Two photons into π<Superscript>0</Superscript>π<Superscript>0</Superscript>

We perform a theoretical study based on dispersion relations of the reaction γγ → π ⁰ π ⁰ emphasizing the low-energy region. We discuss how the ƒ ⁰(980) signal emerges in γγ → ππ within the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave γγ → ππ amplitude above the threshold. This allows us to make sharper predictions for the cross-section at lower energies and our results could then be used to distinguish between different ππ isoscalar S-wave parameterizations with the advent of new precise data on ππ → π ⁰ π ⁰. We compare our dispersive approach with an updated calculation employing the unitary chiral perturbation theory (U _gC PT). We also pay special attention to the role played by the σ-resonance in γγ → ππ and calculate its coupling and width to γγ, for which we obtain Γ(σ → γγ) = (1.68 ± 0.15) keV.     

Processes e<Superscript>+</Superscript>e<Superscript>−</Superscript> → π<Superscript>0</Superscript>(π<Superscript>0</Superscript>′) γ in extended NJL model

The processes of electron-positron annihilation into π⁰γ and into π′(1300)γ are considered within an extended NJL model. The intermediate vector mesons ρ ⁰, ω ρ′(1450), and ω(1420) are taken into account. The latter two mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of a polynomial form factor. Numerical predictions for the cross-sections of these processes are received for the center-of-mass energies below 2 GeV. Our results for the π⁰γ production are in agreement with experimental data obtained in the energy region 600–1020 MeV.     

Photoproduction of π<Superscript>0</Superscript>π<Superscript>+</Superscript> pairs on proton and deuteron

The reaction of π⁰π⁺ photoproduction on free and quasi-free protons with γ-ray energies from 0.5 to 1.5 GeV has been studied. Its cross section was measured in the range θ _π ⁰ ≥ 20°. The distributions of π⁰π⁺, π⁰n, and π⁺n invariant masses were analyzed. The experiment was performed using the Compton back-scattered γ-ray beam at the GRAAL facility (Grenoble, France), applying liquid deuterium and hydrogen targets and a large-aperture (almost 4π) detector. Particular attention was paid to analysis of systematic errors related to the neutron detection efficiency.     

A new determination of the γπ → ππ anomalous amplitude via πe<Superscript>-</Superscript> → π<Superscript>-</Superscript>e<Superscript>-</Superscript>π<Superscript>0</Superscript> data

We discuss the reaction π^-e^- → π^-e^-π⁰ with the purpose of obtaining information on the γπ → ππ anomalous amplitude _3π. We compare a full calculation at (p⁶) in chiral perturbation theory and various phenomenological predictions with the existing data of Amendolia et al. By integrating our theory results using Monte Carlo techniques, we obtain σ = 2.05 nb at (p⁶) and σ = 2.17 nb after including the dominant electromagnetic correction. Both results are in good agreement with the experimental cross-section of σ = (2.11±0.47) nb. On the basis of the ChPT results one would extract from the experimental cross-section as amplitudes _3π^(0)extr = (9.9±1.1) GeV^-3 and _3π^(0)extr = (9.6±1.1) GeV^-3, respectively, which have to be compared with the low-energy theorem _3π = e/(4π²F_π³) = 9.72GeV^-3. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain _3π with smaller uncertainty.     

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.     

<Emphasis Type="Italic">J</Emphasis><Superscript>π</Superscript>0<Superscript>−</Superscript> levels in <Superscript>156</Superscript>Gd and <Superscript>158</Superscript>Gd

The 0^? states in the ¹⁵⁶Gd nucleus at E = 1952.38 keV and in the ¹⁵⁸Gd nucleus at E = 2269.16 keV are established on the basis of an analysis of available data on even-even deformed nuclei. From data on the deexcitation of the levels and on the probability of their population by beta transitions, it is found that these states have a two-particle proton structure. A comparison of our data with information about the 0^? levels in the ¹⁷⁰Yb and ¹⁷⁶Hf nuclei makes it possible to conclude that J^π0^? two-particle states exist at an excitation energy of about 2 MeV and higher.     

Potential energy of <Superscript>∞</Superscript>H<Stack><Subscript>2</Subscript><Superscript>-</Superscript></Stack>(<Superscript>2</Superscript>∑<Stack><Subscript>u</Subscript><Superscript>+</Superscript></Stack> in the bound-state region

An accurate calculation of the lowest negative electronic state of H ₂ ^- (fixed nuclei) is reported using the CCSD(T) method and doubly augmented cc-pv5z basis set. Comparison has been made with the reference data by Senekowitsch et al. [Chem. Phys. Lett. 111 (1984) 211]. Owing to larger size of the basisset and inclusion of triple excitations, no vertical shift in this work is necessary to reproduce the asymptotics of H + H ^-. In addition, the effect of basis-set truncation is estimated, based on the complete-basis-set extrapolation method. The contribution of correlated electron-proton motion to the electron-energy curve for H₂ ^– dynamics is pointed out.Dedicated to Prof. Jií Horáek on the occasion of his 60th birthday.     

