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°.     

The e + e −→π0π0γ process below 1.0 GeV

The e ⁺ e ^?→π⁰π⁰ γreaction was studied in the energy range 0.36–0.97 GeV on a VEPP-2M e ⁺ e ^? collider with an SND detector. The decay probabilities were found to be B(ω→ π⁰π⁰γ)= (7.8 ±2.7±2.0)×10^?5 and B(π→ π⁰π⁰γ)= (4.8 _?1.8 ^+3.4 ±0.2)×10^?5.     

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.     

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.     

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.     

Radiative decay ofJ/ψ into γ π+ π−

The radiative decayJ/ψ → γ π⁺ π^? has been studied using the 8.6 millionJ/ψ produced in the DM2 experiment at the DCIe ⁺e^? storage rings at Orsay. The π⁺ π^? mass spectrum shows a cleanf ₂ (1270) signal, and the possible presence of two other states at thef ₂ (1720) andf ₄ (2030) masses. For thef ₂ (1270), the branching ratio BR(J/ψ →γf)xBR(f→π⁺ π^?) is measured to be (7.50±0.30±1.12)×10^?4, and the spin analysis prefers theJ=2 assignment, with helicity parametersx=0.83±0.06 andy=0.01±0.06. The existence of higher mass states is discussed.     

Natural left-right symmetry,atomic parity experiments and asymmetries in high energy e+e− collisions in petra and pep regions

The previously proposed left-right-symmetric SU(2)_L × SU(2)_R × U(1) theory permits one of the two neutral gauge particles N₁ and N₂ to be particularly light (<mW⁺_L) compatible with all neutrin-data and the present atomic parity experiments. Distinguishing features of this theory (with the light mass solution) for e^?e⁺ → μ⁺μ^? and π⁺π^? at PETRA and PEP energies as compared to the SU(2) × U(1) predictions are given.     

A study of the centrally produced π+π−π0 system formed in the reactionpp→p f (π+π−π0)p s at 300 GeV/c

The reactionpp→p _f (π⁺π^?π⁰)p _s , where the π⁺π^?π⁰ system is centrally produced, has been studied at 300 GeV/c. The π⁺π^?π⁰ mass spectrum shows evidence for the η, ω anda ₂ (1320) as well as an enhancement in thea ₁ (1260) region. A Dalitz plot analysis of the π⁺π^?π⁰ system has been performed. Thea ₁ (1260) parameters coming from the fit of the 1⁺ S wave arem=1208±15 MeV and Γ=430±50 MeV. No evidence is found for theh ₁(1170) orh ₁(1380).     

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.     

Measurement of the branching ratio and π° energy spectrum for K°L → π+π−π°

The K°_L → π⁺π^?π° decay was studied in a bubble chamber experiment at an average momentum of 1.3 GeV/c. We measure the branching ration Γ(K°_L → π⁺π^?π°)/Γ(K°_L → charged) to be 0.1605 ± 0.0038. The data are well fitted with a linear matrix element in the π° kinetic energy with a slope g = 0.612 ± 0.032.     

Measurement of elastic ω photoproduction at HERA ZEUS Collaboration

The reaction γp →ωp(ω → π⁺π^?π⁰ and π⁰ → γ γ) has been studied in ep interactions using the ZEUS detector at photon-proton centre-of-mass energies between 70 and 90GeV and ∣t∣ < 0.6GeV², where t is the squared four momentum transferred at the proton vertex. The elastic ω photoproduction cross section has been measured to be σ_{γp → ωp} = 1.21 ±0.12 ±0.23 μb. The differential cross section dσ_γp→ωp/d¦t¦ has an exponential shape e^?b∣t∣ with a slope b =10.0 ± 1.2 ± 1.3 GeV^?2. The angular distributions of the decay pions are consistent with s-channel helicity conservation. When compared to low energy data, the features of ω photoproduction as measured at HERA energies are in agreement with those of a soft diffractive process. Previous measurements of the ρ⁰ and ? photoproduction cross sections at HERA show a similar behaviour.     

Contribution of the π<Superscript>0</Superscript>γ and ηγ intermediate states to vacuum polarization and the muon anomalous magnetic moment

Using new experimental data, we calculated, with a high precision, a contribution to the muon anomalous magnetic moment from the vacuum-polarization intermediate states π⁰γ and ηγ taking into account a correction for the trapezoidal rule: aμ(π⁰γ+aμ(ηγ)=(53.1± 1.5)×10^?11. We also determined a small contribution from the e⁺e^?π⁰, e⁺e^?η, and μ⁺μ^?π⁰ intermediate states, which was found to be equal to 0.5×10^?11.     

