Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar D^*[`(D)]<sup>*</sup>{D}^{\ast}{\bar {D}}^{\ast}, D<sub>s</sub><sup>*</sup>[`(D)]_s^*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B^*[`(B)]<sup>*</sup>{B}^{\ast}{\bar {B}}^{\ast} and B<sub>s</sub><sup>*</sup>[`(B)]_s^*{B}_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about (250–500) MeV above the corresponding D ^*–[`(D)]<sup>*</sup>{\bar{D}}^{\ast}, D <sub>s</sub> <sup>*</sup>–[`(D)]_s^*{\bar {D}}_{s}^{\ast}, B ^*–[`(B)]<sup>*</sup>{\bar{B}}^{\ast} and B <sub>s</sub> <sup>*</sup>–[`(B)]_s^*{\bar {B}}_{s}^{\ast} thresholds, the Y(4140) is unlikely a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state. The scalar D<sup>*</sup>[`(D)]^*D^{\ast}{\bar{D}}^{\ast}, D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B<sup>*</sup>[`(B)]^*B^{\ast}{\bar{B}}^{\ast} and B_s^*[`(B)]<sub>s</sub><sup>*</sup>B_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states maybe not exist, while the scalar D￠<sup>*</sup>[`(D)]^￠*{D'}^{\ast}{\bar{D}}^{\prime\ast}, D_s^￠*[`(D)]<sub>s</sub><sup>￠*</sup>{D}_{s}^{\prime\ast}{\bar{D}}_{s}^{\prime\ast}, B<sup>￠*</sup>[`(B)]^￠*{B}^{\prime\ast}{\bar{B}}^{\prime\ast} and B_s^￠*[`(B)]_s^￠*{B}_{s}^{\prime\ast}{\bar{B}}_{s}^{\prime\ast} molecular states maybe exist.     

Chiral color quark symmetry and possible constraints on the <Emphasis Type="Italic">G</Emphasis>′-boson mass from tevatron and LHC data

A gauge model featuring a chiral color symmetry of quarks was considered, and possible manifestations of this symmetry in proton-antiproton and proton-proton collisions at the Tevatron and LHC energies were studied. The cross section s_{t[`(t)]</sub>\sigma _{t\bar t} for the production of t[`(t)]t\bar t quark pairs at the Tevatron and the forward-backward asymmetry A_FB<sup>p[`(p)]</sup>A_{FB}^{p\bar p} in this process were calculated and analyzed with allowance for the contributions of the G′-boson predicted by the chiral color symmetry of quarks, the G′-boson massm <sub>G′</sub> and the mixing angle θ <sub>G</sub> being treated as free parameters of the model. Limits on m <sub>G′</sub> versus θ <sub>G</sub> were studied on the basis of data from the Tevatron on s<sub>t[`(t)]}\sigma _{t\bar t} and A_FB^p[`(p)]A_{FB}^{p\bar p}, and the region compatible with these data within one standard deviation was found in the m _G′-θ _G plane. The region ofm _G′-mass values that is appropriate for observing the G′-boson at LHC is discussed.     

A new approach to diffusion-limited reaction rate theory

A new approach to the diffusion-limited reaction rate theory is developed on the base of a similar approach to consideration of Brownian coagulation, recently proposed by the author. The traditional diffusion approach to calculation of the reaction rate is critically analyzed. In particular, it is shown that the traditional approach is applicable only to the special case of reactions with a large reaction radius, [`(r)]<sub>A</sub> << R<sub>AB</sub> << [`(r)]_B\bar r_A \ll R_{AB} \ll \bar r_B (where [`(r)]<sub>A</sub>\bar r_A, [`(r)]_B\bar r_B are the mean interparticle distances), and becomes inappropriate to calculation of the reaction rate in the case of a relatively small reaction radius, R_AB << [`(r)]<sub>A</sub>R_{AB} \ll \bar r_A, [`(r)]_B\bar r_B. In the latter, most general case particles collisions occurmainly in the kinetic regime (rather than in the diffusion one) characterized by a homogeneous (at random) spatial distribution of particles. Homogenization of particles distribution occurs owing to particles diffusion mixing on the length scale of the mean interparticle distance with the characteristic diffusion time being small in comparison with the characteristic reaction time. The calculated reaction rate for a small reaction radius in 3D formally (and casually) coincides with the expression derived in the traditional approach for reactions with a large reaction radius, however, notably deviates at large times from the traditional result in the plane (2D) geometry.     

