Analytical potential energy function for the ground state $$ (\tilde X^1 A_1 ) $$ of hydrogen isotopic D2O molecule

The present work is to construct the potential energy function of isotopic molecules. The so-called molecular potential energy function is the electronic energy function under Born-Oppenheimer approximation, in which the nuclear motions (translational, rotational and vibration motions) are not included, therefore, its nuclear vibration motion and isotopic effect need to be considered. Based on group theory and atomic and molecular reactive statics (AMRS), the reasonable dissociation limits of D₂O are determined, its equilibrium geometry and dissociation energy are calculated by density-functional theory (DFT) B3lyp, and then, using the many-body expansion method the potential energy function of D₂O is obtained for the first time. The potential contours are drawn, in which it is found that the reactive channel D + OD→D₂O has no threshold energy, so it is a free radical reaction. But the reactive channel O + DD→D₂O has a saddle point. The study of collision for D₂O is under way. Supported by the National Natural Science Foundation of China (Grant No. NSAF10676022)     

On the leptonic decay of a heavy quarkonium with a Higgs-boson emission

The leptonic () decay of a heavy quark-antiquark bound state T( Q) with a Higgs-boson H emission is investigated. Applying the low-energy theorem to meson-Higgs coupling allows one to estimate the probability of the decay T( Q) → H. Only the simple version of the Standard Model extension containing two-Higgs doublet is considered. The text was submitted by the author in English.     

Trajectory attractors for dissipative 2D Euler and Navier-Stokes equations

A trajectory attractor is constructed for the 2D Euler system containing an additional dissipation term −ru, r > 0, with periodic boundary conditions. The corresponding dissipative 2D Navier-Stokes system with the same term −ru and with viscosity v > 0 also has a trajectory attractor, . Such systems model large-scale geophysical processes in atmosphere and ocean (see [1]). We prove that → as v → 0+ in the corresponding metric space. Moreover, we establish the existence of the minimal limit of the trajectory attractors as v → 0+. We prove that is a connected invariant subset of . The connectedness problem for the trajectory attractor by itself remains open. Dedicated to the memory of Leonid Volevich Partially supported by the Russian Foundation for Basic Research (projects no 08-01-00784 and 07-01-00500). The first author has been partially supported by a research grant from the Caprio Foundation, Landau Network-Cento Volta.     

Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields

We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the superfields defined on a (4,2)-dimensional supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariance of the corresponding four (3+1)-dimensional (4D) Lagrangian density that describes the interaction between the U(1) gauge field and the charged complex scalar fields. The above 4D field theoretical model is considered on a (4,2)-dimensional supermanifold parametrized by the ordinary four space-time variables x ^μ (with μ = 0, 1, 2, 3) and a pair of Grassmannian variables θ and (with θ ² = ² = 0, θ + θ = 0). Geometrically, the (anti-)BRST invariance is encoded in the translation of the super-Lagrangian density along the Grassmannian directions of the above supermanifold such that the outcome of this shift operation is zero.      

On the LHC observation of gluinos from the Egret-preferred region

Prospects for observation of a SUSY-like signal from two gluinos are investigated within a certain region of the mSUGRA parameter space, where the cross section of the two-gluino production in pp-collisions at the LHC ( = 14 TeV) is estimated at a rather high level of 17.3 pb. In this so-called EGRET-preferred region, the lightest stable neutralinos χ ₁⁰ can serve as cold-dark-matter particles and can naturally explain the excess of diffuse Galactic gamma rays observed by the EGRET space apparatus. The -event selection relies on a clear signature when decay products of each gluino contain one b pair, one or two l pair(s) or one or two light q pair(s), and a neutralino. Rather high transverse missing energy carried away by the two neutralinos is the essential signature of the events using of which allows the relevant Standard Model background to be reduced significantly. Furthermore, distributions of the reconstructed invariant masses of two opposite-charged-lepton or light-jet pairs produced by the χ ₂⁰ → χ ₁⁰ l ⁺ l ⁻ and χ ₂⁰ → χ ₁⁰ q three-body decays have kinematic end points which measure the difference between masses of χ ₂⁰ and χ ₁⁰. In particular, it was found that these signatures of selected processes demonstrate good prospects for discovery of gluinos at the LHC. These signatures allow one to distinguish different mSUGRA parameters m _1/2 within the EGRET-preferred region (at a higher than 6σ confidence level with 300 fb⁻¹ data). The text was submitted by the authors in English.     

