Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Validity of the equivalent-photon approximation for the production of massive spin-1 particles

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q ²|≪M ², in addition to the usual condition |q ²|≪W ²,W being theV ⁺ V ⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q ²||q′²|W ⁴ ≪ 16M ⁸, in addition to |q ²| ≪M ², |q′²| ≪M ² and |q ²| ≪W ², |q′²| ≪W ². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q ²| ≪W ² and |q′²| ≪W ². We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q ²||q′²|W ⁴ ≪ 16M ⁸ is shown to be removed.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

A Derivative Formula for the Free Energy Function

We consider bond percolation on the Z ^d lattice. Let M _n be the number of open clusters in B(n)=[−n,n] ^d . It is well known that E _p M _n /(2n+1) ^d converges to the free energy function κ(p) at the zero field. In this paper, we show that s²_p(M_n)/(2n+1)^d\sigma^{2}_{p}(M_{n})/(2n+1)^{d} converges to −p(1−p)κ′(p).     

Modern energy density functional for nuclei and the nuclear matter equation of state

We discuss a method of determining a modern energy density functional (EDF) in nuclei. We adopt a Skyrme type EDF and fit the Skyrme parameters to an extensive set of experimental data on the ground-state binding energies, radii, and the breathing mode energies of a wide range of nuclei. We further constrain the values of the Skyrme parameters by requiring positive values for the slope of the symmetry energy S, the enhancement factor κ, associated with the isovector giant dipole resonance, and the Landau parameter G ₀^′. This is done within the approaches of Hartree-Fock (HF) and HF with the inclusion of correlation effects, using a simulated-annealing based algorithm forminimizing χ ².We also present results of HF based random phase approximation for the excitation strength function of the breathing mode and discuss the current status of the nuclear matter incompressibility coefficient.     

Self-consistent treatment of the quark condensate and hadrons in nuclear matter

We calculate the contribution of pions to the $\bar qq$-expectation value κ(ρ) =<M|ˉq q|M> in symmetric nuclear matter. We employ exact pion propagator renormalized by nucleon-hole and isobar-hole excitations. Conventional straightforward calculation leads to the “pion condensation” at unrealistically small values of densities, causing even earlier restoration of chiral symmetry. This requires a self-consistent approach, consisting in using the models, which include direct dependence of in-medium mass values on κ(ρ), e.g. the Nambu–Jona-Lasinio–model. We show, that in the self-consistent approach the ρ-dependence of the condensate is described by a smooth curve. The “pion condensate” point is removed to much higher values of density. The chiral restoration does not take place at least while ρ < 2.8ρ₀ with ρ₀ being the saturation value. Validity of our approach is limited by possible accumulation of heavier baryons (delta isobars) in the ground state of nuclear matter. For the value of effective nucleon mass at the saturation density we found m ^*(ρ₀) = 0.6m, consistent with nowadays results of other authors. Received: 8 October 1998     

The Harmonic Oscillator on Three-Dimensional Spherical and Hyperbolic Spaces: Curvature Dependent Formalism and Quantization

A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, S_k³S_{\kappa }^{3} (κ>0) and H_k³H_{k}^{3} (κ<0), is studied using geodesic spherical coordinates (r,θ,φ). The curvature κ is considered as a parameter and the results are formulated in explicit dependence of κ. The first part of the paper is concerned with the existence of Killing vectors, the existence of Noether symmetries and the properties of the Noether momenta. The second part is devoted to the transition from classical to quantum mechanics. The classical system is quantized by obtaining a κ-dependent invariant measure dμ _κ and expressing the Hamiltonian as a function of the Noether momenta.     

