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.     

Lepton decay channels of egret gluinos at the LHC

Prospects for observing 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) via gluon-gluon fusion (gg → ) is estimated at a rather high level of 17.3 pb. In this so-called EGRET region, the lightest stable neutralinos can serve as cold dark matter particles and are natural explanations of the excess of diffuse galactic gamma rays observed by the EGRET space apparatus. The -event selection relies on a very clear signature when decay products of each gluino contain one b-anti-b pair, one or two lepton-antilepton pair(s) and a neutralino. Rather high transverse-missing energy, carried away by the two neutralinos, is an essential signature of the events and also allows the relevant Standard Model background to be reduced significantly. In particular, it was found that the clear signatures of the selected processes demonstrate good prospects discovering the EGRET gluinos at the LHC. Furthermore, these signatures allow one to distinguish different mSUGRA parameters m _1/2 inside the EGRET region. The text was submitted by the authors 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.     

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.     

On the two-loop $$ \ma thcal{O} $$( αs2) correc tions to the pole mass of the t quark in the MSSM

The paper is devoted to the calculation of two-loop (α _s ²) MSSM corrections to the relation between the pole mass of the t quark and its running mass in the scheme. Firstly, the value of the second-order contribution from large-mass expansion in mt/M _SUSY is studied. Contrary to our expectations, this contribution turned out to be negligible. As a by-product of this calculation, the two-loop anomalous dimension of the running quark mass is obtained in the supersymmetric QCD. Secondly, the influence of the two-loop corrections to the t-quark mass on the predicted superpartner masses is investigated. The text was submitted by the authors in English.     

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.     

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.     

Analyzing powers in the 12C( \vec d ,p)13C reaction at the energy T d = 270 MeV

The preliminary results on the tensor T₂₀ analyzing power for the ¹²C(,p)¹³C* reaction with the excitation of ¹³C levels and the d(,p)X reaction at the energies T _d = 140, 200 and 270 MeV at the emission angle Θ _cm = 0° are presented. The data on the tensor A _yy and vector A _y analyzing powers for the ¹²C(,p)¹³C* reaction at the energy T _d = 270 MeV in the angular range from 4° to 18° in the laboratory are also obtained.     

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.     

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.     

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.     

The small axial charge of the N(1535)-resonance

There is a natural cancellation between the contributions of the qqq and qqqq components to the axial charge of the N(1535)-resonance. While the probability of the former is larger than that of the latter, its coefficient in the axial charge expression is exceptionally small. The magnitude of two of the corresponding coefficients of the qqqq components is in contrast large and has the opposite sign. This result provides a phenomenological illustration of the recent unquenched lattice calculation result that the axial charge of the N(1535)-resonance is very small, if not vanishing (T.T. Takahashi, T. Kunihiro, arXiv: 0801.4707 [hep-lat]). The result sets an upper limit on the magnitude of the probability of qqqq components as well.     

Identifying functions determined by linear functional operators

The new identifying problem is formulated for general linear functional operators F = Σc _j F ○ a _j which significantly generalizes in particular the well-known Ulam stability problem. The results obtained can be very useful when processing experimental data of any kind as they enable to determine with high precision the structure of a compactly supported Banach-valued function F by using a rather restricted information concerning F. Dedicated to the memory of Leonid Volevich     

Feynman-Kac and feynman formulas for evolution pseudodifferential equations in superspace

In the paper, evolution pseudodifferential equations in the space of superanalytic functions (X) of an infinite-dimensional argument with symbols in the space (Y) of Fourier supertransforms of distributions on the dual superspace are considered. For these equations, the “weak” Cauchy problem is posed and the existence theorem for the solutions of this problem is proved. The main result of the paper is the theorem concerning the representation of solutions of the “weak” Cauchy problem by the Feynman path integral in the phase superspace (the Feynman-Kac formula). The Feynman integral is understood in the sequential sense. Thus, the Feynman formula becomes an immediate consequence of the Feynman-Kac formula.     

Inhomogeneous symbols, the Newton polygon, and maximal L p -regularity

We prove a maximal regularity result for operators corresponding to rotation invariant symbols (in space) which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary-value problems. The result is obtained by extending the Newton polygon approach to variables living in complex sectors and combining it with abstract results on the -calculus and -bounded operator families. As an application, we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson correction. Dedicated to the memory of Leonid Romanovich Volevich     

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)     

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.     

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     

Weak gravitational field and Coriolis potential

In mechanics of the mass point passage from one frame of reference to another moving with velocity consists in subtracting this vector from the velocity of the particle. In general case the vector is not constant, as, for example, when passing through a rotating frame, this operation creates inertial forces. Analysis of this phenomenon from the point of view of Lagrangian and Hamiltonian mechanics is interesting from the general relativistic point of view due to Einstein’s principle of equivalence. We show that the vector plays the role of vector potential which, however, essentially differs from vector potential known in classical electrodynamics. Comparative analysis of the two kinds of vector potentials is completed.