Measurement of the slope of the π0-electromagnetic form factor

Using a magnetic spectrometer, we have studied 30 000 π⁰ → e⁺e^?γ events coming from K_π2⁺ decays in flight. We find a positive value for the slope of the neutral-pion electromagnetic form factor: a = +0.10 ± 0.03 (or a = +0.05 ± 0.03 without radiative corrections). This value is higher than the predictions of vector meson models.     

The ω(782)→5π decay

The partial widths of the decays ω→2π⁺2π^?π⁰ and π⁺π^?3π⁰ are evaluated and their excitation curves in e ⁺ e ^? annihilation are obtained.     

A study of hadronic decays of the ϒ′

We present a detailed study of the decays ?′ → π⁺π^?? and ?′ → π⁰π⁰?, where the ? decays subsequently to e⁺e^? or μ⁺μ^?. The results are obtained from a sample of 146 000 ?′ decays observed with the CUSB detector at the Cornell Electron Storage Ring. We derive branching fractions of (18.9 ± 2.6)% for ?′ → π′π^?? and (10.3 ± 2.3)% for ?′ → π⁰π⁰?, and determined partial widths for these decays. Invariant mass and angular distributions of both the π⁺π^? and π⁰π⁰ systems are presented. We also set a limit on the branching fraction for ?′ → η? of less than 0.2% at the 90% confidence level.     

The evaluation of the branching ratios of the decays φ(1020)→2π<Superscript>+</Superscript>2π<Superscript>−</Superscript>π<Superscript>0</Superscript>, π<Superscript>+</Superscript>π<Superscript>−</Superscript>3π<Superscript>0</Superscript>

Combining the Okubo-Zweig-Iizuka rule in the decay φ→ρπ→π⁺π^?π⁰ with the ρ→4π decay amplitudes, we calculate the φ→2π⁺2π^?π⁰ and φ→π⁺π^?3π⁰ ones. The partial widths of the above φ decays are evaluated, and the excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the parameters characterizing the anomalous terms of the HLS Lagrangian. The evaluated branching ratios B_φ→π⁺_π^?_3π⁰ ≈ 2 × 10^?7 and B_φ→2π⁺_2π^?_π⁰ ≈ 7 × 10^?7 are such that, with the luminosity L=500 pb^?1 attained at DAΦNE φ factory, one may already possess about 1685 events of the decays φ→5π.     

Observation of the π0 → e+e− decay

We have observed for the first time the very rare π⁰ → e⁺e^? decay. The tagged π⁰'s come from K⁺ → π⁺π⁰ decays in flight. We find the branching ratio to be (2.23_?1.1^+2.4) × 10^?7 (90% C.L.). This value is well above the QED unitary limit and comes in rough agreement with a second-order electromagnetic process mediated by vector mesons.     

Pionic contribution to the muon magnetic moment

A procedure is developed to derive an optimal lower bounds for the pionic contribution to the muon magnetic moment from analyticity of the pion form factor F(t), its normalization F(0)=1 and from experimental information from both the processes e^?p → e^?π⁺n and e⁺e^? → π⁺π^?. It represents essentially the solution of a certain kind of optimization problem in Hilbert space. Numerical results are presented and compared to the recent data for the muon magnetic moment; we find a_μ(π⁺π^?) ? 42 × 10^?9.     

Testing chiral models of vector mesons in multipion decays of ρ(770) and ω(782)

Predictions of the models based on effective chiral Lagrangians of vector mesons ρ(770) and ω(782) are considered for such measurable quantities as the partial widths of various ρ → 4π and ω → 5π decays and their corresponding excitation curves. Analogous curves for the channel ρ? → (4π)? are obtained for τ lepton decays. The angular distributions for various combinations of the final pions from the ρ → 4π and ω → 5π decays in the e ⁺ e ^?-annihilation and photoproduction are also found. A simple method for the order-of-magnitude estimation of the partial widths based essentially on the threshold character of the above multipion decays is presented.     