Neutral-meson production in <Emphasis Type="Italic">pp</Emphasis> collisions at RHIC and QCD test of <Emphasis Type="Italic">z</Emphasis> scaling

New experimental data on inclusive cross section of neutral-vector-meson (ω ⁰, ϕ, K _S ⁰) production in proton-proton collisions at = 200 GeV obtained at RHIC are analyzed in the framework of z scaling. Properties of z-presentation are used to predict hadron yields over a wide range of transverse momentum p _T and collisions energy . The next-to-leading-order perturbative QCD calculations of inclusive cross sections of π ⁰ mesons produced in pp and collisions over a wide range of and p _T are compared with ISR, S pS, RHIC data and predictions of z scaling. The dependence of the spectra in p _T and z presentations for different parton distribution and fragmentation functions is studied. The sensitivity of the obtained results to the choice of the renormalization (μ _R ), initial-state factorization (μ _F ), and final-state factorization (fragmentation) (μ _H ) scales is verified. It is shown that self-similar features of particle production dictated by the z scaling give strong restriction on the asymptotic behavior of the inclusive spectra in high-p _T region. The text was submitted by the author in English.     

On pair production of scalar top quarks in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> collisions at ILC and a possibility of their mass reconstruction

We study pair production of scalar top quarks (stop, ) in e ⁺ e ⁻ collisions with the subsequent decay of the top squarks into b quarks and charginos . We simulate this process by using PYTHIA6.4 for the beam energy 2E _b = = 350, 400, 500, 800, 1000 GeV. A set of criteria for physical variables is proposed, which provides good separation of stop signal events from top quark pair production being the main background. These criteria allow us to reconstruct the mass of the top squark with an integrated luminosity of 1000 fb⁻¹ provided that the neutralino mass is known. The article is published in the original.     

Properties of integral least squares method

A new modification of the least squares method (LSM) is proposed. The main idea is to consider the fitting parameters β _i as independent random variables with a certain distribution density F(β₁, β₂, ..., β _k ; φ₁, ..., φ _m ), which depends on a set of m experimental points φ _j . Within this approach, the estimates of the parameters minimize squared deviations and are equivalent to means of the probability distribution = = ∫β _i F(β₁, β₂, ..., β _k ; φ₁, ..., φ _m )dβ₁ dβ₂...dβ _k . Original Russian Text ? I.D. Gorlachev, B.B. Knyazev, A. Kuketayev, F.M. Pen’kov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 257–260.     

Algebrodynamics over complex space and phase extension of the Minkowski geometry

First principles should predetermine physical geometry and dynamics both together. In the “algebrodynamics” they follow solely from the properties of biquaternion algebra and the analysis over . We briefly present the algebrodynamics over Minkowski background based on a nonlinear generalization to of the Cauchi-Riemann analyticity conditions. Further, we consider the effective real geometry uniquely resulting from the structure of multiplication and found it to be of the Minkowski type, with an additional phase invariant. Then we pass to study the primordial dynamics that takes place in the complex space and brings into consideration a number of remarkable structures: an ensemble of identical correlated matter pre-elements (“duplicons”), caustic-like signals (interaction carriers), a concept of random complex time resulting in irreversibility of physical time at macrolevel, etc. In partucular, the concept of “dimerous electron” naturally arises in the framework of complex algebrodynamics and, together with the above-mentioned phase invariant, allows for a novel approach to explanation of quantum interference phenomena alternative to recently accepted wave—particle dualism paradigm. The text was submitted by the author in English.     