A possible minimal gauge–Higgs unification

A possible minimal model of the gauge–Higgs unification based on the higher dimensional spacetime M ⁴⊗(S ¹/Z ₂) and the bulk gauge symmetry SU(3) _C ⊗SU(3) _W ⊗U(1) _X is constructed in some detail. We argue that the Weinberg angle and the electromagnetic current can be correctly identified if one introduces the extra U(1) _X above and a bulk scalar triplet. The VEV of this scalar as well as the orbifold boundary conditions will break the bulk gauge symmetry down to that of the standard model. A new neutral zero-mode gauge boson Z′ exists that gains mass via this VEV. We propose a simple fermion content that is free from all the anomalies when the extra brane-localized chiral fermions are taken into account as well. The issues on recovering a standard model chiral-fermion spectrum with the masses and flavor mixing are also discussed, where we need to introduce the two other brane scalars which also contribute to the Z′ mass in the similar way as the scalar triplet. The neutrinos can get small masses via a type I seesaw mechanism. In this model, the mass of the Z′ boson and the compactification scale are very constrained being, respectively, given in the ranges: 2.7 TeV<m _Z′<13.6 TeV and 40 TeV<1/R<200 TeV.     

Inflationary scenario in the supersymmetric economical 3-3-1 model

We construct the supersymmetric economical 3-3-1 model which contains inflationary scenario and avoids the monopole puzzle. Based on the spontaneous symmetry breaking pattern (with three steps), the F-term inflation is derived. The slow-roll parameters ∈ and η are calculated. By imposing as experimental five-year WMAP data on the spectral index n, we have derived a constraint on the number of e-folding N _Q to be in the range from 25 to 50. The scenario for large-scale structure formation implied by the model is a mixed scenario for inflation and cosmic string, and the contribution to the CMBR temperature anisotropy depends on the ratio M _X /M _Pl. From the COBE data, we have obtained the constraint on the M _X to be M _X ∈ [1.22 × 10¹⁶, 0.98 × 10¹⁷] GeV. The upper value M _X ≃ 10¹⁷ GeV is a result of the analysis in which the inflationary contribution to the temperature fluctuations measured by the COBE is 90%. The coupling α varies in the range: 10⁻⁷−10⁻¹. This value is not so small, and it is a common characteristics of the supersymmetric unified models with the inflationary scenario. The spectral index n is a little bit smaller than 0.98. The SUGRA corrections are slightly different from the previous consideration. When ξ ≪ 1 and α lies in the above range, the spectral index gets the value consistent with the experimental five-year WMAP data. Comparing with string theory, one gets ξ < 10⁻⁸. Numerical analysis shows that α ≈ 10⁻⁶. To get inflation contribution to the CMBR temperature anisotropy ≈90%, the mass scale M _X < 3.5 × 10¹⁴ GeV.     

New physics hints in B decays and collider outlook

There are currently two hints for new physics involving CP violation in b → s transitions: ΔS ≡ S _f − S _J ^ϕK ≠ 0, and difference in direct CP asymmetry ΔA _Kπ ≡ A _K+π ⁰ − A _K+π ⁻ ≠ 0. We explore the two scenarios with a large and unique new CP phase in b ↔ s transitions. Motivated by ΔS ≠ 0, we update on the right-handed strange-beauty squark sb _1R at TeV scale. Motivated by ΔA _Kπ ≠ 0, we explore sequential fourth generation t′ and b′ quarks. Both scenarios can survive constraints such as SM level b → sγ, sll and B _s mixing, and predict sizable CP violation in B _s mixing. The fourth generation picture predicts sizable K _L → π ⁰ vv. Direct search for sb _R, b′ and t′ at hadronic colliders, such as Tevatron Run II and LHC, can complement further CP violation studies at these machines, as well as at the future Super B factory.     

Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field

We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Z α ² ≤ κ ₀ for a sufficiently small κ ₀, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Z α ² is fixed, the ground state energy of the system is given by a two term expansion c ₁ Z ^7/3 + c ₂(κ) Z ² + o(Z ²). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.     

The K* 0(800) scalar resonance from Roy–Steiner representations of πK scattering

We discuss the existence of the light scalar meson K^* ₀(800) (also called κ) in a rigorous way, by showing the presence of a pole in the πK→πK amplitude on the second Riemann sheet. For this purpose, we study the domain of validity of two classes of Roy–Steiner representations in the complex energy plane. We prove that one of them is valid in a region sufficiently broad in the imaginary direction. From this representation, we compute the l=0 partial wave in the complex plane neither making any additional approximation nor having model dependence, relying only on experimental data. A scalar resonance with strangeness S=1 is found with the following mass and width: M_κ=658±13 MeV and Γ_κ=557±24 MeV.     

