∼70 Mev is dominated by bremsstrahlung from primary and reentrant albedo electrons rather than by π0 decays. The derived intensity versus depth deviates distinctly from the commonly assumed linear growth of the secondary flux with increasing depth. Our results on the functional depth dependence are useful for determining the contribution from atmospheric secondaries to measurements of the electron (and photon) flux at balloon altitudes.

On the η → 3π decay puzzle

The various problems associated with understanding the η → 3π decay are reviewed. We discuss in detail pole models and the conventional current-current model for the electromagnetic Hamiltonian and show that they fail to explain the decay rate, although the slope in the Dalitz plot comes out in agreement with experiment in almost all models. We study a scalar density model for the electromagnetic Hamiltonian and show that the ensuing σ-terms induce a certain degree of freedom; we exhibit the effect of the σ-terms on the decay rate. We give a reason behind the universality of the slope in the Dalitz plot.

Charge exchange of 70 MeV π− on C, Al, Cu and Pb

The integrated cross sections for the total charge exchange of 70 MeV π− on natural carbon, aluminium, copper and lead have been measured by detecting the π0 decay γ-rays. For lead, the cross section per proton was found to be about 12 times smaller than for a free proton. The dependence of the cross section per proton on the mass number A is compared with theoretical predictions and a value for the cross section of the elementary pion-nucleon interaction inside the nucleus is derived.

Application of a vector-meson dominance model to K3π and η3α decaysdecays

p-wave contributions to K→3π and η→3π decays are studied by means of a vector-meson dominance model. Thep-wave decay rate for Ks→3π is estimated. Dalitz-plot fits using the energy dependence of matrix elements from the above model, andp-wave decay rate estimates using a generalized spurion concept yield reasonably consistent results for thep-wave contribution to these decays.

Pion amplitudes in a nonchiral world

The popular strong PCAC (i.e., pion pole dominance of all Green's functions involving the divergence D of the axial vector current) and good chiral SU(2) × SU(2) symmetry framework has led to many successful predictions. It also, however, leads to some difficulties since, for example, it predicts the approximate vanishing of the K l 3 form factor ratio ξ = f − f + , of the π 0 → γγ decay amplitude F π (except in models with anamolous PCAC), and of the η → 3π decay amplitude A η . We therefore propose an alternate framework based on weak PCAC (i.e., pion pole dominance of physical matrix elements of D) and good SU(3). We show that a precise formulation of these older ideas can reproduce all of the good results of the chiral scheme and none of the bad ones. We assume the usual Gell-Mann current algebra and the (3, 3) + ( 3, 3) symmetry breaking Hamiltonian H′ = α 0 S 0 + α 8 S 8. We make, and motivate with reference to a composite picture of the hadrons, the following four assumptions: (1) approximate SU(3), (2) weak PCAC, (3) minimal subtractions, (4) Regge theory. In this framework, the dominance of a given Green's function T by the pion pole depends on the nature of the despersion relations it satisfies in variables for which the absorptive part is expressible in terms of physical matrix elements of D. An unsubtracted dispersion relation leads to pole dominance but a subtracted one introduces a constant (or worse) difference between T and the corresponding on-shell pion amplitude. From assumptions (2)–(4), we derive the following successful results of the chiral framework: the Adler consistency condition, the Adler-Weisberger relation, the Weinberg-Tomozawa pion-target scattering lengths, the Weinberg π-π scattering lengths, the Fubini one-pion production relations, the Weinberg-Callan-Treiman K l 4 form factors, and the K 3 π – K 2 π relations. The extra parameters (subtraction constants) encountered in applying weak PCAC, as determined by Regge theory, turn out not to contribute to these relations. Adding assumption (1), we obtain the further results: (α 0/ 2 α ∞)≃−0.17 , ξ ≅ −1, and an excellent simultaneous fit to the S-wave and P-wave hyperon decays. Here our extra parameters turn out to be present precisely in the places where they are required to insure the consistency of our approach. (For example, the σ terms in our scheme need not be small). None of these results are common to the chiral framework. We show further that F π and A η need not approximately vanish in our framework. We therefore conclude that our theory seems to provide a better description of the present empirical situation than does the chiral theory.

Study of the ø meson by e +e − annihilation into charged K mesons and tests of vector dominance models

We have measured the e +e − → ø reaction by its K +K − decay mode. Using our previous results on K O K O and the 3π decay mode of the ø mesons, we compute Γ ø → e +e − and then compare the whole Orsay results to theoretical predictions.

