Lie Superalgebra Structures in <Emphasis Type="Italic">H</Emphasis><Superscript>⋅</Superscript> (<Emphasis Type="Italic">g</Emphasis>;<Emphasis Type="Italic">g</Emphasis>)

Let g=vect(M) be the Lie (super)algebra of vector fields on any connected (super)manifold M; let - be the change of parity functor, C ⁱ and H ⁱ the space of i-chains and i-cohomology. The Nijenhuis bracket makes into a Lie superalgebra that can be interpreted as the centralizer of the exterior differential considered as a vector field on the supermanifold associated with the de Rham bundle on M. A similar bracket introduces structures of DG Lie superalgebra in L ^* and for any Lie superalgebra g. We use a Mathematica-based package SuperLie (already proven useful in various problems) to explicitly describe the algebras l ^* for some simple finite dimensional Lie superalgebras g and their relatives - the nontrivial central extensions or derivation algebras of the considered simple ones.     

Intrinsic <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> factors of odd-mass <Superscript>167–179</Superscript>Lu isotopes

In this paper, g _K -factors of the intrinsic magnetic moments and effective spin gyromagnetic factors (g _s^eff) of the ^167–179Lu isotopes have been studied within the Tamm-Dancoff approximation (TDA) (Kuliev et al, Sov. J. Nucl. Phys. 9, 185 (1969)) by using a realistic potential such as Woods-Saxon potential for the first time. The effects of the spin-spin and spin-isospin interactions on magnetic moments were investigated. The results of the theoretical calculations are compared with the experimental data for related nuclei. The experimental values of g _K and g _s^eff were computed from the observed magnetic moments (Georg et al, Eur. Phys. J. A3, 225 (1998)) using the spin matrix elements. The theoretical predictions for the g _K factors exhibit good agreement with the experimental g _K factors with increasing mass number A of the lutetium isotopes. The strongest influence of the neutron-proton spin interaction occurs at q = −1. Sufficient agreement between the calculated and the experimental values of g _K is obtained for κ = (45/A) MeV and q = −1.     

QCD sum rules for the coupling constants <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">KYN</Emphasis></Subscript> and <Emphasis Type="Italic">g</Emphasis><Subscript>KYΞ</Subscript>

New relations between Borel QCD sum rules for the strong couplings of baryons to kaons are derived. It is shown that, on the basis of the sum rules for the coupling constants g _πΣΣ and g _πΣΛ, the corresponding sum rules can be directly obtained for the coupling constants g _KYN and g _KYΞ, Y = Σ,Λ. The values of these coupling constants are calculated in the fiducial interval 1.0 ≤ M ² ≤ 1.4 GeV² at t = ?1.     

On mass corrections to the decay <Emphasis Type="Italic">P</Emphasis> → <Emphasis Type="Italic">l</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">l</Emphasis><Superscript>−</Superscript>

The Mellin-Barnes representation is used to improve the theoretical estimate of mass corrections to the width of a light pseudoscalar meson decay into a lepton pair, P → l ⁺ l ⁻. The full resummation of the terms ln(m _l ²/Λ²)(m _l ²/Λ²) ⁿ and (m _l ²/Λ²) ⁿ to the decay amplitude is performed, where m _l is the lepton mass and Λ ≈ m _ρ is the characteristic scale of the P → γ*γ* form factor. The total effect of the mass corrections for the e ⁺ e ⁻ channel is negligible and, for the μ⁺μ⁻channel, its order is of a few percent. The text was submitted by the authors in English.     

Fine structure of the string spectrum in <Emphasis Type="Italic">AdS</Emphasis><Subscript>5</Subscript> × <Emphasis Type="Italic">S</Emphasis><Superscript>5</Superscript>

The spectrum of an infinite spinning string in AdS ₅ does not precisely match the spectrum of dual gauge theory operators, interpolated to the strong coupling regime with the help of Bethe-ansatz equations. We show that the mismatch is due to interactions in the string σ-model which cannot be neglected even at asymptotically large’ t Hooft coupling.     

Deviation from the standard model in the decay <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">νγ</Emphasis>

A precise investigation of radiative pion decay (π⁺ → e⁺νγ) in a pion beam from the meson factory of the Paul Scherrer Institute (Switzerland) was performed by the PIBETA Collaboration with the aid of the PIBETA detector. This resulted in finding 41 601 events of radiative pion decay in three kinematical regions. The absolute values of the branching ratio for radiative pion decay were determined in each of these regions. To a precision approximately four times higher than that known previously, the ratio of the axial-vector to the vector form factor was found to be γ ≡ F _A /F _V = 0.443 (15), the latter being fixed at F _V = 0.0259. The number of events found in the kinematical region specified by photon energies of E_γ > 55.6 MeV, positron energies of E _e > 20.0 MeV, and angles of θ_{γ, e} > 40° between the momenta of the corresponding particles (B region) was 5233. In region B, the measured branching ratio for radiative pion decay, R_π→evγ(expt) = 11.6(3) × 10^?8, proved to be smaller by eight standard deviations than that which follows from the Standard Model, R_π→evγ (theor) = 14.34(1) × 10^?8.     