Spectroscopic factors in the <Superscript>7</Superscript>Li → d + <Superscript>5</Superscript>He{α} fragmentation channel

The spectroscopic S _d factors of the separation of deuterons in the d + ⁵He channel were calculated using the two-body αt model of ⁷Li nucleus and various ⁵He{αn} wave function models.     

<Superscript>16</Superscript>O/<Superscript>18</Superscript>O oxygen isotope exchange kinetics in MnO<Stack><Subscript>4</Subscript><Superscript>−</Superscript></Stack> as probed by <Superscript>55</Superscript>Mn NMR

The effect of the ¹⁶O ? ¹⁸O substitution in the coordination sphere of permanganate anion MnO ₄ ^? on the chemical shift of ⁵⁵Mn nuclei have been studied by ¹⁷O and ⁵⁵Mn NMR. Time constants τ _n,k of oxygen exchange in the water–permanganate anion system have been estimated. In nearly neutral solutions (pH ≈ 6.8–7.2), the oxygen exchange time is on the order of tens of hours. Bubbling gaseous HCl through this solution for a few seconds leads to the equilibrium distribution of oxygen isotopes in the manganese coordination sphere. The observed temperature dependences of isotope-induced ⁵⁵Mn NMR shifts in Mn¹⁶ O _44-n ¹⁸ O _n ^– (n = 0–4) have been treated as a result of rovibrational averaging of Mn–O bond lengths. The change in the Mn—O bond length in caused by the ¹⁶O → ¹⁸O isotope substitution is on the order of 10^–4 Å.     

Rare decay π<Superscript>0</Superscript> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> as a test of standard model

Experimental and theoretical progress concerning the rare decay π⁰ → e ⁺ e ⁻ is briefly reviewed. It includes the latest data from KTeV and a new model-independent estimate of the decay branching which show the deviation between experiment and theory at the level of 3.3σ. The predictions for η and η′ decays into lepton pair are presented. We also comment on the impact on the pion rare decay estimate of the data of BABAR collaboration on the pion transition form factor at large momentum transfer.     

Investigation of the low-lying nucleon resonances in reactions of π<Superscript>+</Superscript>π<Superscript>−</Superscript> pair electroproduction on protons

The cross sections of the reaction ep → e′p′π⁺π^? for small photon virtualities were measured on a CEBAF large acceptance spectrometer (CLAS detector) at the Thomas Jefferson National Accelerator Facility for the first time. A complete set of one-dimensional cross sections of the reaction was obtained for photon virtualities in the range 0.2 GeV² < Q ² < 0.6 GeV² and invariant masses of the final hadronic system in the range 1.3 GeV < W < 1.6 GeV. A preliminary analysis of the obtained data in the framework of the phenomenological model demonstrated that the Q ² dependence of the electromagnetic form factors for the P ₁₁ (1440) and D ₁₃ (1520) resonances can be determined in the kinematic region (which is the most sensitive to the contribution from the meson cloud) and that the axial transition form factor p → Δ can be derived.     

Exclusive ωπ<Superscript>0</Superscript> production with muons<Superscript>⋆</Superscript>

Using 160GeV muon scattering data collected with the COMPASS experiment at CERN, the exclusive production of ωπ⁰ via virtual photons was studied. Selective population of a peak around 1250MeV is observed. Possible contributions from spin-parity 1^- are searched for, inspecting decay angular correlations. In particular, the orientation of the ω decay plane may allow a distinction from the 1⁺ b ₁(1235) state. Our observation is compared with indications of a (1250) in annihilation and in γp . Original article based on material presented at HADRON 2007.     

Inversion of the <Emphasis Type="Italic">K</Emphasis><Superscript>π</Superscript>=1<Superscript>−</Superscript> states in <Superscript>156</Superscript>Gd and <Superscript>170</Superscript>Yb

For the ¹⁵⁶Gd and ¹⁷⁰Yb nuclei, where the inversion of levels in the K^π=1^? bands is observed, the energies of rotational levels are calculated on the basis of the Coriolis interaction model for the states of two bands whose quantum numbers are K^π=1^?. New 0^? levels are introduced in ¹⁷⁰Yb, and the structure of ¹⁷⁰Er is refined. The interaction parameters calculated for six nuclei are considered within the structure predicted by the quasiparticle-phonon model.     

Measurement of the Dalitz-decay branching ratio of the π<Superscript>0</Superscript>

The ratio is measured by comparing the production rates of the π⁰ in the two decay channels. The analysis is based on approximately four million hadronic decays of the Z boson recorded by the ALEPH detector in the years 1991 to 1995. The value of is determined to be . A recalculation of the Particle Data Group world average gives rise to a slightly improved error, and moves the world average closer to the theoretical value.     

