Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Strange hadron production in Σ-<Emphasis Type="Italic">A</Emphasis> interactions in the SELEX experiment

We report our observations on the resonance signals of masses of 1520, 1670, 1810 (1 820), and 2100 MeV c ⁻², produced inclusively in the reaction Σ⁻ + C(Cu) → p + K⁻ + X, and the signals of masses of 1020 and 1525 MeV c ⁻², produced inclusively in the reaction Σ⁻ + C(Cu) → K⁺ + K⁻ + X, with a 600-GeV c ⁻¹- momentum hyperon beam in the SELEX experiment at the Fermilab. The masses, widths, and branching ratios were measured. The resonance signal of mass of 1520 MeV c ⁻² correspond to the known Λ(1520) hyperon. The signals of masses of 1020 and 1525 MeV c ⁻² in the K⁺K⁻ system correspond to the φ⁰(1020)- and f ₂′(1525) mesons, respectively. The branching ratio of the resonance of mass of 1670 MeV c ⁻² relative to Λ(1520) is (24.92 ± 0.45 ± 0.48)%, while that of the resonance of mass of 1810 (or 1 820) MeV c ⁻² relative to Λ(1520) is (16.13 ± 0.38 ± 0.45)%. The branching ratio of the f ₂′(1525) resonance relative to φ⁰(1020) is (10.75 ± 0.25 ± 0.45)%. Data analysis was performed over 6 × 10⁷ trigger events registered by the SELEX setup on the FNAL Tevatron.     

Pseudovector heavy quarkonia in e + e −2 collisions

It is shown that BR(χ _b1(1 P)→e ⁺ e ⁻)≃3.3· 10⁻⁷ and BR(χ _c1(1 P)→e ⁺ e ⁻)≃10⁻⁸. This gives realistic possibilities for searching for the production of χ _b1(1 P) and ξ _c1(1 P) states in e ⁺ e ⁻ collisions, even on the present-day colliders, to say nothing of b and c-τ factories. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 569–574 (25 April 1996)     

Electromagnetic mass splittings of heavier hadrons in quantum chromodynamics

The electromagnetic mass splittings of heavier hadrons are estimated in the framework of gauge theory model where ligher quarks are taken to behave relativistically and the spatial wave functions are described by the spin-spin interaction affected relative distances between quarks. The predictions for (Ξ⁻-Ξ⁰), (Σ*⁰−Σ*⁺), (Ξ^*−-Ξ^*0), (D _c ⁺−D _c ⁰) and (D _c ^*+ −D _c ^*0 ) are in fair agreement with the experimental data available whereas those for (D _b ⁻ −D _b ⁰ ) and (D _b ^*− −D _b ^*0 ) are in qualitative agreement with other theoretical estimates.     

Stability of Three-Body Coulomb Systems with J = 1 in the Oscillator Representation

The oscillator representation is applied to calculate the energy spectrum of three-body Coulomb systems with total angular momentum ^J. For three-body Coulomb systems with J = 1 and arbitrary masses the region of stability is determined. For the systems (A ⁺ A ⁻ e ⁻), (pe ⁻ C ⁺), (pB ⁻ e ⁻), and (D ⁺ e ⁻ e ⁺), the values of the critical masses of the particles A, B, C, and D are obtained as m _A = 2.22m _e , m _B = 1.49m _e , m _C = 2.11m _e and m _D = 4.15m _e . Received November 6, 1995; received December 4, 1995; accepted for publication January 22, 1996     

Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

Converging lower bound to the critical screening parameterD _c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10⁻³% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD _c ^ms ≈ [0.764435n ⁻²+0.617737n ⁻³]⁻¹ wheren is the principal quantum number. The predictedD _c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.     

Analysis of various polarization asymmetries in the inclusive b→s?+?? decay in the fourth-generation standard model

In this study a systematical analysis of various polarization asymmetries in inclusive b→s ℓ ⁺ ℓ ⁻ decay in the standard model (SM) with four generation of quarks is carried out. We found that the various asymmetries are sensitive to the new mixing and quark masses for both of the μ and τ channels. Sizable deviations from the SM values are obtained. Hence, b→s ℓ ⁺ ℓ ⁻ decay is a valuable tool for searching physics beyond the SM, especially in the indirect searches for the fourth-generation of quarks (t′,b′).     

