Exponential-trigonometric basis functions in the coulomb four-body problem

Basis functions of a new type—specifically, exponential-trigonometric functions depending on all six interparticle distances—have been proposed for the Coulomb four-body problem. A method has been developed for computing nine-dimensional integrals determining the matrix elements of the Hamiltonian for a four-body system and featuring these functions. The efficiency of the approach that relies on the proposed basis functions has been tested by calculating the e ⁺ e ^? e ⁺ e ^?, p ⁺μ^? p ⁺μ^?, μ⁺ e ^?μ⁺ e ^?, and p ⁺ e ^? p ⁺ e ^? molecules.     

Effect of triple gluon coupling in semi-inclusive polarized scattering processes

We show that the gluon helicity inside a proton and a photon can be deduced from a knowledge of a special combination of cross sections of the semi-inclusive processese+p→e+π+π+... ande ⁺+e ^?→e ⁺+e ^?+π+π+... Such a measurement could thus be used to check the QCD prediction that the gluon helicity increases linearly with lnQ ².     

Partial hypervirial theorems for atomic-molecular systems

A family of partial hypervirial theorems for physical properties of pairs of particles in three-and four-particle atomic-molecular systems is considered. The partial hypervirial theorems generalize the partial virial theorems proposed earlier. The sum rule is formulated, according to which the expectation values of the derivatives with respect to the interparticle distances are related to the products of the charges of pairs of the particles. This rule is used to check the accuracy of the calculation of variational wave functions for the positronium ion e ^? e ^? e ⁺. It is shown that the sum rule is two orders of magnitude more sensitive to the inaccuracy of the calculation of the wave function than the partial virial theorems and is five or six orders of magnitude more sensitive to it than the conventional virial theorem.     

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.     

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%.     

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.     

The production of neutral vector mesons by bremsstrahlung in electron-positron colliding beams

We study the bremsstrahlung production of the ? meson in the reaction e⁺e^? → e⁺e^?? (→ e⁺e^?π⁺π^?). This reaction gives a C = ?1 background which complicates the study of C = +1 two-photon processes at the new colliding-beam facilities. The cross section for the reaction rises from approximately 0.3 nb to 0.7 nb as the beam energy increases from 2 GeV to 15 GeV. From a study of the distributions of the final leptons and pions, we find a suitable choice of cuts which will reduce the event rate down to a small fraction of R. It is not possible to attribute the three-prong events seen at DELCO and PLUTO to this particular production mechanism.     

Current algebra calculation of e+e-→4π± and determination of ϱ′(1600) parameters

A current algebra calculation of e⁺e^-→4π^± cross section is carried out using the axial current matrix element obtained from τ→π?ν. Assuming ?′→?+2π(I=0, l=0), the following results are obtained: for the A₁ resonance, 1.05?m_A ?1.15 GeV; for ?′, Γ?′(total)≈0.23 GeV, M_?′≈1.5 GeV, Γ(?′→e⁺e^-)≈0.4 keV×B^?1(?′→?′ →?π⁺π).     

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.     

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.     

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 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.     

On the possible existence of a vector meson ϱ' (1250)

By combining new results obtained at C.M. energies of 1.2 and 1.3 GeV with previous data obtained at lower energies from the e⁺e^? annihilation process e⁺e^? → π⁺π^?π^oπ^o, we get an indication in favour of the existence of a new vector meson of the ? type, ?' (1250), the first daughter of the ? in the predictions of the Veneziano model. Further results on the annihilation process e⁺e^? → π (1600) → π⁺π^?π⁺π^? are also presented.     

Pion pair production in photon-photon collisions

The process γγ→π⁺π^? was measured using the detector MD-1 at VEPP-4. The two-photon reactionse ⁺ e ^?, μ⁺ μ^? and π⁺ π^? pair production were separated using scintillation counters, Cherenkov counters and shower-range chambers. A radiation widthГ _γγ(f ₂(1270))=3.1±0.35±0.35 keV was obtained.     

Evidence for twoρ′ (1600) resonances

The data on the reactionse ⁺ e ^?→π ⁺ π ^?, 2π ⁺2π ^?,π ⁺ π ^? π ⁰ π ⁰ andγp ⁺ γ ^? p, 2γ ⁺2γ ^? p,γ ⁺ γ ^? γ ⁰ γ ⁰ p are analysed. It is found that to obtain a consistent picture it is necessary to postulate two vector resonances with masses of 1.465±0.025 GeV and 1.700±0.025 GeV with widths of 0.235±0.025 GeV and 0.220±0.025 GeV respectively. A key feature in correlating all the data is the importance of off-diagonal terms in the photoproduction of states withJ ^p =1^? and a contribution from states withJ ^P ≠1^?. The results are compatible with thep-wave ππ scattering amplitude.     

Diffractive production of the charmed baryon Λ+c at the CERN ISR

In a sample of diffractive events of high multiplicity a sharp five standard deviation signal is observed at M = 2255 MeV/c² in the K^?pπ⁺ mass distribution and, although with less statistical strength, at the same mass in the Λ⁰π⁺π⁺π^? channel. These signals are identified as being due to the decay of the charmed baryon Λ⁺_c which is produced with a cross section times branching ratio σ_cB in the range 0.7?1.8 μb for the K^?π⁺p decay and 0.3?0.7 μb for the Λ^-π⁺π⁺ π^? system.     

The Condition of Invariance of the Energy of an Atomic-Molecular System with Respect to Rotations of the Jacobi Coordinates

An additional condition for the wave functions of the ground and excited states of atomic-molecular systems, which follows from the energy invariance with respect to rotations of the Jacobi coordinates, is studied. This condition makes a substantial contribution to the conventional criterion of the quality of wave functions, based on the variational principle for the average energy value. The explicit form of this condition is found for an arbitrary interaction potential dependent on the particle-particle distances and the requirements for realization of this condition are ascertained. Variational calculations of ³He²⁺ μ^? e ^? and ⁴He²⁺ μ^? e ^? mesoatoms in the basis of correlated exponential functions dependent on the particle-particle distances are performed with a detailed optimization of all nonlinear parameters for each individual energy level. A high sensitivity of the condition under study to the quality of approximate wave functions and the efficiency of the detailed optimization of the nonlinear variational parameters in calculation of each individual energy level are demonstrated.     

Dynamical connections between quark fragmentation functions

Assuming that the quark kicked by a virtual photon emits pions one by one, integral equations connecting the fragmentation functions D_u^π+ (z) and D_u^π? (z) are obtained. It is shown that they have a plateau the height of which can be determined from the multiplicity difference N_p^π+ (z) ? N_p^π? (z). Comparison with experiment is made.     

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°.     

Saturation of counterterms by resonances inK →πe + e − decays

The decaysK ⁺→π ⁺ e ⁺ e ^?,K _S→π ⁰ e ⁺ e ^? andK _L→π ⁰ e ⁺ e ^? are reinvestigated within the framework of chiral perturbation theory. The counterterms induced by strong, electromagnetic and weak interactions are determined assuming the resonance exchange. The weak deformation model, the factorization model and the largeN _c limit are used to create a weak Lagrangian. It is found that the results of the first two approaches depend on theH ₁ coupling, defined in the effective chiral Lagrangian of theO(p ⁴) order. The set of parameters used in the extended Nambu and Jona-Lasinio model can accommodeteK ⁺→π ⁺ e ⁺ e ^? decay rate within the factorization approach. The CP violatingK _L→π ⁰ e ⁺ e ^? decay rate is discussed.