Analysis of the X(1835) and related baryonium states with Bethe-Salpeter equation

In this article, we study the mass spectrum of the baryon-antibaryon bound states p [`(p)] \bar{{p}} , S \Sigma [`(S)] \bar{{\Sigma}} , X \Xi [`(X)] \bar{{\Xi}} , L \Lambda [`(L)] \bar{{\Lambda}} , p [`(N)] \bar{{N}}(1440) , S \Sigma [`(S)] \bar{{\Sigma}}(1660) , X \Xi [`(X)]<sup>￠</sup> \bar{{\Xi}}^{{\prime}}_{} and L \Lambda [`(L)] \bar{{\Lambda}}(1600) with the Bethe-Salpeter equation. The numerical results indicate that the p [`(p)] \bar{{p}} , S \Sigma [`(S)] \bar{{\Sigma}} , X \Xi [`(X)] \bar{{\Xi}} , p [`(N)] \bar{{N}}(1440) , S \Sigma [`(S)] \bar{{\Sigma}}(1660) , X \Xi [`(X)]^￠ \bar{{\Xi}}^{{\prime}}_{} bound states maybe exist, and the new resonances X(1835) and X(2370) can be tentatively identified as the p [`(p)] \bar{{p}} and p [`(N)] \bar{{N}}(1440) (or N(1400)[`(p)] \bar{{p}} bound states, respectively, with some gluon constituents, and the new resonance X(2120) may be a pseudoscalar glueball. On the other hand, the Regge trajectory favors identifying the X(1835) , X(2120) and X(2370) as the excited h^￠ \eta^{{\prime}}_{}(958) mesons with the radial quantum numbers n = 3 , 4 and 5, respectively.     

Features of the crystal structure of disperse carbides in alpha titanium

Investigations of disperse nonmetallic inclusions in unalloyed alpha titanium VT1-0 have been performed by using transmission electron (including scanning and high-resolution) microscopy. Characteristic electron energy losses spectroscopy has shown that these inclusions are titanium carbide particles. It has been revealed that the disperse carbides are formed in the titanium hcp matrix as a phase based on the fcc sublattice of titanium atoms. The inclusion–matrix orientation relationship corresponds to the well-known Kurdyumov–Sachs and Nishiyama–Wassermann relationships [ 2[`11] 0 ]<sub>\upalpha</sub> ||[ 011 ]<sub>\updelta</sub> \text and ( 000[`1] )_\upalpha ||( 1[`1] 1 )_\updelta {\left[ {2\overline {11} 0} \right]_{{\upalpha }}}\parallel {\left[ {011} \right]_{{\updelta }}}{\text{ and }}{\left( {000\overline 1 } \right)_{{\upalpha }}}\parallel {\left( {1\overline 1 1} \right)_{{\updelta }}} .     

Spin correlations of \varLambda[`\varLambda]\varLambda{\bar{\varLambda}} pairs as a probe of quark–antiquark pair production

The polarizations of Λ and [`\varLambda]{\bar{\varLambda}} are thought to retain memories of the spins of their parent s quarks and [`(s)]{\bar{s}} antiquarks, and are readily measurable via the angular distributions of their daughter protons and antiprotons. Correlations between the spins of Λ and [`\varLambda]{\bar{\varLambda}} produced at low relative momenta may therefore be used to probe the spin states of s [`(s)]s {\bar{s}} pairs produced during hadronization. We consider the possibilities that they are produced in a ³P₀ state, as might result from fluctuations in the magnitude of á[`(s)] s ?\langle {\bar{s}} s \rangle, a <sup>1</sup>S<sub>0</sub> state, as might result from chiral fluctuations, or a <sup>3</sup>S<sub>1</sub> or other spin state, as might result from production by a quark–antiquark or gluon pair. We provide templates for the p [`(p)]p {\bar{p}} angular correlations that would be expected in each of these cases, and discuss how they might be used to distinguish s [`(s)]s {\bar{s}} production mechanisms in pp and heavy-ion collisions.     