CP-violation and unitarity triangle test of the Standard Model

Phenomenological issues of CP violation in the quark sector of the Standard Model are discussed. We consider quark mixing in the SM, standard, and Wolfenstein parametrization of the CKM mixing matrix and unitarity triangle. We discuss the phenomenology of CP violation in K _L ⁰ and B _d ⁰()-decays. The standard unitarity triangle fit of the existing data is discussed. In appendix A we compare the K ⁰ ⇆ , B _d,s ⁰ ⇆ , etc. oscillations with neutrino oscillations. In Appendix B we derive the evolution equation for the M − system in the Weisskopf-Wigner approximation. The text was submitted by the author in English.     

Status of the investigation of the spin structure of d, 3H, and 3He at VBLHE using polarized and unpolarized deuteron beam

The investigation of the spin structure of d, ³H, and ³He has been performed at the RIKEN acceleration research facility and VBLHE. Vector A _y and tensor A _yy , A _xx , A _xz analyzing powers for d → ³Hen and d → ³Hp are presented at 270 MeV. Themirror channels (³Hen and ³Hp) are comparedto each other in order to find possible manifestation of charge-symmetry breaking. The preliminary results on the polarization observables for d → ³Hp at 200MeV are also presented. The obtained data are compared with one-nucleon-exchange calculations.As a byproduct, d → pX and ¹²C → pX breakup reactions are investigated at 140, 200, and 270MeV. The experimental data on p elastic scattering were obtained at 270, 880, and 2000 MeV at the Nuclotron. The polarization of the deuteron beam was measured at 270 MeV at the internal target station. The preliminary data on the vector A _y and tensor A _yy , A _xx analyzing powers for the p elastic scattering at 880 MeV are presented. The calculations on A _y , A _yy , and A _xx analyzing powers for the p elastic scattering at 880 MeV were performed in the framework of the multiple-scattering model. The text was submitted by the authors in English.     

Trajectory attractor of a reaction-diffusion system with a series of zero diffusion coefficients

We study a reaction-diffusion system of N equations with k nonzero and N − k zero diffusion coefficients. More exactly, the first k equations of the system contain the terms a _i Δu _i − f _j (u, v), i = 1, …, k, with the diffusion coefficient a _i > 0. The right-hand sides of the other N − k equations contain only nonlinear interaction functions −h _j (u, v), j = k + 1, …, N, with zero diffusion. Here u = (u ₁, …, u _k ) and v = (υ _k+1, …, υ _N ) are unknown concentration vectors. Under appropriate assumptions on the interaction functions f(·) and h(·), we construct the trajectory attractor of this reaction-diffusion system. We also find the trajectory attractors , δ = (δ ₁, …, δ _k ), for the analogous reaction-diffusion systems having the terms δ _j Δυ _j − h _j (u, v), j = k + 1, …, N, with small diffusion coefficients δ _j ⩾ 0 in the last N − k equations. We prove that the trajectory attractors converge to (in an appropriate topology) as δ → 0+. Dedicated to the memory of Vladimir Borovikov Partially supported by the Russian Foundation for Basic Research (projects nos. 08-01-00784 and 07-01-00500).     

Recent Beijing Spectroscopy (BES) results

Recent experimental results from Beijing Spectroscopy (BES) are reviewed, including the hadron spectroscopy from J/ψ decays, and a number of new states are found or confirmed, including σ, κ, X(1835), ωφ threshold enhancement in J/ψ→γωφ, a broad resonance in J/ψ→K ⁺ K ⁻ π ⁰, decay studies of ψ(2S) and χ _CJ , as well as the results of ψ(3770) non-D decays. The current status of BEPCII/BESIII, the major upgrade of BEPC/BESII, is also reported. Supported by the National Natural Science Foundation of China (Grant No. 10491300)     

