Structures of the f 0(980), a 0(980) mesons and the strong coupling constants g_{f_0 K^+ K^-} , g_{a_0 K^+ K^-} with light-cone QCD sum rules

Making the assumption of explicit isospin violation arising from f ₀(980)-a ₀(980) mixing, we take the point of view that the scalar mesons f ₀(980) and a ₀(980) have both strange and non-strange quark-antiquark components and evaluate the strong coupling constants within the framework of the light-cone QCD sum rules approach. The large strong scalar-KK couplings through both the and components , , and will support the hadronic dressing mechanism; furthermore, in spite of the constituent structure differences between the f ₀(980) and a ₀(980) mesons, the strange components have larger strong coupling constants with the K ⁺ K ^- state than the corresponding non-strange ones, and . From the existing controversial values, we cannot reach a general consensus on the strong coupling constants and the mixing angles.Received: 9 January 2004, Revised: 23 July 2004, Published online: 2 September 2004     

The Invariant Eigen-Operator Method for?N?Harmonically Coupled Identical Oscillators

In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of arbitrary number of coupled identical oscillators and derive their invariant eigen-operator. The results show that, (1) for the system of arbitrary number of identical harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator of system always has the form of or ; (2) the energy level gap of the system has two kinds of possibilities: one is that gap only related to ω that the frequency of oscillators; another one is that gap not only related to ω that the frequency of oscillators, but also related to the number of the coupling oscillators.     

The Invariant Eigen-Operator Method for Hamiltonians with Coordinates-Coordinates Coupling Terms

In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of harmonic oscillator with couplings and derive their invariant eigen-operator. We first discuss decoupling of coupled harmonic oscillators with the two different quality and frequencies. And then, we propose an operator Hamiltonian to describe the linear lattice chain with Born–von Karman boundary condition. The vibrating spectrum is thus obtained. The results show that, for the system of coupled harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator of system always has the form of or .     

<Emphasis Type="Italic">X</Emphasis>(3872) and other possible heavy molecular states

We perform a systematic study of the possible molecular states composed of a pair of heavy mesons such as , , in the framework of the meson exchange model. The exchanged mesons include the pseudoscalar, scalar and vector mesons. Through our investigation, we find the following results. (1) The structure X(3764) is not a molecular state. (2) There exists strong attraction in the range r<1 fm for the system with J=0,1. If future experiments confirm Z ⁺(4051) as a loosely bound molecular state, its quantum number is probably J ^P =0⁺. Its partner state Φ ^**0 may be searched for in the π ⁰ χ _c1 channel. (3) Vector meson exchange provides strong attraction in the channel together with pion exchange. A bound state solution may exist with a reasonable cutoff parameter Λ∼1.4 GeV. X(3872) may be accommodated as a molecular state dynamically although drawing a very definite conclusion needs further investigation. (4) The molecular state may exist.     

SL(4, R)-invariant chiral fields

Using a method developed before a set of exact solutions of the chiral equations , wheregSL(4,R) are presented.Work supported in part by CONACYT, México.     

Low-lying four-quasiparticle state in 82Rb

The g-factor of the 6⁺ 191.3 keV excited state with a half-life T_1/2=12.3(6) ns in ⁸²Rb populated in the ⁷⁹Br(⁴He,n) and ⁸¹Rb(³He,2n) reactions has been measured by the TDPAD method. On the basis of the experimental g-factor g_exp=+0.670(8) the four-quasiparticle configuration \(\left[ {\pi g_{9/2} \otimes \nu \left( {g_{9/2} } \right)_{7/2}^3 } \right]_{6^ + }\) involving an anomalous neutron coupling has been assigned to this state.     

Another tetraquark structure 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 exists a scalar hidden charm tetraquark state in the π ⁺ χ _c1 invariant mass distribution, and we study its mass using the QCD sum rules. The numerical result M _Z =(4.36±0.18) GeV is consistent with the mass of the Z(4250). The Z(4250) may be a tetraquark state, but other possibilities, such as a hadro-charmonium resonance and a molecular state, are not excluded.     

A Generalisation of Brinkmann's Theorem

Brinkmann has shown that conformally related Einstein spaces are either Ricci flat pp-waves or conformally flat spaces with one as de Sitter space and the other being flat. We herewith show that if g_ikand are distinct metrics for which , then both represent (generalised) pp-waves; and w_,iis a homothetic conformal Killing vector of g_ik. It is further observed that in the situation we can have many (and also non-conformally flat) conformally related solutions, unlike in Einstein spaces. In particular for perfect fluid coupling, we show that the conformally related solutions have to be Friedman-Robertson-Walker metrics with equation of state as , or pp-waves depending on whether w_,iis timelike, spacelike or null.     

Global entanglement and coherent states in an {\sf N}-partite system

We consider a quantum system consisting of N parts, each of which is a “quKit” described by a K dimensional Hilbert space. We prove that in the symmetric subspace, , a pure state is not globally entangled, if and only if it is a coherent state. It is also shown that in the orthogonal complement all states are globally entangled.     