Inclusive <Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis> photoproduction and polarization at HERA in the <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>-factorization approach

We investigate the inclusive photoproduction of J/ψ mesons at HERA within the framework of the k _T -factorization QCD approach. Our study is based on the color singlet model supplemented with the relevant off-shell matrix elements and the CCFM and KMR unintegrated gluon densities in a proton and in a photon. Both the direct and resolved photon contributions are taken into account. Our predictions are compared with the recent experimental data taken by the H1 and ZEUS collaborations. Special attention is put on the J/ψ polarization parameters λ and ν, which are sensitive to the production dynamics.     

Higher <Emphasis Type="Italic">η</Emphasis><Subscript>c</Subscript>(<Emphasis Type="Italic">nS</Emphasis>) and <Emphasis Type="Italic">η</Emphasis><Subscript>b</Subscript>(<Emphasis Type="Italic">nS</Emphasis>) mesons

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using experimental data on dielectron widths. Relativistic correlations are taken into account together with the smearing of spin-spin interaction. The radius of smearing is fixed by known G/ψ−η _c(1S), ψ(2S)−η _c′(2S) splittings, which appears to be small, r _ss ≅ 0.06 fm. Nevertheless, even with such a small radius, substantial suppression of hyperfine splittings (∼50%) is observed in bottomonium. For nS b states (n = 1, 2, ..., 6), our predicted splittings (in MeV) are 28, 12, 10, 5, 6, 3. For the 3S and 4S charmonium states, the splittings 16(2) and 12(4) MeV are obtained. The text was submitted by the authors in English.     

Possible tetraquark states in the <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">χ</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>1</Subscript> invariant-mass distribution

In this article, we assume that there exist hidden charmed tetraquark states with spin–parity J ^P=1⁻, and we calculate their masses with the QCD sum rules. The numerical result indicates that the masses of the vector hidden charmed tetraquark states are about M _Z =(5.12±0.15) GeV or M _Z =(5.16±0.16) GeV, which are inconsistent with the experimental data on the π ⁺ χ _c1 invariant-mass distribution. The hidden charmed mesons Z ₁, Z ₂ or Z may be scalar hidden charmed tetraquark states, hadro-charmonium resonances or molecular states.     

Another tetraquark structure in the <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">χ</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>1</Subscript> invariant mass distribution

In this article, we assume that there exists a scalar hidden charm tetraquark state in the π ⁺ χ _c1 invariant mass distribution, and we study its mass using the QCD sum rules. The numerical result M _Z =(4.36±0.18) GeV is consistent with the mass of the Z(4250). The Z(4250) may be a tetraquark state, but other possibilities, such as a hadro-charmonium resonance and a molecular state, are not excluded.     

Near-threshold radiative 3<Emphasis Type="Italic">π</Emphasis> production in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation

We consider the π⁺π^?π₀γ final state in electron-positron annihilation at c.m.s. energies not far from the threshold. Both initial-and final-state radiations of the hard photon are considered, but without interference between them. The amplitude for the final-state radiation is obtained by using the effective Wess-Zumino-Witten Lagrangian for pion-photon interactions valid for low energies. In real experiments, energies are never so small that ρ and ω mesons would have a negligible effect. So a phenomenological Breit-Wigner factor is introduced in the final-state radiation amplitude to account for the vector mesons' influence. Using radiative 3π production amplitudes, a Monte Carlo event generator was developed which could be useful in experimental studies.     

Fine structure of the strength function for β<Superscript>+</Superscript>/<Emphasis Type="Italic">EC</Emphasis> decay of <Superscript>160<Emphasis Type="Italic">g</Emphasis></Superscript>Ho (25.6 min)

A strength function for the β⁺/EC decay of the deformed ^160g Ho (25.6 min) nucleus has been obtained from experimental data. The fine structure of the strength function S _β(E) is analyzed. It is found to have a pronounced resonant structure for Gamow-Teller transitions. In S _β(E) with μ_τ = +1 the Gamow-Teller resonance has been observed to split into two components. This splitting is associated with anisotropy of isovector density oscillation in deformed nuclei. The β⁺/EC strength function for first-forbidden transitions is obtained in the Coulomb (ξ) approximation. It is shown that S _β(E) for first-forbidden transitions does not have a pronounced resonant structure. The text was submitted by the authors in English.     