<Superscript>1</Superscript>H Spin–Lattice Relaxation Study of Dynamical Inequivalence of Methyl Groups in Solid 1,2-<Emphasis Type="Italic">O</Emphasis>-(1-Ethylpropylidene)-α-<Emphasis Type="SmallCaps">d</Emphasis>-Glucofuranose

We investigated the dynamics of methyl groups in organic polycrystalline 1,2-O-(1-ethylpropylidene)-α-d-glucofuranose by the proton spin–lattice relaxation method. The temperature and nuclear magnetic resonance Larmor frequency dependence of relaxation time is presented and interpreted in terms of simple possible dynamical model for the reorientation of methyl groups: the random hopping for methyl groups, which are in a, b, and c sites in the crystal. The energy E _a of 13.5 kJ mol⁻¹ for the a-type methyl groups is typical for methyl groups in ethyl groups. In contrast, the b- and c-methyl groups characterized by the lower E _a values of 9.5 and 6.5 kJ mol⁻¹ are located in the crystal structure where the intermolecular interactions significantly influence the potential, leading to a decrease in the total energy.     

Enhanced direct <Emphasis Type="Italic">CP</Emphasis> violation and branching ratios in bottom hadron decays

In the framework of factorization we study direct CP violation in the decays of bottom hadrons containing a strange quark or a charm quark, H _b →f ρ ⁰(ω)→f π ⁺ π ⁻ (H _b is the bottom hadron and f is the product hadron) including the effect of ρ–ω mixing. We find that the CP violating asymmetry can be enhanced greatly via the ρ–ω mixing mechanism when the invariant mass of the π ⁺ π ⁻ pair is in the vicinity of the ω resonance. For the processes associated with b→d transitions, e.g. , , B _c ⁻→D ⁻ π ⁺ π ⁻, B _c ⁻→D ^*− π ⁺ π ⁻, Ξ _b ⁰→Λ π ⁺ π ⁻, and Ω _b ⁻→Ξ ⁻ π ⁺ π ⁻, the maximum CP violating asymmetries can reach about −84%, while for the processes associated with b→s transitions, e.g. , , B _c ⁻→D _s ⁻ π ⁺ π ⁻, B _c ⁻→D _s ^*− π ⁺ π ⁻, Ξ _b ⁻→Ξ ⁻ π ⁺ π ⁻, and Ω _b ⁻→Ω ⁻ π ⁺ π ⁻, the CP violating asymmetries can be enhanced to about 95%. Furthermore, taking ρ–ω mixing into account we calculate the b-hadron decay branching ratios. We also discuss the possibility to observe the predicted CP violating asymmetries at the LHC.     

Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operatorsa ⁻¹ anda ^+-1 by their actions on the number states. We show that the squeezed vacuum exp(1/2;ξa ⁺²]|0> and squeezed first number state exp[1/2;ξa ⁺²]|n=1> are respectively the eigenstates of the operators (a ^†−1 a) and (aa ^+-1) with the eigenvalue ξ.     

Black holes with metric and fields of the same form

We present two rotating black hole solutions with axion ξ, dilaton f{\phi} and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and applying the “Newman–Janis complex coordinate trick” we get a rotating metric g _μν with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric Q _E and magnetic Q _M . Then we find a solution of the equations of motion having this g _μν as metric. Our solution is asymptotically flat and has angular momentum J = M a, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics, the vector fields and the quantity l = x+ie^-2f{\lambda=\xi+ie^{-2\phi}} of our solutions and the solution of: Sen for Q _E , Sen for Q _E and Q _M , Kerr–Newman for Q _E and Q _M , Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstr?m, Schwarzschild are the same function of a, and two functions ρ ² = r(r + b) + a ² cos² θ and Δ = r(r + b) − 2Mr + a ² + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most physically interesting and well known solutions, are listed in an “Appendix”.     