Production of the P-wave excited Bc-states through the Z0 boson decays

In Deng et al. (Eur. Phys. J. C 70:113, 2010), we have dealt with the production of the two color-singlet S-wave (c[`(b)])(c\bar{b})-quarkonium states B<sub>c</sub>(|(c[`(b)])₁[¹S₀]?)B_{c}(|(c\bar {b})_{\mathbf{1}}[^{1}S_{0}]\rangle) and B^*_c(|(c[`(b)])<sub>1</sub>[<sup>3</sup>S<sub>1</sub>]?)B^{*}_{c}(|(c\bar{b})_{\mathbf{1}}[^{3}S_{1}]\rangle) through the Z <sup>0</sup> boson decays. As an important sequential work, we make a further discussion on the production of the more complicated P-wave excited (c[`(b)])(c\bar{b})-quarkonium states, i.e. |(c[`(b)])<sub>1</sub>[<sup>1</sup>P<sub>1</sub>]?|(c\bar{b})_{\mathbf{1}}[^{1}P_{1}]\rangle and |(c[`(b)])₁[³P_J]?|(c\bar{b})_{\mathbf{1}}[^{3}P_{J}]\rangle (with J=(1,2,3)). More over, we also calculate the channel with the two color-octet quarkonium states |(c[`(b)])<sub>8</sub>[<sup>1</sup>S<sub>0</sub>]g?|(c\bar{b})_{\mathbf{8}}[^{1}S_{0}]g\rangle and |(c[`(b)])₈[³S₁]g?|(c\bar{b})_{\mathbf{8}}[^{3}S_{1}]g\rangle, whose contributions to the decay width maybe at the same order of magnitude as that of the color-singlet P-wave states according to the naive nonrelativistic quantum chromodynamics scaling rules. The P-wave states shall provide sizable contributions to the B _c production, whose decay width is about 20% of the total decay width \varGamma _{Z⁰? Bc}\varGamma _{Z^{0}\to B_{c}}. After summing up all the mentioned (c[`(b)])(c\bar {b})-quarkonium states’ contributions, we obtain \varGamma _{Z⁰? Bc}=235.9^+352.8_-122.0\varGamma _{Z^{0}\to B_{c}}=235.9^{+352.8}_{-122.0} KeV, where the errors are caused by the main sources of uncertainty.     

The Combined Effect of Connectivity and Dependency Links on Percolation of Networks

Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity and dependency links. This formalism was applied to study Erdős-Rényi (ER) networks that include also dependency links. For an ER network with average degree [`(k)]\bar{k} that is composed of dependency clusters of size s, the fraction of nodes that belong to the giant component, P <sub>∞</sub>, is given by P<sub>￥</sub>=p<sup>s-1</sup>[1-exp(-[`(k)]pP_￥) ]^sP_{\infty}=p^{s-1}[1-\exp{(-\bar{k}pP_{\infty})} ]^{s} where 1−p is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks and find a formula for the size of the giant component in the percolation process: P _∞=p ^s−1(1−r ^k ) ^s where r is the solution of r=p ^s (r ^k−1−1)(1−r ^k )+1, and k is the degree of the nodes. These general results coincide, for s=1, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to s=1, where the percolation transition is second order, for s>1 it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency clusters, removal of even a finite number (zero fraction) of the infinite network nodes will trigger a cascade of failures that fragments the whole network. Specifically, for any given s there exists a critical degree value, [`(k)]<sub>min</sub>\bar{k}_{\min}, such that an ER network with [`(k)] ￡ [`(k)]_min\bar{k}\leq \bar{k}_{\min} is unstable and collapse when removing even a single node. This result is in contrast to RR networks where such cascades and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network.     