Decays of baryon resonances into ΛK<Superscript>+</Superscript>, ΣK<Superscript>+</Superscript> and Σ<Superscript>+</Superscript>K<Superscript>0</Superscript>

Cross-sections, beam asymmetries, and recoil polarisations for the reactions γp → K ⁺Λ;γp → K ⁺Σ⁰, and γp → K ⁰Σ⁺ have been measured by the SAPHIR, CLAS, and LEPS Collaborations with high statistics and good angular coverage for centre-of-mass energies between 1.6 and 2.3 GeV. The combined analysis of these data with data from π and η photoproduction reveals evidence for new baryon resonances in this energy region. A new P₁₁ state with mass 1840 MeV and width 140 MeV was observed contributing to most of the fitted reactions. The data demand the presence of two D₁₃ states at 1875 and, optimistically, at 2170 MeV.     

Tensor asymmetry of π<Superscript>−</Superscript>-meson photoproduction on polarized deuterons

The tensor asymmetry of exclusive π^?-meson photoproduction on polarized deuterons was investigated. The T ₂₀ and T ₂₂ components of the reaction analyzing power contribute to the measured asymmetry. The detector made it possible to record two outgoing protons in coincidence in the range of polar angles θ_1,2 = 44° ? 88° and in the momentum range p _1,2 = 350 ? 700 MeV c ^?1. The measurements were performed at the VEPP-3 storage ring (Novosibirsk) using an internal target. The experimental results are compared with theoretical calculations.     

Nucleon-nucleon correlations in the (γ, π<Superscript>−</Superscript><Emphasis Type="Italic">p</Emphasis>) and (γ, π<Superscript>−</Superscript><Emphasis Type="Italic">pp</Emphasis>) reactions on the <Superscript>12</Superscript>C nucleus

The photoproduction of negative pions on the carbon nucleus in the (γ, π^?p) and (γ, π^?pp) reactions has been studied experimentally. The measurements are interpreted using a model of the formation of an intermediate Δ nuclear state (Δ nucleus) that decays with the emission of a pion and a nucleon.     

Hyperfine Interactions in Pb<Superscript>3+</Superscript>F<Stack><Subscript>8</Subscript><Superscript>−</Superscript></Stack>F<Stack><Subscript>a</Subscript><Superscript>−</Superscript></Stack> clusters in fluorite crystals

The parameters of hyperfine interactions in Pb³⁺F ₈ ^? F _a ^? tetragonal clusters of MeF₂ crystals (Me=Ca, Sr, Ba) are interpreted. The contributions of the spin polarization to the parameters of the proper hyperfine interaction and additional (ligand) hyperfine interactions are calculated in the approximation of weak binding between a charge-compensating ion F _a ^? and a cubic fragment in the tetragonal cluster. It is demonstrated that correct inclusion of the contributions from the spin polarization to the ligand isotropic hyperfine interaction for the F _a ^? ion leads to anomalously large parameters of this interaction for MeF₂ crystals. These results are in agreement with experimental data.     

Two-neutrino positron double-beta decay of <Superscript>106</Superscript>Cd for the 0<Superscript>+</Superscript> → 0<Superscript>+</Superscript> transition

The two-neutrino positron double-beta decay of ¹⁰⁶Cd for the 0 ⁺ 0⁺ transition has been studied in the Hartree-Fock-Bogoliubov model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions of ¹⁰⁶Cd and ¹⁰⁶Pd nuclei has been tested by comparing the theoretically calculated results for yrast spectra, reduced B(E2: 0⁺ 2⁺) transition probabilities, quadrupole moments Q(2⁺) and gyromagnetic factors g(2⁺) with the available experimental data. In the second step, the nuclear transition matrix element M₂ and the half-life T_1/2² for the 0 ⁺ 0⁺ transition have been calculated with these wave functions. Moreover, we have studied the effect of deformation on the nuclear transition matrix element M₂.     

Study of the reaction π–<Emphasis Type="Italic">A</Emphasis> π<Superscript>+</Superscript>π<Superscript>–</Superscript>π<Superscript>–</Superscript><Emphasis Type="Italic">A</Emphasis> at large statistics with VES setup

Partial wave analysis of the π–A π⁺π^–π^– system produced by 29 GeV/cπ^– beam on a beryllium target is presented. About 30 × 10⁶ |events in the wide t′|range 0–0.8 GeV²/c ² are collected with upgraded VES setup. The size of the data sample is 2.5 times larger than one previously analyzed by VES. Data are analyzed using formalism of the density matrix with unlimited rank. We discuss status of the a ₁(1420) a ₂(1700) a ₃(1875) states and a structure of exotic ρ(770)π P-wave with J ^PC = 1^-+. Parameters of a ₃(1875) are estimated as M = 1985 ± 20 MeV/c ², Γ = 200 ± 50 MeV/c ² (preliminary).