Morphologies of solid-liquid interface and surface steps during rapid growth of BaB<Subscript>2</Subscript>O<Subscript>4</Subscript> single crystals

The evolution of solid-liquid interface during BBO single crystal growth was studied by the differential interference microscopy. And the step morphology on (0001) surface of the as-grown crystal was observed by the atomic force microscopy as well. It was found that the transition from a flat solid-liquid interface to a skeletal shape will occur in case of rapid growth. However, AFM images of surface steps revealed morphology differences correlated with crystallographic directions. The steps advancing along 〈10 0〉 direction form the step flow, whereas those steps propagating along 〈01 0〉 direction shape into step segments. Measurements of step heights by AFM indicated that it is the high anisotropy of the dimension of growth unit and step bunching due to the enlargement of concentration difference along the surface that results in the anisotropy of step morphologies. Supported by the National Natural Science Foundation of China (Grant No. 50331040) and the Innovation Funds from Shanghai Institute of Ceramics, Chinese Academy of Sciences (Grant No. SCX0623)     

Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph

For the kernel of the Laplace operator Δ^Λ with potential Σ _j=1 ^k c _j δ _{q j} (x) on a manifold, (the operator is given by a Lagrangian plane Λ ⊂ ℂ ^k ⊕ ℂ ^k ), an isomorphism Γ: ker Δ^Λ → Λ ∩ L is described, where L is a special Lagrangian plane (whose explicit form is evaluated). A similar assertion holds for the Laplace operator on a decorated graph; for such a graph (obtained by decorating a connected finite graph with n edges and v vertices) with “continuity” conditions, the inequality 1 ≤ dimker ≤ n − v + 2 is obtained. It is also proved that the quantity n − v + 1-dim ker cannot reduce when adding new edges and manifolds. The first terms of the expansion of Tr(exp(-tH ^Λ)) are found. Dedicated to the memory of V. A. Geyler     

Quasi-elliptic and weakly coercive systems in Sobolev spaces of vector functions

The purpose of this paper is to investigate a connection between l-quasi-ellipticity and weak coercivity of systems acting on the spaces of vector functions Π (ℝ ⁿ ). Moreover, we extend some of our earlier results to the matrix case. We also show that an l-quasielliptic system in the sense of O. V. Besov is q-quasi-elliptic in the sense of L. R. Volevich. Dedicated to the blessed memory of L. R. Volevich, an outstanding mathematician     

Effect of spin fluctuations on the superconducting phase of Hubbard fermions in the t-t′-t″-J* model

The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components $ P_{0\sigma ,\bar \sigma 0} The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components of strength operator . It is shown that spinfluctuation scattering processes in the one-loop approximation for the t-t′-t″-J* model taking into account long-range hoppings and three-center interactions are reflected by normal (P _{0σ, 0σ}) and anomalous () components of the strength operator. Three-center interactions result in different renormalizations of the kernels of the integral equations for the superconducting d phase in the expressions for the self-energy and strength operators. In this approximation for the d-type symmetry of the order parameter for the superconducting phase, the system of integral equations is reduced to a system of nonhomogeneous equations for amplitudes. The resultant dependences of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and spin-fluctuation processes leads to strong renormalization of the superconducting phase region. Original Russian Text ? V.V. Val’kov, A.A. Golovnya, 2008, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 6, pp. 1167–1180.     

Charmed meson rescattering in the reaction $$ \bar pd \uparrow \bar DDN $$

We examine the possibility to extract information about the DN and interactions from the reaction. We utilize the notion that the open-charm mesons are first produced in the annihilation of the antiproton on one nucleon in the deuteron and subsequently rescatter on the other (the spectator) nucleon. The latter process is then exploited for investigating the DN and interactions. We study different methods for isolating the contributions from the D ⁰ p and D ⁻ p rescattering terms.     

Torelli Theorem for the Deligne–Hitchin Moduli Space

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let denote the corresponding Deligne–Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on X.