Pion-pion amplitude from the πN→ππN reaction

The possibilities of extracting parameters of ππ interaction from the experimental data on the πN→ππN reaction are analyzed in detail. The interval 300<P_lab<500 MeV/c is shown to be the smoothness domain of the πN→ππN amplitude. The expression for the background part of the amplitude is developed model-independently. The ππ scattering is described by four parameters to be extracted from experimental data (along with 11 background parameters).     

Symmetry breaking and the decays ψ′ → J/ψπ(η) and J/ψ → η(η′) γ

The theoretical mechanisms for the decays ψ′ → ψπ⁰ and ψ′ → ψη, which violate SU₂ and SU₃, respectively discussed. It is argued that symmetry breaking in the decay amplitudes may be as important as π⁰ −η −η′ mixing. The π⁰ −η mechanism ψ′ → ψν → ψπ⁰ leads to Γ(ψ′ → ψπ⁰) = (3.3±1.0) × 10⁻³ Γ(ψ′ → ψν), but this number may be enhanced by a factor as large as 12 by π⁰−η′ mixing and isospin violation in the decay amplitude. The related decays ψ → ηγ and ψ → η′γ are also discussed.     

The decay ω(782)→5π in chiral theory.

The arguments are put forward that the many pion decays ω→2π⁺2π⁻π⁰ and π⁺π⁻3π⁰ provide an ideal test site for testing the predictions of chiral models of the vector meson decays into many pions. Using the approach based on the Weinberg Lagrangian or, in a new language, the Lagrangian of hidden local symmetry added with the term induced by the anomalous Lagrangian of Wess and Zumino, the partial widths of these decays are evaluated, and their excitation curves in e⁺e⁻ annihilation are obtained. The discussed are the perspectives of the experimental study of the decays ω→5π in e⁺e⁻ annihilation and photoproduction.     

Experimental study of the time-dependent rate of K → πππ

The time-dependence of the decay rate of initially pure K⁰ into the final state (π⁺π⁻π⁰) has been studied in search for the decay k_S⁰→π⁺π⁻π⁰. No evidence is found in a sample of 384 observed events. The ratio of the CP -violating K_S⁰ amplitude and the K_L⁰ amplitude is η₊₋₀ = (0.13_−0.20^+0.17) + i(0.17_−0.26^+0.27); the ratio of the CP-conserving K_S⁰ amplitude and the K_L⁰ amplitude is < 0.4. The energy dependence of the K⁰→π⁺π⁻π⁰ matrix element is found to be a₊₋₀ = −0.31 ± 0.03.     

Study of impulse model in reaction Kd → pΛπ+ neutrals

In an analysis of 1114 events of the type K⁻d → pΛ⁰π⁻+ neutrals with ‘spectator’ proton momentum in excess of 0.11 GeV/c we have found that the number of protons having a momentum in the range 0.25–1.2 GeV/c exceeds that predicted on the basis of the impulse model using the Hulthén distribution by 3 : 1. Final-state interactions in which the proton does not form resonances with the other final-state particles are mainly held responsible for this effect.     

Search for narrow NNπ resonances in exclusive pp→ppππ measurements

Narrow structures in the range of a few MeV have been searched for in ppπ⁺ and ppπ⁻ invariant mass spectra (M_ppπ⁺ and M_ppπ⁻) obtained from exclusive measurements of the pp→ppπ⁺π⁻ reaction at T_p=725,750 and 775 MeV using the PROMICE/WASA detector at CELSIUS. The selected reaction is particularly well suited for the search for dibaryon resonances decoupled from NN and/or NΔ. In the mass range 2020 MeV/c²<m_dibaryon<2085 MeV/c² no narrow structures could be identified on the 3σ level of statistical significance neither in M_ppπ⁻ nor in M_ppπ⁺ giving an upper limit (95% C.L.) for dibaryon production in this reaction of σ<20 nb.     

Radiative decay of ρ and φ mesons in a chiral unitary approach

We study the ρ⁰ and φ decays into π⁺π⁻γ, π⁰π⁰γ and φ into π⁰ηγ using a chiral unitary approach to deal with the final state interaction of the MM system. The final state interaction modifies only moderately the large momenta tail of the photon spectrum of the ρ⁰→π⁺π⁻γ decay. In the case of φ decay the contribution to π⁺π⁻γ and π⁰π⁰γ decay proceeds via kaonic loops and gives a distribution of ππ invariant masses in which the f₀(980) resonance shows up with a very distinct peak. The spectrum found for φ→π⁰π⁰γ decay agrees with the recent experimental results obtained at Novosibirsk. The branching ratio for φ→π⁰ηγ, dominated by the a₀(980), is also in agreement with recent Novosibirsk results.     