Searches for new neutral gauge Z′ bosons at the e+e? International Linear Collider and their identification

The potential of the electron-positron International Linear Collider for searches for and the separation of signals induced by new neutral gauge bosons predicted by various classes of models featuring an extended gauge sector is investigated. The analysis presented in this article was performed for processes of annihilation fermion-pair production and was based on the use of differential polarization observables, which ensure a higher sensitivity (in relation to integrated observables) of the processes being considered to Z′-boson parameters. Thresholds for discovering and identifying new neutral gauge bosons associated with models belonging to the E ₆ and LR, as well as the ALR and SSM, classes are determined. In particular, it is shown that polarization experiments at a 0.5-TeV electron-positron collider of integrated luminosity 100 fb⁻¹ would make it possible to identify unambiguously the entire set of Z′-boson models (Z′_SSM, Z′ _φ , Z′ _η , Z′ _χ , Z′_LRS, and Z′_ALR) for M _Z′ < 6√s and to improve considerably the respective estimates expected from experiments with unpolarized particles.     

A spin-3/2 Ising model on a square lattice

The spin-3/2 Ising model described by the most general Hamiltonian with up-down symmetry, −βH=Σ_〈ij〉{JS _i S _j +KS ₂ ⁱ S ₂ ^j +LS ₃ ⁱ S ₃ ^j +M/2(S _i S ₃ ^j +S _j S ₃ ⁱ )}−ΔΣ_i S ₂ ⁱ , is investigated on a square lattice. It is shown that this model is reducible to an eight-vertex model on a surface in the parameter space spanned by the coupling constants J, K, L, and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space. Consequently, the critical behavior and, in particular, the critical temperature for the second-order phase transitions of the model is found exactly. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 270–275 (25 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the Connectivity of Cobordisms and Half-Projective TQFT's

We consider a generalization of the axioms of a TQFT, the so-called half-projective TQFT's, where we inserted an anomaly, , in the composition law. Here μ₀ is a coboundary (in a group cohomological sense) on the cobordism categories with non-negative, integer values. The element of the ring over which the TQFT is defined does not have to be invertible. In particular, it may be zero. This modification makes it possible to extend quantum-invariants, which vanish on S ¹×S ², to non-trivial TQFT's. Note, that a TQFT in the ordinary sense of Atiyah with this property has to be trivial all together. We organize our discussions such that the notion of a half-projective TQFT is extracted as the only possible generalization under a few very natural assumptions. Based on separate work with Lyubashenko on connected TQFT's, we construct a large class of half-projective TQFT's with . Their invariants all vanish on S ¹×S ², and they coincide with the Hennings invariant for non-semisimple Hopf algebras and, more generally, with the Lyubashenko invariant for non-semisimple categories. We also develop a few topological tools that allow us to determine the cocycle μ₀ and find numbers, ϱ(M), such that the linear map associated to a cobordism, M, is of the form . They are concerned with connectivity properties of cobordisms, as for example maximal non-separating surfaces. We introduce in particular the notions of “interior” homotopy and homology groups, and of coordinate graphs, which are functions on cobordisms with values in the morphisms of a graph category. For applications we will prove that half-projective TQFT's with vanish on cobordisms with infinite interior homology, and we argue that the order of divergence of the TQFT on a cobordism, M, in the “classical limit” can be estimated by the rank of its maximal free interior group, which coincides with ϱ(M). Received: 20 October 1997 / Accepted: 18 March 1998     

Uncertainties on <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> in global PDF analyses and implications for predicted hadronic cross sections

We determine the uncertainty on the strong coupling α _S due to the experimental errors on the data fitted in global analysis of hard-scattering data, within the standard framework of leading-twist fixed-order collinear factorisation in the [`(MS)]\overline{\mathrm{MS}} scheme, finding that α _S (M _Z ²)=0.1202_−0.0015^+0.0012 at next-to-leading order (NLO) and α _S (M _Z ²)=0.1171_−0.0014^+0.0014 at next-to-next-to-leading order (NNLO). We do not address in detail the issue of the additional theory uncertainty on α _S (M _Z ²), but an estimate is ±0.003 at NLO and at most ±0.002 at NNLO. We investigate the interplay between uncertainties on α _S and uncertainties on parton distribution functions (PDFs). We show, for the first time, how both these sources of uncertainty can be accounted for simultaneously in calculations of cross sections, and we provide eigenvector PDF sets with different fixed α _S values to allow further studies by the general user. We illustrate the application of these PDF sets by calculating cross sections for W, Z, Higgs boson and inclusive jet production at the Tevatron and LHC.     

