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.     

On the calculation of spin dependence in the absorption model for π-exchange

A generalization of the absorption model of Williams done for the reaction π^?p → π^?π⁺n is presented for arbitrary π⁺B final states in the reaction Bp → Bπ⁺n. For small values of the π⁺B crossing angle we can express the results in terms of the π⁺B scattering amplitude instead of the π⁺B partial-wave amplitudes. By this a considerable simplification of the general formalism is achieved. Some of the predictions which can be made turn out to be independent of the π⁺B amplitudes. This allows a sensitive test also in the case of B = π or K, where the πB amplitudes are unknown.     

A comparative study of the NNπ system: (I). The πd → πd, πd → NN channels

Numerical results are presented for πd → πd, πd NN observables for 290 ? T_π (MeV) ? 50. We discuss sensitivity of predictions for various input elements like the deuteron form factor, the range of the NNπ vertex and the parametrization of the background part of the P₁₁πN scattering matrix and remark on possible parallels for A(π, π) and A(π, 2N) amplitudes. A comparison is made with previously obtained results of similar scope.     

Results from a π−p slow proton trigger experiment at 12 GeV/c

A study of the reaction π^?p → X^?p based on 1.27 × 10⁶ events, corresponding to a mean sensitivity of 200 events/μb, is presented. Properties of the exclusive channels π^?p → π^?π⁰p, π⁺π^?π^?p, π⁺π^?π^?π⁰p, π⁺π⁺π^?π^?π^?p and π⁺π⁺π^?π^?π^?π⁰p are discussed.     

Growing networks with preferential deletion and addition of edges

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π₁>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π₂ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π₃=1−π₁−π₂<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction p_k of vertices with degree k, and solving this recursion reveals that, for π₃<1/3, we have p_k∼k^{−(3−7π₃)/(1−3π₃)}, while, for π₃>1/3, the fraction p_k decays exponentially at rate (π₁+π₂)/2π₃. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.     

Observation of diffraction excitation in pp → (pπ+π−)+X at the CERN-ISR and tests of limiting fragmentation

In a single-arm magnetic spectrometer experiment at the CERN Intersecting Storage Rings (ISR), a prominent diffractive enhancement is observed for inclusive production of (pπ⁺π^?) systems near x ～ 1 at √s = 53 and 35 GeV. In testing limiting fragmentation and scaling for this system, inclusive pπ⁺π^? diffractive excitation into a fixed invariant mass range is found to possess a cross-section independent of s to within (3 ± 5)%. The main component in the (pπ⁺π^?) system is Δ(1236)π, with a charge structure compatible with the break-up of an isotopic spin $\text{1}\text{2}$ system.     

Measurement of π−p→π0π0n at 25 GeV/c

The reaction π^?p→π⁰π⁰n has been measured with a 648 channel hodoscope spectrometer for the detection of the four γ's from the π⁰ decays. The π⁰π⁰ D-wave is fully compatible with the f⁰ contribution as it is determined in high-statistics π⁺π^? experiments. The magnitude of the π⁰π⁰ S-wave and the cosinus of its phase angle (relative to the known D-wave) are determined from fits to the π⁰π⁰ angular distributions. Argand diagrams for the I = 0 amplitude S₀ are given for the range 1000 to 1500 MeV/c². Two solutions exist. One exceeds the unitarity limit above 1200 MeV/c². The other remains within the unitarity limit and is nearly elastic up to 1450 MeV/c². It indicates an S₀ wave resonance around 1300 MeV/c².     

Measurement of pp annihilation cross sections into charged particles in the momentum range 374–680 MeV/c

$\text{p}\text{p}$ annihilation cross sections into 2-, 4- and 6-prong topologies, and the exclusive annihilation cross sections for the π⁺π^?, K⁺K^?, π⁺π^?π⁰, π⁺π⁺π^?π^?, π⁺π⁺π^?π^?π⁰, π⁺π⁺π⁺π^?π^?π^?, and π⁺π⁺π⁺π^?π^?π^?π⁰ channels in the momentum range 374–680 MeV/c were measured. No prominent structure was observed in the momentum dependence of any of the above cross sections, but a small enhancement in the cross section was observed at 490 MeV/c corresponding to the S meson mass in the topological, and π⁺π^?π⁰ and π⁺π⁺π^?π^?π⁰ cross sections. If the extensive of the S meson with a mass and width of 1935.5 and 2.8 MeV/c² is assumed, our measurement gives a total resonant annihilation cross section into charged particles of 10.0±3.0 mb.     