Drug delivery using novel nanoplexes against a <Emphasis Type="Italic">Salmonella</Emphasis> mouse infection model

A novel methodology for incorporating gentamicin into macromolecular complexes with anionic homo- and block copolymers via cooperative electrostatic interactions is described. Block copolymers of poly(ethylene oxide-b-sodium acrylate) (PEO-b-PAA^{− +}Na) or poly(ethylene oxide-b-sodium methacrylate) (PEO-b-PMA^{− +}Na) were blended with PAA⁻ Na⁺ and complexed with the polycationic antibiotic gentamicin. Gentamicin nanoplexes made with PEO-b-PMA^{− +}Na/PAA^{− +}Na (PMPG) and analogous nanoplexes with PEO-b-PAA^{− +}Na/PAA^{− +}Na (PAPG) had mean intensity average diameters of 120 and 90 nm, zeta potentials of −17 and −11 mv, and incorporated 26% and 23% by weight of gentamicin, respectively. Gentamicin release rates at physiological pH from nanoplexes were relatively slow. PAPG and PMPG as drug delivery systems for treating murine salmonellosis at doses similar to the free gentamicin experiments resulted in reduced numbers of viable bacteria in the liver and spleen. Polymeric nanoplexes developed by this methodology can potentially improve targeting of intracellular pathogens.     

Conservation laws for classical and relativistic collisions. I

On the basis of simple kinematic arguments it is shown that any quantity, depending only on the nature and velocity of a particle, that is conserved in a collision must, in classical mechanics, be of the form λ+Σ_iμ_iυ_i+1/2vυ ² or in relativistic mechanics of the form λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc [1−(υ ²/c ²)]^−1/2 where λ,μ _i, andν are particle parameters.     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

The (D+1)-dimensional (β,β′)-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk (J. Phys., A Math. Gen. 39, 10909, 2006), leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′=2β up to first order over deformation parameter β. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for b < \frac18m²c²\beta<\frac{1}{8m^{2}c^{2}} which leads to an isotropic minimal length in the interval 10⁻¹⁷ m<(ΔX ⁱ )₀<10⁻¹⁵ m. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.     

On Meson Masses

It is shown that in the framework of an analytical confinement, when quark and gluon propagators are induced by a vacuum self-dual gluon field with constant strength, the masses of mesons with quantum numbers Q = (J ^P ,n), where n is the radial quantum number, and quark constituents m ₁, m ₂ are described with reasonable accuracy by the formula The positive parameter A _Q is unique for all mesons with a fixed quantum number Q. Sets of mesons J ^P = 1⁻, 0⁺, 1⁺, 2⁺, 3⁻ for n = 0 and 1⁻ , 2⁺ for n > 0 and different flavor constituent quarks (u = d, s, c, b) are considered.     

Positron scattering from hydrocarbons

The total cross sections for positron impact on hydrocarbons have been calculated using the additivity rule in which the total cross section for a molecule is the sum of the total cross section for the constituent atoms. The energy range considered is from a few eV to several thousand eV. The total cross sections for positron impact on an atom are calculated by employing a complex spherical potential which comprises of a static, polarization and an absorption potential. We have good agreement with the experimental results for hydrocarbons for positron energy ⩾100 eV. Our results also agree with the available calculations for CH₄ and C₂H₂ which employed full molecular wavefunctions beyond 100 eV. Our absorption cross sections also agree with molecular wave-function calculations for C₂H₂ and CH₄ beyond 100 eV. We have shown the Bethe plots fore ⁺−C ande ⁺−H scattering systems and Bethe parameters have been extracted. We have fitted the cross section for positron impact on hydrocarbons in the formσ _t(C _n H _m )=naE ⁻ b+mcE ⁻ d in the energy range 300–5000 eV wherea=195.0543,b=0.7986,c=371.1757 andd=1.1379 withE in eV andσ _t in 10⁻¹⁶ cm².