Electronic structure and ground state parameters of Ru<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript><Emphasis Type="Italic">Me</Emphasis><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Al refractory alloys

The electronic structure and ground state parameters of B2 RuAl-based refractory alloys have been investigated in the framework of the density functional theory using the exact muffin-tin orbital method in combination with the coherent potential approximation. It has been demonstrated that the number of states at the Fermi level for the Ru_{1 − x} Me _x Al alloys as a function of the alloying metal content has a minimum, which indicates a change in the Fermi surface topology and the presence of specific features in the behavior of elastic constants. It has been concluded that the electronic structure of the alloys can be described in terms of the rigid band model. The nonlinear variations of the lattice parameters of the alloys has been explained.     

Scalar mesons in <Emphasis Type="Italic">η</Emphasis>′ → <Emphasis Type="Italic">ηπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> decay

The decay η′ → ηπ ⁰ π ⁰ is studied in the framework of isobar model. It is shown, that good agreement with the experiment is achieved if α ₀- and σ-meson contributions are taken into account. The contribution of α ₀-meson is dominant, but σ-meson is necessary to reproduce the form of the Dalitz plot. Instead of the usual Breit-Wigner form of σ-meson propagator we use parametrization of the ππ-amplitude, which satisfies analyticity, crossing, unitarity and chirality constraints. This amplitude has a pole in the complex plane, which corresponds to σ-meson and describe experimental data on ππ-scattering in K _e4 decay.     

Near-threshold <Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis>-meson photoproduction on nuclei

On the basis of the first-collision model that relies on the nuclear spectral function and which includes incoherent processes involving charmonium production in proton–nucleon collisions, the photoproduction of J/ψ mesons on nuclei is considered at energies close to the threshold for their production on a nucleon. The absorption of final J/ψ mesons, their formation length, and the binding and Fermi motion of target nucleons are taken into account in this model along with the effect of the nuclear potential on these processes. The A dependences of the absolute and relative charmonium yields are calculated together with absolute and relative excitation functions under various assumptions on the magnitude of the cross section for J/ψN absorption, the J/ψ-meson formation length, and their inmedium modification. It is shown that, at energies above the threshold, these features are virtually independent of the formation length and the change in the J/ψ-meson mass in nuclear matter but are rather highly sensitive to the cross section for J/ψN interaction. The calculations performed in the present study can be used to determine the unknown cross section for J/ψ-meson absorption in nuclei from a comparison of their results with data expected from experiments in the Hall C of the CEBAF (USA) facility upgraded to the energy of 12 GeV. It is also shown that the absolute and relative excitation functions for J/ψ mesons in photon–nucleus reactions at subthreshold energies are sensitive to the change in the meson mass and, hence, carry information about the properties of charmonium in nuclear matter.     

The <Emphasis Type="Italic">A</Emphasis> dependence of <Emphasis Type="Italic">K</Emphasis><Superscript>0</Superscript> and Λ Neutrinoproduction on nuclei

The A dependence of the production of K ⁰ and Λ is investigated for the first time in neutrino-nuclear reactions using the data obtained with the SKAT bubble chamber. An exponential parametrization (∼A ^β) of the particle yields results in = 0.20 ± 0.05 for V ⁰ particles (K ⁰ and Λ), while for π ⁻ mesons the A dependence is much weaker ( = 0.068 ± 0.007). A nuclear enhancement of the ratio K ⁰/π ⁻ is found; this ratio increases from 0.055 ± 0.013 for vN interactions up to 0.070 ± 0.011 at A ≈ 21 and 0.099 ± 0.011 at A ≈ 45. It is observed that the multiplicity rise of V ⁰ occurs predominantly in the backward hemisphere of the hadronic system. It is shown that the A dependence of the Λ⁰ and π ⁻ yields can be reproduced in the framework of a model incorporating the secondary intranuclear interactions of pions originating from the primary vN interactions. The text was submitted by the authors in English.     

The nature of low-lying <Emphasis Type="Italic">K</Emphasis><Superscript><Emphasis Type="Italic">π</Emphasis></Superscript> = 0<Superscript>+</Superscript> bands in nuclei

Low-lying K ^π = 0⁺ bands are one of the most fundamental excitation modes in the spectra of deformed nuclei; however, very little is known about the nature of these excitations. We report on some new lifetime measurements using the GRID technique at ILL, and high-precision (p, t) reactions to elucidate the character of low-lying K ^π = 0⁺ bands in deformed nuclei. We also present results from a recent calculation on the nature of 0⁺ states using the projected shell model.