ππ scattering in the I = 2 channel

I=2π⁺π⁺ scattering is studied in π⁺p reactions at 5.45 GeV/c. The π⁺π⁺ cross sections and phase shifts have been determined from the reaction π⁺p → π⁺π⁺n using first a pure and then a modified Chew-Low extrapolation to the pion pole.     

Coherent two pion photoproduction on 12C

We develop the formalism for coherent two pion photoproduction in nuclei and perform actual calculations of cross sections for π⁻π⁺ and π⁰π⁰ photoproduction on ¹²C. We find that due to the isospin symmetry the cross section for π⁰π⁰ production is very small and has a maximum when the pions propagate together. However, the kinematical region where the energies and polar angles of the two π⁰ mesons are equal and their relative azimuthal angle Ø = 180° is forbidden. Conversely in the π⁻π⁺ production the pions prefer to have a relative azimuthal angle 180° and the production of the pions propagating together is suppressed. The dominant one-body mechanism in both channels is related to the excitation of the Δ isobar. Hence the reaction can serve as a source of information about Δ's properties in nucleus. We have found that the reaction is sensitive to effects of the pion and Δ renormalization in the nuclear medium, similar to those found in the coherent (γ, π⁰) reaction, but magnified because of the presence of the two pions.     

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.     

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.     

Pion and nucleon dissociation in π−p→π−π+π−p at 205 GeV/c

In a 48 000-picture exposure of the Fermilab 30-inch hydrogen bubble chamber to a 205 GeV/cπ^?beam, we have measured 169 events of the reaction, π^?p→π^?π⁺π^?p, with a cross section of 635 ± 61 μb. This reaction proceeds almost entirely via low mass π^? → 3π and p → pππ dissociation. Factorization is satisfied for p → pππ dissociation in πp and pp interactions.     

Investigation of the double diffraction dissociation reaction pp → (pπ+π−) (pπ+π−) at 24 GeV/c

Data from a high-statistics bubble chamber experiment at 24 GeV/c are used to study the double diffraction dissociation reaction pp→(pπ⁺π^?) (pπ⁺π^?) where both protons of the initial state dissociate into pπ⁺π^? systems. Cross section, mass spectra and dσ/dt' distributions have been determined and are compared with the results found for the single diffraction dissociation reaction pp → p(pπ⁺π^?), which have been obtained from the same experiment. All our findings agree well with what is expected from the factorization hypothesis.     

Study of the centrally produced ωρ0 and ωω systems inpp interactions at 300 GeV/c

We have performed a search for vector-vector final states centrally produced in proton proton interactions at 300 GeV/c using the CERN Ω spectrometer. Evidence is found for ωρ⁰ production in the reactionpp→p _f (2π⁺2π^?2π⁰)p _s and for ωω production in the reactionpp→p _f (2π⁺2π^?2π⁰)p _s . However no evidence is found for ωø production in the reactionpp→p _f (K ⁺ K ^?π⁺π^?π⁰)p _s .     

Photoproduction of charmed F mesons at γ energies of 20–70 GeV

Evidence is presented for inclusive photoproduction of F^± mesons in three decay modes, ηπ^±, ηπ^±π⁺π^? and ηπ^±π⁺π⁺π^?π^?. The average mass of the F^± is found to be 2.020±0.010 GeV.     

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.     

The reaction γp → pπ+π−π+π− for photon energies from 25 to 70 GeV

Measurements of the reaction γp → pπ⁺π^?π⁺π^? are presented, in which π⁺π^?π⁺π^? systems with masses up to 3 GeV are produced from fragmentation of the incident photon. The reaction is dominated by production of the large peak of the ?′(1600) meson and, at higher masses ?2 GeV, y production of jet-like 4π systems. The ?′(1600) meson is produced by a predominantly s-channel helicity conserving mechanism. At higher masses there are also indications of ?π peaks, of masses 1.3 GeV (the A₂ meson) and 1.75 GeV, produced with a recoiling π meson by a mechanism consistent with the Deck effect.     

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.