The Third Order Helicity of Magnetic Fields via Link Maps

We introduce an alternative approach to the third order helicity of a volume preserving vector field B, which leads us to a lower bound for the L ²-energy of B. The proposed approach exploits correspondence between the Milnor [`(m)]<sub>123</sub>{\bar{\mu}_{123}} -invariant for 3-component links and the homotopy invariants of maps to configuration spaces, and we provide a simple geometric proof of this fact in the case of Borromean links. Based on these connections we develop a formulation for the third order helicity of B on invariant unlinked domains of B, and provide Arnold’s style ergodic interpretation of this invariant as an average asymptotic [`(m)]₁₂₃{\bar{\mu}_{123}} -invariant of orbits of B.     

The Transformations from the New Intermediate Entangled State

The new intermediate entangled state |η;θ〉 is proposed by virtue of IWOP technique, which is the common eigenvector of [([^(x)]₁ - [^(x)]₂)cosq-([^(p)]₁ - [^(p)]₂)sinq][(\hat{x}_{1} - \hat{x}_{2})\cos\theta -(\hat{p}_{1} - \hat{p}_{2})\sin\theta ] and [([^(x)]₁ +[^(x)]₂)sinq+ ([^(p)]₁ + [^(p)]₂)cosq][(\hat{x}_{1} +\hat{x}_{2})\sin\theta + (\hat{p}_{1} + \hat{p}_{2})\cos\theta ]. The squeezing transformation operator, Hadamard transformation operator, Fresnel transformation operator and Radon transform operator are constructed by |η;θ〉.     

Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) with QCD sum rules

In this article, we assume that there exists a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state in the J/ψ φ invariant mass distribution, and we study its mass using the QCD sum rules. The predictions depend heavily on the two criteria (pole dominance and convergence of the operator product expansion) of the QCD sum rules. The value of the mass is about M<sub>Ds<sup>*</sup>[`(D)]s^*</sub>=(4.43±0.16)M_{D_{s}^{\ast}{\bar{D}}_{s}^{\ast}}=(4.43\pm0.16)  GeV, which is inconsistent with the experimental data. The D_s^*[`(D)]_s^*D_{s}^{\ast}{\bar{D}}_{s}^{\ast} is probably a virtual state and is not related to the meson Y(4140). Another possibility, such as a hybrid charmonium, is not excluded.     

Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Light flavor asymmetry of nucleon sea

The light flavor antiquark distributions of the nucleon sea are calculated in the effective chiral quark model and compared with experimental results. The contributions of the flavor-symmetric sea-quark distributions and the nuclear EMC effect are taken into account to obtain the ratio of Drell–Yan cross sections σ ^pD/2σ ^pp, which can match well with the results measured in the FermiLab E866/NuSea experiment. The calculated results also match the [`(d)](x)-[`(u)](x)\bar{d}(x)-\bar{u}(x) measured in different experiments, but unmatch the behavior of [`(d)](x)/[`(u)](x)\bar{d}(x)/\bar{u}(x) derived indirectly from the measurable quantity σ ^pD/2σ ^pp by the FermiLab E866/NuSea Collaboration at large x. We suggest to measure again [`(d)](x)/[`(u)](x)\bar{d}(x)/\bar{u}(x) at large x from precision experiments with careful treatment of the experimental data. We also propose an alternative procedure for experimental data treatment.     

Activation energy and conductivity of glasses in the P2O5–V2O5–Li2O system

The conductivity of glasses in the 50\textP_\text2 \textO_\text5 - x\textV_\text2 \textO_\text5 - ( 50 - x )\textLi_\text2 \textO50{\text{P}}_{\text{2}} {\text{O}}_{\text{5}} - x{\text{V}}_{\text{2}} {\text{O}}_{\text{5}} - \left( {50 - x} \right){\text{Li}}_{\text{2}} {\text{O}} system was studied as a function of temperature and composition. For all compositions, the conductivity variation as a function of temperature followed an Arrhenius type relationship. Isothermal variation of conductivity as a function of composition showed a minimum for a molar ratio x near 20. Probable mechanisms for decrease of conductivity with decrease of vanadium oxide concentration were explained. The minimum in room temperature was attributed to increase of V⁴⁺/V⁵⁺ with decrease of vanadium oxide in specific concentrations of vanadium oxide. Activation energy increased with decrease of V₂O₅ content. This behavior was attributed to increase of average spacing between vanadium ions.     