A1 → 3π decay

A1 → 3π decay

Estimates of the ?-ray flux from Sagittarius A

Analysis of the anisotropy of the γ-ray background observed by Clarket al. (1968) has lead to the suggestion that part of the anisotropy be due to a source at the Galactic Centre. The complex structure of radio and infrared emission of the region of Sgr A is considered. The γ-ray flux arising from Compton scattering and π0 decay is calculated. For a value of the magnetic field H≈10−4 Gauss, corresponding to equipartition, the γ-ray flux above 100 MeV at Earth from the Sgr A source is expected to lie between 10−6 and 10−5 gamma/cm2 sec. Such a source should be detectable in the near future.

Final-state interaction and current algebra in K3 π and η3 π decays

In a simple model of final-state interaction, we discuss the validity of the linear extrapolation in K → 3 π and η → 3π decays. Final-state interaction modifies the extrapolation between the physical points where the soft-pion approximation is valid by introducing quadratic and higher terms in the amplitude. Computation of the effect in the frame of the Khuri-Treiman equation shows that they are dominated by the ππ scattering in each of the two pions subchannels, so that the corrections come out mainly from two-body scattering effects. Comparison with current algebra, Veneziano model and experiment for the rates, slopes, quadratic terms in K → 3 π and η → 3π decays is given.

A1→3π decay

The coupling of the A1 to a three-pion system is studied through the analysis of some simple two-body amplitudes where the A1 appears as an either external or internal particle. The A1→3π decay amplitudes to a pion and aP-wave orS-wave ππ system are related in the Veneziano model. The relevant ambiguities in the construction of dual amplitudes involving unnatural-parity trajectories are discussed and some results on the strengths of the decays involving the two ππ systems are presented. Further experimental information of the fourpion decay of the f0 would help to determine the strength of the A1 decay involving the spinless dipion system.

K→3π spectrum and pole dominance

We show that a combination of current algebra and the pole model for K→3π decay is incompatible with experiment unless off-mass-shell corrections are unexpectedly large. Without such corrections the pole terms give much too large an amplitude and do not give all the zeros required by current algebra.

Pion-pion scattering lengths from Veneziano formula and η→3π,K→3π decays

Theη→ 3π decay amplitude is factorized into (a) the transition matrix element fromη toπ0 and (b) Lovelace's expression of the Veneziano type for the pion-pion scattering amplitude. (a) is related with the electromagnetic mass splitting betweenK+ andK0. The absolute value of (b) is then obtained by fitting theη decay width. The pion-pion scattering lengths from (b) are reasonable. Since the analogous treatment ofK→ 3π decay together with a soft-pion determination of theK→π transition matrix element yield very small scattering lengths we suggest that theK→2π transition matrix element depends strongly on the pion masses.

Algebra of Currents

This is a review paper on the most important results obtained from the Algebra of Currents introduced by Gell-Mann. It includes a detailed discussion on the derivation of sum rules (Adler-Weisberger, Cabibbo-Radicati, etc.), either with the p → ∞ method and with the covariant method. Theorems for the emission of zero energy pions are discussed, and applied to leptonic and non leptonic decays of K mesons, and to the 3π decay of the η meson. More recent developments of current algebra like the gauge fields current algebra, the Weinberg sum rules, and the applications of the Bjorken's method to weak and e.m. interactions are also discussed.

Incompatibility of the quark-field (U 6◯U 6) commutation relations with vector-meson dominance in π0 decay

Incompatibility of the quark-field (U 6◯U 6) commutation relations with vector-meson dominance in π0 decay

Like pion spectra and non-linear effects in K → 3π decays

The effects of a non-linear matrix element on the like pion spectra in K → 3π decays are investigated. An effective σ model, which gives a good fit to the unlike pion spectra in all three K → 3π decays, is being used. The spectra are expressed as functions of the like pion kinetic energies, and alternatively, as functions of the Dalitz variables. Significant non-linearity is expected in the kinetic energy spectrum of the like pion as well as in the x-variable distribution in τ′ decay. The x-distribution in τ′ and K2o → π+π−πo should be constant.

Phenomenological analysis of K⇒3π decay

Phenomenological analysis of K⇒3π decay

On a relation between the decays π0→2γ and π+→e++ν+γ

A connection between the decays π0→2γ and π+→e++ν+γ is established, using reduction formalism,G-parity and commutation relations between the electromagnetic field and hadronic currents.

Algebra currents and the deviation from the |ΔI| = 1/2 rule in K → 3π decay

Starting from the usual current-current weak Lagrangian and using current algebra, the deviations from the |ΔI| = 1/2 rule in K→ 3π decays are determined in terms of the K → 2π rates. The need for better data on K → 2π and K → 3π decays is stressed in order to arrive at a possible discrimination between a fundamental or a dynamic |ΔI| = 1/2 rule. As a by-product the PC conserving 3π decay of Ko1 is calculated in the linear approximation.