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.     

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.     

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.     

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.     

Production of triply charmed Ω<Subscript>ccc</Subscript> baryonsin <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation

The total and differential cross sections for the production of triply charmed Ω_ccc baryons in e⁺e^? annihilation are calculated at the Z-boson pole.     

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.     

Investigation of the process <Emphasis Type="Italic">J/ψ</Emphasis> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> with the KEDR detector

The product of the electron width of the J/ψ meson and the probability for its decay to an electron-positron pair was measured by using data from the KEDR experiment at the VEPP-4M electron-positron collider. The result was Γ _ee × Γ _ee /Γ = 0.3392 ± 0.0068(stat.) ± 0.0063(syst.) keV.     

Contribution of final-state interaction to the branching ratio of <Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis><Emphasis Type="Italic">D</Emphasis>

To test the validity of perturbative QCD (pQCD) and investigate its range of application, one should look for a suitable process. B→J/ψ D is a promising candidate. The linear momentum of the products is relatively small, so that there may exist a region where exchanged gluons are soft and the perturbative treatment may fail, so that the non-perturbative effect would be significant. We attribute such non-perturbative QCD effects to the long-distance final-state interaction (FSI) which is estimated in this work. We find that the contribution from the FSI to the branching ratio is indeed sizable and may span the rather wide range of 10⁻⁶∼10⁻⁵ and cover a region where the pQCD prediction is of the same order. A more accurate measurement of its branching ratio may provide important information about the application region of pQCD and help to clarify the picture of inelastic rescattering (i.e. FSI), which is generally believed to play an important role in B decays.     

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.     

Static spherically symmetric solution of (<Emphasis Type="Italic">R</Emphasis> ± <Emphasis Type="Italic">μ</Emphasis><Superscript>4</Superscript>/<Emphasis Type="Italic">R</Emphasis>) gravity

The static spherically symmetric solution for R ± μ ⁴/R model of f(R) gravity is investigated. We obtain the metric for space-time in the solar system that reduces to the Schwarzschild metric, when μ tends to zero. For the obtained metric, the deviation from Einstein gravity is very small. This result is different from the other results have been obtained by equivalence between f(R) gravity and scalar tensor theory. Also it is shown that the vacuum solution in the solar system depends on the shape of matter distribution which differ from the Einstein’s gravity.     

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.     

Process <Emphasis Type="Italic">γ</Emphasis>*<Emphasis Type="Italic">γ</Emphasis> → <Emphasis Type="Italic">σ</Emphasis> at large virtuality of <Emphasis Type="Italic">γ</Emphasis>*

The process γ*γ → σ is investigated in the framework of the SU(2)×SU(2) chiral NJL model. The form factor of the process is derived for arbitrary virtuality of γ* in the Euclidean kinematic domain. The asymptotic behavior of this form factor resembles the asymptotic behavior of the γ*γ → π form factor.     

Rare radiative leptonic decays <Emphasis Type="Italic">B</Emphasis><Stack><Subscript>d,s</Subscript><Superscript>0</Superscript></Stack> → ℓ<Superscript>+</Superscript>ℓ<Superscript>−</Superscript><Emphasis Type="Italic">γ</Emphasis>

The rare radiative leptonic decays \(\bar B_{d,s}^0 \to \ell ^ + \ell ^ - \gamma \) are studied. The contributions to the respective amplitude from the emission of photons from the quark loop, bremsstrahlung from leptons, and weak-annihilation effects are taken into account in relevant calculations. Results are presented for the partial widths and distributions of leptons in the final state. It is shown that the previously disregarded contributions of vector resonances associated with virtual-photon emission from the light valence quark of the B meson have a significant effect on the mass spectra of dileptons.     

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.     

One-loop electro-weak corrections to three-jet observables of <Emphasis Type="Italic">b</Emphasis>-quarks <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilations

We compute the full one-loop EW contributions of entering the electron–positron into two b-quarks and one gluon cross section at the Z peak and LC energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W ^± and Z bosons. Their importance for the measurement of α _S from jet rates and shape variables is explained qualitatively and illustrated quantitatively. Their impact on the forward–backward asymmetry is also analysed. Work supported in part by the U.K. Science and Technology Facilities Council (STFC), by the European Union (EU) under contract MRTN-CT-2006-035505 (HEPTOOLS FP6 RTN) and by the Italian Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) under contract 2006020509_004. An erratum to this article can be found at     

One-loop electro-weak corrections to three-jet observables of <Emphasis Type="Italic">b</Emphasis>-quarks <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilations

We compute the full one-loop EW contributions of \({\mathcal{O}}(\alpha_{\mathrm{S}}\alpha_{\mathrm{EM}}^{3})\) entering the electron–positron into two b-quarks and one gluon cross section at the Z peak and LC energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W ^± and Z bosons. Their importance for the measurement of α _S from jet rates and shape variables is explained qualitatively and illustrated quantitatively. Their impact on the forward–backward asymmetry is also analysed.