The process e + e − → ωπ0 near the Φ resonance

The reaction e ⁺ e ^?→ωπ⁰ near a Φ resonance was studied with a spherical neutral detector at VEPP-2M e ⁺ e ^? collider. Both main modes of decay of a ω meson were investigated: ω→π⁺π^?π⁰ and ω→π ⁰γ. The probability of decay Φ→ωπ⁰ was obtained from the magnitude of the interference wave in the cross section for the reaction e ⁺ e ^?→ωπ⁰→ π⁺π^?π⁰π⁰: B(Φ→ωπ⁰) = (5.5 _?1.4 ^+1.6 ±0.3) ×10^?5. The ratio of the partial widths of the ω meson was obtained from the ratio of the cross sections for the two modes: Γ(ω→π⁰γ )/Γ(ω→π⁺π^?π⁰) = 0.0994 ± 0.0036 ± 0.0038.     

Pionic and radiative decays of vector mesons in the chiral bag model

It is shown that a mechanism, within the framework of the cloudy bag model, analogous to that fore ⁺ e ^?→2ψ in QED accounts qualitatively for the decays ?→2π, ω→πψ and ?→πψ with a bag radii 0.8–1.0 fm, and averaged momenta for decay particles. For the radiative decays, the process identical to that in the vector-dominance model gives about 60% of the total calculated width. It also explains small decay widths previously calculated, using the single quark transition process.     

Two-photon annihilation into pion pair

The first experimental study of the interaction γγ → π⁺π^t- has been carried out in the region of ?(660) through the reaction e⁺e^? → e⁺e^?π⁺π^?. Based on two observed events, the γγ width of ?(660) is obtained to be Γ_?γγ = 9.6_?8.0^+12.3 keV. Applied on this, theory of P.C.D.C. anomaly predicts R_∞ = 5.8_?3.5^+3.2 for the asymptotic value of σ(e⁺e^? → hadrons)/σ(e⁺e^? → μ⁺μ^?).     

Limits on the couplings of ϱ′ (1300 Me) and rhov;″ (1700 MeV) to the photon and to the (ππ) system

The analysis of the reaction e⁺e^?→π⁺π^? measured at the e⁺e^? colliding beam machine ADONE shows that, if ?′ and ?″ exist, the cross sections compare as follows (taking the ? as the reference point): $\text{σ(}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→ ? → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$: σ(e⁺e^? → ?′ → π⁺π^?): σ(e⁺e^? → ?″ → π⁺π^?) = 1: (7 ± 4) × 10^?3: (1 ± 5) × 10^?4. The square of the product of their couplings to the photon (γ_?) and the γγ system (g_?ππ) are derived.     

Probing hadronic polarizations with dilepton anisotropies

We investigate the production of e ⁺ e ^? pairs from p + Be and nucleus-nucleus collisions from 2 GeV/A to 200 GeV/A within a covariant transport approach and focus on the dilepton angular anisotropies as a function of the dilepton invariant mass. Whereas the low mass regime yields information about the Dalitz decays of the Δ, η and ω, above M ≈ 0.5 GeV the angular anisotropies provide additional information about the π ⁺ π ^? → ρ ⁰ → e ⁺ e ^? channel in the medium. The anisotropy coefficient is found to change its sign for M > 0.5 GeV in case of nucleus-nucleus reactions when increasing the bombarding energy from 2 GeV/A to 200 GeV/A which sheds some light on the ππ → ρ dynamics.     

Study of the process e + e − → π+π− in the energy region 400 < \sqrt s < 1000 MeV^\P

The cross section of the process e ⁺ e ^? → π⁺π^? was measured in the spherical neutral detector experiment at the VEPP-2M collider in the energy region $400 < \sqrt s < 1000 MeV$ . This measurement was based on about 12.4 × 10⁶ selected collinear events, which include 7.4 × 10⁶ e ⁺ e ^? → e ⁺ e ^?, 4.5 × 10⁶ e ⁺ e ^? → π⁺π^?, and 0.5 × 10⁶ e ⁺ e ^? → μ⁺μ^? selected events. The systematic uncertainty of cross section determination is 1.3%. The ρ-meson parameters were determined as m _ρ = 774.9±0.4±0.5 MeV, Γ _ρ = 146.5±0.8±1.5 MeV, and σ(ρ → π⁺π^?) = 1220 ± 7 ± 16 nb and the parameters of the G-parity suppressed decay ω → π⁺π^? as σ(ω → π⁺π^?) = 29.9 ± 1.4 ± 1.0 nb and φ_ρω = 113.5±1.3±1.7°.     