Measurement of the relative probability of the decay φ → η′γ in the channel η′ → ηπ0π0, η → γγ

The process e ⁺ e ^? → η′γ, η′ → η π⁰π⁰, η → γγ is investigated by an SND detector in experiment on a VEPP-2M equipment with colliding electron-positron beams. The analysis of experimental data yields a value of B(? → η′γ)=(6.7 _?4.2 ^+5.0 ±1.5)×10^?5 for the decay probability. Taking into account a previous measurement of this quantity by an SND detector in the decay channel η′ → π⁺π^?η, one finally obtains B(?→η ′γ)=(6.7 _?2.4 ^+2.8 ±0.8)×10^?5.     

Observation of the (π−, π−n) and (π+, π+p) reactions at 165 MeV

The (π^?, π^?n) and the (π⁺, π⁺p) reactions were studied on C, Fe, and Bi at 165 MeV by coincidence measurement o outgoing particles. The nucleon-knockout reaction is the dominant inelastic process at backward pion-scattering angles at this energy. The quasifree (π^?, π^?n) and (π⁺, π⁺p) cross sections were determined from the π-N an correlations. Their σ_qf(π^?, π^?n)/σ_qf(π⁺, π⁺p) ratio is consistent with unity for C and is larger than the N/Z ratio for the heavier nuclei.     

π+/π− Ratio and two particle production in Proton's fragmentation region by Monte Carlo simulation

Hadron jet at lowp _T is generated by Monte Carlo method using several models including our quark cascade model in which the recombination mechanism is taken into account. The predicted results from those models on π⁺/π^? ratio,K ⁺ /K ^? ratio, π^± meson spectra and π⁺/π^? ratio under π^± meson and Λ particle trigger, ratio between invariant two particle cross-section (p→π ⁺ /π ^? )/(p→π ^? /π ^? are compared with the experimental data. The effects of the asymmetric initialu- andd-quark distributions the scaling and its violation of particle spectra and particle ratios under the other particle trigger are discussed. Predictions from our recombination model fit to the experimental data fairly well.     

High-twist correction for inclusive hadron production in photon-photon collisions

The contribution of the QCD high-twist subprocess γq→πq′ to the inclusive cross section for e⁺ e^? → e⁺ e^? + π^± + X is calculated both in the PETRA/PEP and the LEP energy range, in the equivalent-photon approximation. Superposed on the Born cross section and its O(α_s) correction, it gives agreement with the data at relatively low transverse momenta. It is suggested that this high-twist contribution may be further isolated experimentally by triggering simultaneously on both a fast hadron and the opposite-side jet.     

Study of the π+π+π-π- system centrally 0 produced by incident π+ andp beams at 85 GeV/c

The reactions π⁺ p→π⁺(π⁺π⁺π^-π^-)p andpp→p(π⁺π⁺π^-π^-)p, where the (π⁺ π⁺ π^- π^-) system is centrally produced have been studied at 85 GeV/c. The π⁺π⁺π^-π^- mass spectrum shows evidence for thef ₁ (1285) meson with a mass of 1278±2 MeV and width 41±12 MeV which decays mainly through ρ⁰(770)π⁺π^-. Thef ₁(1285) is also observed in the ηπ⁺π^- channel. There is no significant evidence for ηππ or 4π decay modes of thef ₁(1420). The ρ⁰ρ⁰ production is found to be small. A Dalitz plot analysis of the 3π system shows evidence fora ₂ (1320) production and for a large contribution of theJ ^PC=1⁺⁺ ρπ wave.     

Multipion production below 1.1 GeV by e+e− annihilation

The production of multipion events by e⁺e^? annihilation has been measured at centre of mass energies 915,990 and 1076 MeV. Both channels e⁺e^?→π⁺π^?π^o and e⁺e^?→π⁺π^?π⁺π^? have been analysed. An energy threshold effect analysed. An energy threshold effect around 919 MeV (m_ω + m_π^o) has been evidenced for the π⁺π^?π^oπ^o channel and the cross section is consistent with the quasi two-body process e⁺e^?→ωπ^o. The cross section for π⁺π^?π⁺π^? is lower by an order of magnitude and increases with the energy.     

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^?).