Electromagnetic structure of W± bosons in the e–e+ → W+W– reaction

A model-independent analysis of anomalous gauge coupling constants of W ^± bosons is presented and the corresponding restrictions on them and on the electromagnetic characteristics of W ^± bosons following from the experiments on measuring the e⁺ e^- ? W⁺ W^- ? ( e

A New Interpretation of MOND Based on Mach Principle and Generalized Equivalence Principle

A new interpretation is introduced for MOND based on the Sciama’s interpretation of Mach principle and an Unruh like effect, in the context of a generalized equivalence principle. It is argued that in a locally accelerated frame with acceleration a the appearance of a Rindler horizon may give rise to a constant acceleration a ₀ as the local properties of cosmological horizon or Hubble length. The total gravitational acceleration inside this frame becomes the combination of a with a ₀. For a≫a ₀, the conventional gravitational mass m _g interacts with the dominant acceleration as m _g a and application of Sciama’s interpretation leads to the standard Newtonian dynamics. For a≪a ₀, however, a reduced gravitational mass [`(m)]<sub>g</sub>\bar{m}_{g} interacts with the dominant acceleration as [`(m)]_ga₀\bar{m}_{g}a_{0} and the application of Sciama’s interpretation on this reduced gravitational mass leads to MOND. This introduces a third proposal for MOND: The modification of gravitational mass.     

Ionization of Coulomb Systems in {\mathbb{R}^3} by Time Periodic Forcings of Arbitrary Size

We analyze the long time behavior of solutions of the Schrödinger equation ${i\psi_t=(-\Delta-b/r+V(t,x))\psi}We analyze the long time behavior of solutions of the Schr?dinger equation iy_t=(-D-b/r+V(t,x))y{i\psi_t=(-\Delta-b/r+V(t,x))\psi}, x ? \mathbbR³{x\in\mathbb{R}^3}, r =  |x|, describing a Coulomb system subjected to a spatially compactly supported time periodic potential V(t, x) =  V(t +  2π/ω, x) with zero time average.     

Possible molecular states of D*s[`(D)]*sD^{*}_{s}\bar{D}^{*}_{s} system and Y(4140)

The interpretation of Y(4140) as a D^*_s[`(D)]<sup>*</sup><sub>s</sub>D^{*}_{s}\bar{D}^{*}_{s} molecule is studied dynamically in the one boson exchange approach, where σ, η and φ exchange are included. Ten allowed D<sup>*</sup><sub>s</sub>[`(D)]^*_sD^{*}_{s}\bar{D}^{*}_{s} states with low spin parity are considered, and we find that the J ^PC =0⁺⁺, 1⁺⁻, 0⁻⁺, 2⁺⁺ and 1⁻⁻ D^*_s[`(D)]<sup>*</sup><sub>s</sub>D^{*}_{s}\bar{D}^{*}_{s} configurations are most tightly bound. We suggest that the most favorable quantum numbers are J <sup>PC</sup> =0<sup>++</sup> for Y(4140) as a D<sup>*</sup><sub>s</sub>[`(D)]^*_sD^{*}_{s}\bar{D}^{*}_{s} molecule; however, J ^PC =0⁻⁺ and 2⁺⁺ cannot be excluded. We propose to search for the 1⁺⁻ and 1⁻⁻ partners in the J/ψ η and J/ψ η′ final states, which is an important test of the molecular hypothesis of Y(4140) and the reasonability of our model. The 0⁺⁺ B^*_s[`(B)]^*_sB^{*}_{s}\bar{B}^{*}_{s} molecule should be deeply bound; experimental search in the ϒ(1S)φ channel at Tevatron and LHC is suggested.     

Thermodynamic Formalism for Contracting Lorenz Flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential [^( j)]_t(x,y,z):=-tlogJ_(x,y,z)^cu\hat{ \varphi }_{t}(x,y,z):=-t\log J_{(x,y,z)}^{cu} for the contracting Lorenz flow and for t in an interval containing [0,1]. We also analyse the Lyapunov spectrum of the flow in terms of the pressure.