Determination of the radiative widths of the η′ and A2 from two-photon exchange production

From the two-photon exchange processes e⁺e^? → e⁺e^?η' (958) → e⁺e^??⁰γ and e⁺e^? → e⁺e^?A₂ (1310) → e⁺e^?π⁺π^?π⁰ observed using the CELLO detector at PETRA the radiative widths of the η' and A₂ have been determined with the results: Γ_γγ(η') = 5.4 ± 1.0[stat.] ± 0.7[syst.] keV; Γ_γγ(A₂) = 0.59 ± 0.14[stat.] _?0.08^+0.31[syst.] keV.     

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.     

Manifestation of ρ-recurrences in e+e−-annihilation

Within the framework of the dispersion method the combined analysis of the data on e⁺e^? → π⁺π^?, e⁺e^? → 4π and ππ phase shift is carried out. The model for inelastic effects in F_π is constructed; investigation of various assumptions shows that the model with ρ° (1250) in πω system and ρ″(1600) in ρ? system, both coupled weakly with ππ, is the most preferable one. The characteristics of ρ′ are estimated.     

Application of the hidden local symmetry effective chiral Lagrangian to evaluation of the <Emphasis Type="Italic">ω</Emphasis>(782), <Emphasis Type="Italic">ϕ</Emphasis>(1020) → 5<Emphasis Type="Italic">π</Emphasis> decay widths

The amplitudes obtained from the effective chiral Lagrangian with anomalous terms based on hidden local symmetry are applied to the evaluation of the partial widths of the decays ω → 2π⁺2π^?π⁰ and ω → π⁺π^?3π⁰. Combining the Okubo-Zweig-Iizuka rule, applied to the five-pion final state, with the Adler condition of vanishing of the amplitude at the vanishing of four-momentum of any final pion in the chiral limit, the ? → 2π⁺2π^?π⁰ and ? → π⁺π^?3π⁰ decay amplitudes are also calculated. The partial widths of the above decays are evaluated, and the resonance excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the free parameters characterizing the anomalous terms of the Lagrangian. The evaluated branching ratios \(Br_{\phi \to \pi + \pi - 3\pi ^0 } \approx 2 \times 10^{ - 7} \) and \(Br_{\phi \to 2\pi + 2\pi - \pi ^0 } \approx 5 \times 10^{ - 7} \) are such that with the luminosity L = 500 pb^?1, attained at the DAΦNE ? factory, one may already possess about 1340 events of the decays ? → 5π.     

Analysis of e + e −→π+π−π+π− and e + e −→π+π−π0π0 processes in the energy range of \sqrt 2 = 0.98 - 1.38 GeV in experiments with a spherical neutral detector

The cross sections of the e ⁺ e ^?→π⁺π^?π ⁺π^?, e ⁺ e ^?→π⁺π^?π⁰π ⁰, and e ⁺ e ^?→ωπ→ π⁺π^?π ⁰π⁰ processes, as well as the e ⁺ e ^?→π⁺π^?π⁰π⁰ process with subtracted contribution of the ωπ intermediate state, are measured in experiments with a spherical neutral detector on the VEPP-2M collider in the energy range 0.98–1.38 GeV. About 41 000 events of the e ⁺ e ^?→π⁺π^?π⁺π ^? process and more than 54 000 events of the e ⁺ e ^?→π⁺π ^?π⁰π⁰ process have been selected in experiment. The statistical error in determining the cross section is 2–20%, while the systematic error is 7 and 8%.     

Energy dependence of e + e − → 6π and e + e − → N\bar N cross sections near N\bar N the threshold

Using recent BABAR, CMD-3 and SND data, the sum of e ⁺ e ^? → 3(π⁺π^?), 2(π⁺π^?π⁰), \(p\bar p\) , \(n\bar n\) cross sections is obtained. Unlike e ⁺ e ^? 3(π⁺π^?) and e ⁺ e ^? → 2(π⁺π^?π⁰) processes, no structures in total cross section are found near the \(N\bar N\) threshold within the limits of measurement errors.