CP test in J/ψ→γφφ decay

We propose to test CP symmetry in the decay J/ψ→γφφ, for which large data sample exists at BESII, and a data sample of 10¹⁰ J/ψ's will be collected with BESIII and CLEO-C program. We suggest some CP asymmetries in this decay mode for CP test. Assuming that CP violation is introduced by the electric- and chromo-dipole moment of charm quark, these CP asymmetries can be predicted by using valence quark models. Our work shows a possible way to get information about the electric- and chromo-dipole moment of charm quark, which is little known. Our results show that with the current data sample of J/ψ, electric- and chromo-dipole moment can be probed at order of 10⁻¹³ e cm. In the near future with a 10¹⁰ data sample, these moments can be probed at order of 10⁻¹⁴ e cm.     

η,η′→ππγ with coupled channels

The decays η,η′→π⁺π⁻γ are investigated within an approach that combines one-loop chiral perturbation theory with a coupled channel Bethe–Salpeter equation which satisfies unitarity constraints and generates vector mesons dynamically from composite states of two pseudoscalar mesons. It is furthermore shown that the inclusion of the η′ as a dynamical degree of freedom does not renormalize the Wess–Zumino–Witten term.     

“Missing moment” and perturbative methods for polynomial iterated function systems

An iterated function system (IFS) over a compact metric space X is defined by a set of contractive maps w_i: X → X, i = 1,…,N, with associated nonzero probabilities p_i > 0, p_i = 1. The “parallel” action of the maps defines a unique compact invariant attractor set A X which supports an invariant measure μ and which is balanced with respect to the p_i. For linear , the invariance of μ yields a relation between the moments g_n = ∫ χⁿ dμ which permits their recursive computation from the initial value g₀ = 1. For nonlinear w_i, however, the moment relations are incomplete and do not permit a recursive computation. This paper describes two methods of obtaining accurate estimates of the moments when the IFS maps w_i are polynomials: (i) application of the necessary Hausdorff conditions on the g_i to obtain convergent upper and lower bounds and (ii) a perturbation expansion approach. The methods are applied to some model problems.     

Chiral-loop and vector-meson contributions to η → ππγγ decays

The process η → π⁰π⁰γγ is discussed in Chiral Perturbation Theory (ChPT). Special attention is deveted to one-loop corrections, η-η′ mixing effects and vector-meson dominance of ChPT counter-terms. The less interesting η → π⁺π⁻γγ transition is briefly discussed too.     

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f₀ and a₀ resonances. The ππ → ππ, phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π⁰η and mass distributions in the T = 1 channel. Furthermore, the total and partial strong decay widths of the f₀ and a₀ resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below GeV.     

Rigorous pion-pion scattering lengths from threshold πN → ππN data

A new evaluation of the universal ππ scattering length relation is used to extract the ππ s-wave scattering lengths from threshold pion production data. Previous work has shown that the chiral perturbation series relating threshold pion production to ππ scattering lengths appears to converge well only for the isospin-2 case, giving a₂ = −0.031 ± 0.007m_π⁻¹. A model-independent and data-insensitive universal curve then implies a₀ = 0.235 ± 0.03m_π⁻¹ for the isospin-0 scattering length.     

Model amplitude analysis of πp→ππn

We present an amplitude analysis of the process π⁻p→π⁺π⁻n at 15 GeV/c assuming spin and phase coherence of the production amplitude. The bearing of the results on aspects of dipion production phenomenology is discussed.     

Zeeman-tuned slowing of rubidium using σ and σ polarized light

Experimental results are presented for Zeeman-tuned slowing of an atomic rubidium beam in both the σ⁺ and σ⁻ polarized light configurations. A model of Zeeman slowing is applied to ideal magnetic fields, realistic fields, and the actual measured fields in order to clarify the similarities and differences between σ⁺ and σ⁻ slowing. The dependence of the final slowed velocity on the laser frequency detuning is studied and good agreement is found between the experimental results and both computer simulations and approximate analytic expressions.     

χ and J/ψ production in double-diffractive proton-proton collisions

It was pointed out earlier, that double-diffractive J/ψ production may serve as an important instrument to probe the odderon. However, double-diffractive production of χ′s due to pomeron-pomeron fusion, subsequently decaying into J/ψ + γ is a possibly troublesome background. Therefore, we calculate the corresponding differential cross sections for χ production and compare the obtained J/ψ yield to the rate of J/ψ directly produced by pomeron-pomeron fusion. We show that χ production is strongly suppressed. Hence, we conclude that double-diffractive exclusive J/ψ production could be the ideal process to search for the odderon.     

η → 3π to one loop

We calculate the amplitude of the decays η → π⁰π⁺π⁻ and η → π⁰π⁰π⁰ to first non-leading order in the low-energy expansion. It is shown that the infrared singularities of chiral perturbation theory strongly enhance the perturbation generated by the quark mass term. The corrections of order m_s increase the current algebra prediction for the rate by more than a factor of two and remove the well-known discrepancy between the low-energy theorems of current algebra and experiment.     

Note on the angular analysis of the decay J/ψ→f(→ππ)+γ

We derive the general (4-parameter) angular decay distribution for the cascade decay J/ψ→f(→ππ)+γ and determine its angular coefficients from the absorptive and dispersive contributions of the lowest order QCD diagram.