The Semileptonic Decay Modes {\bar{B} \rightarrow D\ell \bar{\nu}} and {\bar{B}_{s} \rightarrow D_{s} \ell \bar{\nu}}: A New Analysis in Potential Model

We consider the Schrödinger equation with a combination of Deng–Fan-type and harmonic terms. To solve the corresponding differential equation, we split the equation to two parts: the parent and the perturbation terms. We use the Nikiforov–Uvarov technique to solve the parent part. For the perturbation part, we apply the series expansion method. Next, using the calculated wave function, we investigate some bottom and charm mesons within the Isgur–Wise function formalism. We present especially semileptonic \({\bar{B} \rightarrow D\ell \bar{\nu}}\) and \({\bar{B}_{s} \rightarrow D_s \ell \bar{\nu }}\) decay widths, branching ratios and \({|V_{cb}|}\) (element of the CKM matrix). Masses of some pseudoscalar mesons are also indicated. Comparisons of our results with experimental values and other approaches are included.     

NNLO corrections to \bar{B}\to X_{u}\ell \bar{\nu}_{\ell} and the determination of |V ub |

We study the impact of next-to-next-to-leading order (NNLO) QCD corrections on partial decay rates in $\bar{B}\to X_{u}\ell \bar{\nu}_{\ell}$ decays, at leading-order in the 1/m _b expansion for shape-function kinematics. These corrections are implemented within a modified form of the BLNP framework, which allows for arbitrary variations of the jet scale μ _i ～1.5 GeV. Our analysis includes a detailed comparison between resummed and fixed-order perturbation theory, and between the complete NNLO results and those obtained in the large-β ₀ approximation. For the default choice μ _i =1.5 GeV used in current extractions of |V _ub | within the BLNP framework, the NNLO corrections induce significant downward shifts in the central values of partial decay rates with cuts on the hadronic variable P ₊, the hadronic invariant mass, and the lepton energy. At the same time, perturbative uncertainties are reduced, especially those at the jet scale, which are the dominant ones at next-to-leading order (NLO). For higher values of μ _i and in fixed-order perturbation theory, the shifts between NLO and NNLO are more moderate. We combine our new results with known power-suppressed terms in order to illustrate the implications of our analysis on the determination of |V _ub | from inclusive decays.     

Contribution of vector resonances to the \bar{B}_{d}^{0}\to\bar {K}^{*0}\mu^{+}\mu^{-} decay

The fully differential angular distribution for the rare flavor-changing neutral current decay $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) \mu^{+}\mu^{-} $ is studied. The emphasis is placed on accurate treatment of the contribution from the processes $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) V $ with intermediate vector resonances V=??(770),??(782),?(1020),J/??,??(2S),?? decaying into the ?? ⁺ ?? ^? pair. The dilepton invariant-mass dependence of the branching ratio, longitudinal polarization fraction f _L of the $\bar{K}^{*0}$ meson, and forward?Cbackward asymmetry A _FB is calculated and compared with data from Belle, CDF and LHCb. It is shown that inclusion of the resonance contribution may considerably modify the branching ratio, calculated in the SM without resonances, even in the invariant-mass region far from the so-called charmonia cuts applied in the experimental analyses. This conclusion crucially depends on values of the unknown phases of the B ⁰??K ^?0 J/?? and B ⁰??K ^?0 ??(2S) decay amplitudes with zero helicity.     

(Q\bar{q}) \to \ell \widetilde{v} _\ell decay constant in the covariant simultaneous approach

In the framework of the covariant simultaneous approach in quantum field theory, an expression is obtained for the decay constant of the decay bound state of quark and antiquark of different masses into a lepton pair.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 101–103, February, 1992.     

Tau Leptonic Decay τ→lVlVτ in Littlest Higgs Model＊

We consider the τ leptonic decay $\tau\rightarrow l\bar{\nu}_{l}\nu_{\tau}$ in the framework of the littlest Higgs (LH) model and calculate the corrections of new particles to this decay. We find that the contributions of the charged scalars can be safely ignored and the LH model is in perfect agreement with the universality of the couplings of the SU gauge bosons to the leptonic charged currents. The corrections of the LH model to the τ leptonic decay $\tau\rightarrow l\bar{\nu}_{l}\nu_{\tau}$ are not sensitive to the parameter c, but depend strongly on the parameters f and x. The precision measured data about the τ leptonic decay demand that the parameter f approximately equal 3.5 TeV and x>0.1, while agree with the general expectation based on other phenomenological explorations.     