NLO contributions to <Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">KK</Emphasis><Superscript>*</Superscript> decays in the pQCD approach

We calculate the important next-to-leading-order (NLO) contributions to the B→KK ^* decays from the vertex corrections, the quark loops, and the magnetic penguins in the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the CP-averaged branching ratios are , , and Br(B ⁰→K ⁺ K ^*−+K ⁻ K ^*+)≈1.3×10⁻⁷, which agree well with both the experimental upper limits and the predictions based on the QCD factorization approach. Furthermore, the CP violating asymmetries of the considered decay modes are also evaluated. The NLO pQCD predictions for and decays are and .     

Extraction of nuclear coupling constants from data on nuclear charge form factors

A possibility of extracting nuclear coupling constants from data on nuclear charge form factors is discussed. The method exploits analytic properties of form factors in the momentum transfer plane. As an illustration the form factor of⁴He is considered in detail. In this case the value \(g_{4_{He^3 He(^3 H)} }^2 /4\pi = 16 \pm 1\) has been obtained in excellent agreement with earlier determinations by means of other methods. Similar analysis of the¹⁶O form factor yields the first estimate of the oxygen-nucleon coupling∶ \(g_{16_{O^{15} O(^{15} N)N} }^2 /4\pi = 64\) .     

New information on the T1/2 = 47 s isomer in the 136I nucleus

The ¹³⁶I nucleus, populated in the spontaneous fission of ²⁴⁸Cm, was studied by means of prompt γ-ray spectroscopy using the EUROGAM2 array. The observation in this work of the 42.6keV prompt-γ, M1 + E2 transition de-exciting the 7^- level in ¹³⁶I indicates that this level, interpreted as the configuration, does not correspond to the T = 47s, β-decaying isomer in ¹³⁶I. The isomer is placed 42.6keV below the 7^- level. It has spin 6^- and is interpreted as the configuration. This and other members of both multiplets can be reproduced properly only if one assumes that the πd_5/2 orbital in ¹³⁶I is located 400keV lower than in ¹³³Sb. Possible mechanisms causing this effect are discussed.     

Analytic solution of the general anharmonic-oscillator problem

The regular and irregular solution of the differential three-dimensional Schrödinger equation with the confining potential , is presented. In full analogy with the recentq=1 conjecture of Singhet al. [1], the corresponding Green's function is constructed in terms of the extended continued fraction. For the simplest example withV(r)=r ²+² r ⁴, its convergence is proved and the resulting energy spectrum is numerically tested.     

Loss of collectivity in 79Rb

High-spin states in ⁷⁹Rb were populated in the reaction at E(beam) = 60 MeV. The lifetimes of the excited states of the positive-parity yrast band and of the negative-parity band in ⁷⁹Rb were measured by the Doppler Shift Attenuation Method. The deduced transition quadrupole moments Q_t are found to have a decreasing trend with rotational frequency for both the bands, consistent with those found experimentally in neighbouring nuclei. An erratum to this article is available at .     

Non-hermitian quantum mechanics in non-commutative space

A recent investigation of the possibility of having a -symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a -symmetric deformation of this space. Specifically, a -symmetric harmonic oscillator together with an iC(x ₁+x ₂) interaction are discussed in this space, and solutions are obtained. We show that in the deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative parameters. However, it is shown that in standard non-commutative space, the iC(x ₁+x ₂) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not -symmetric. A complex interacting anisotropic oscillator system also is discussed.     

Analysis of Ωb? (bss) and Ωc0 (css) with QCD sum rules

We calculate the masses and the pole residues of the heavy baryons Ω _c ⁰(css) and Ω _b ⁻(bss) with the QCD sum rules. The numerical values  GeV (or  GeV) and  GeV (or  GeV) are in good agreement with the experimental data.     

Integrable Discrete Nets in Grassmannians

We consider discrete nets in Grassmannians , which generalize Q-nets (maps with planar elementary quadrilaterals) and Darboux nets (-valued maps defined on the edges of such that quadruples of points corresponding to elementary squares are all collinear). We give a geometric proof of integrability (multidimensional consistency) of these novel nets, and show that they are analytically described by the noncommutative discrete Darboux system.      

SU(1,1) Coherent States for the Generalized Two-Mode Time-Dependent Quadratic Hamiltonian System

The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schrödinger cat states defined as an eigenstate of $\hat{K}_{-}^{2}The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schr?dinger cat states defined as an eigenstate of are also studied. We applied our development to two-mode Caldirola-Kanai oscillator which is a typical example of the time-dependent quadratic Hamiltonian system. The time evolution of the quadrature distribution for the probability density in the coherent states are analyzed for the two-mode Caldirola-Kanai oscillator by plotting relevant figures.     

New constraints on short-range forces coupling mass to intrinsic spin

A new device that we refer to as the spherical superconducting torsion balance has been used to search for a new force coupling mass to intrinsic spin. Our experimental approach also employs a novel spin-source geometry that allows unprecedented sensitivity in the range 100 mum10 mm at 1sigma confidence. At a range of 1 mm our most relaxed limit is g_{p};{e}g_{s}<1.5x10;{-24}.     

Epitaxial phase‐change materials

Epitaxial $ {\rm Ge}_{2} {\rm Sb}_{2} {\rm Te}_{5} $ thin layers were successfully grown in the metastable cubic phase on both slightly lattice‐mismatched (GaSb) and highly lattice‐mismatched (Si) templates. The higher quality of the films grown on (111)‐oriented substrates is attributed to the tendency to form layered structures in the stable bulk phase as well as to the nature of distortion in the metastable cubic phase. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)