An $${n = \left( {1,1} \right)}$$ Super-Toda Model Based on OSp $$1|{\kern 1pt} 4$$

We show that a Hamiltonian reduction of affine Lie superalgebras having bosonic simple roots (such as OSp ) does produce supersymmetric Toda models, with superconformal symmetry being nonlinearly realized for those fields of the Toda system which are related to the bosonic simple roots of the superalgebra. A fermionic b-c system of conformal spin is a natural ingredient of such models.     

Theoretical study of collision and collision-free radiative lifetimes of {{\text{S}}_2}\left( {{{\text{B}}^3}\Sigma_{\text{u}}^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right)

We calculate multireference configuration-interaction wavefunctions and the potential-energy curves for the $ {B^3}\Sigma_u^{-} $ and $ {X^3}\Sigma_g^{-} $ states of the collision-free S₂ molecule and the T-shape collision complex S₂?CHe using cc-pVQZ basis sets. We obtain the transition dipole moments of the $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \to {X^3}\Sigma_g^{-} } \right) $ and the Franck?CCondon factors between the vibrational levels of this two states. We evaluate the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ levels of the collision complex and the collision-free molecule and compare them with the experiments. The collision provides little change in the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ according to the previous calculations. We obtain excellent agreement between the theoretical results and the experiments. The data calculated are very useful in the study of the microwave-driven high-pressure sulfur lamp and an S₂ laser pumped by a transverse fast discharge.     

Resolved shear stress of Zn single crystals deformed in (0001)\left\langle {11\bar 20} \right\rangle system

Resolved shear stress (RSS) in basal slip system in Zn, ZnAg 0·2 at. % and ZnGa 0·2 at. % crystals was investigated in the temperature range from 4·2 K to 515 K. The TEM observations of the dislocation structure were also performed. At low temperatures an anomaly was observed, i.e. decrease and subsequent increase of RSS in the range of 4·2 K to 77 K. This effect may result from other properties of the dislocations at low temperatures like those suggested by Wille and Schwink (1985) and based on the zero-point vibrations of dislocations theory.     

Photonic decays involving the2^{ + + } \left( {\bar bb} \right): Partial widths and jets from tensor meson dominance

Tensor meson dominance combined with vector meson dominance, QCD-potentials and the experimental leptonic widths of Γ and Γ′ predicts $$\Gamma _{\Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right)} = 2.8keV$$ and $$\Gamma _{2^{ + + } \left( {\bar bb} \right) \to \gamma \Upsilon \left( {9.46} \right)} = 134keV.$$ The angular distributions of the γ and the jetsj resulting from the decays $$e^ + e^ - \to \Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right) \to \gamma gg \to \gamma jj$$ and $$e^ + e^ - \to \Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right) \to \gamma \bar qq \to \gamma jj$$ with massless vector gluonsg, (coupled gauge invariantly) and quarksq are uniquely determined in TMD. The result for the first process agrees with that of perturbative QCD. No perturbative QCD-prediction for the latter is known.     

Lasing of optically pumped XeF and analysis of the spectrum of the laser transitionB^2 \sum _{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^ + - X^2 \sum _{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^ +

The operating principle of a photodissociation XeF laser (λ?350 nm) is discussed. A laser operating on the gas mixture XeF₂:N₂(SF₆):Ar pumped by radiation from an open high-current discharge is described. The maximum lasing duration is 5 μsec, the maximum output energy is 0.15 J. The vibrational structure of the XeF-molecule transition B²Σ_1/2 ⁺ ? X²Σ_1/2 ⁺, observed in absorption, luminescence, and stimulated emission, is investlgated. The vibrational quantum and the anharmonicity in the upper and lower states are measured: ω_e ^' = 308.7 cm^-1, ω_e ^'x_e ^' = 1.44 cm^-1, ω_e ^'' = 225.7 cm^-1, ω_e ^''x_e ^'' = 11.0 cm^-1. The difference between the equilibrium internuclear distances of the XeF molecule is determined for the excited (B) and ground (X) states, namely r_e ^' - r_e ^'' = 0.33 +- 0.01 Å.     

Off-peak inclusive J/ψ and associated {J \mathord{\left/ {\vphantom {J \psi }} \right. \kern-\nulldelimiterspace} \psi } + c + \bar c and J/ψ+η c production in e + e − annihilation at BELLE

We consider the inclusive and associated production of J/ψ mesons under BELLE conditions. In the framework of QCD perturbation theory and nonrelativistic bound-state formalism, the different production mechanisms are analyzed in detail. The calculations are compared with recent experimental data, and significant disagreement is found in a few cases. For these channels, the predictions of a nonperturbative model are also explored. We find that the J/ψ polarization has a strong dependence on the production dynamics, so that it may serve as a sensitive indicator in future experimental studies.