B-decay CP-asymmetries in SUSY with a U(2)3 flavour symmetry

We study CP asymmetries in rare B decays within supersymmetry with a U(2)³ flavour symmetry, motivated by the SUSY flavour and CP problems, the hierarchies in the Yukawa couplings and the absence so far of any direct evidence for SUSY. Even in the absence of flavour-blind phases, we find potentially sizable CP violating contributions to b→s decay amplitudes. The effects in the mixing-induced CP asymmetries in B→ϕK _S and B→η′K _S , angular CP asymmetries in B→K ^∗ μ ⁺ μ ⁻ and the direct CP asymmetry in B→X _s γ can be in the region to be probed by LHCb and next generation B factories. At the same time, these effects in B decays are compatible with CP violating contributions to meson mixing, including a non-standard B _s mixing phase hinted by current tensions in the CKM fit mostly between S_yKS, e_KS_{\psi K_{S}}, \epsilon_{K} and DM_Bs/DM_Bd\Delta M_{B_{s}}/\Delta M_{B_{d}}.     

The hyperfine splittings in heavy-light mesons and quarkonia

Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the B _q (q = n, s) mesons are shown to be in full agreement with experiment if a universal coupling α _HF = 0.310 is taken in perturbative spinspin potential. It gives M(B*) −M(B) = 45.7(3) MeV, M(B _s ^* ) − M(B _s ) = 46.7(3) MeV (n _f = 4), while in bottomonium Δ_HF(b $ \bar b $ \bar b ) = M(Υ(9460)) − M(η _b (1S)) = 63.4 MeV for n _f = 4 and 71.1 MeV for n _f = 5 are obtained; just the latter agrees with recent BaBar data. For unobserved excited states we predict M(Υ(2S))−M(η _b (2S)) = 36(2)MeV,M(Υ(3S))−M(η _b (3S)) = 28(2)MeV, and also M(B _c ^*) = 6334(4) MeV, M(B _c (2S)) = 6868(4) MeV, M(B _c ^* (2S)) = 6905(4) MeV. The mass splittings between D(2³ S ₁) − D(2¹ S ₀), D _s (2³ S ₁) − D _s (2¹ S ₀) are predicted to be ∼75 MeV, which are significantly smaller than in several other studies but agree with the mass splitting between recently observed D(2533) and D*(2610).     

Systematic trends in the line strengths and radial matrix elements of E1 transitions in the Be isoelectronic sequence

Line strengthS and radial matrix elementσ for the dipole allowed transitions withinn=2 complex of ions in the Be isoelectronic sequence have been fitted in the formsZ ² S=A+B/(Z − C) andZσ=A′ + B′/(Z − C′). The constantsA, B, C andA′, B′, C′ have been calculated by employing a non-linear least square method. The relevant data forS andσ have been taken from calculations which includes correlation effects. It is shown that the fitted yalues ofA andA′ are in excellent accord with their hydrogenic values (Z →α) provided that we express the zeroth-order wavefunction of the ground state 1s²2s^{2 1} S as a quantum-mechanical admixture of the Hartree-Fock (HF) state 1s²2s^{2 1} S and the near-degenerate state 1s²2p^{2 1} S.     

Effect of annealing on structure and magnetic properties of Fe-N and Fe-Ti-N thin films

The structure and magnetic properties of Fe-N and Fe-Ti-N films have been studied as a function of annealing temperature T_a with a transmission electron microscope and a vibrating sample magnetometer. The as-prepared Fe-N films consist of the γ^′-Fe₄N and α^′′-Fe₁₆N₂ phases, and the Fe-Ti-N films are composed of the γ^′-Fe₄N, α^′′-Fe₁₆N₂, and TiN phases. The structural changes with annealing temperature in the Fe-N films are distinct. The α^′′-Fe₁₆N₂ decomposes into α+γ^′ phases in the Fe-N film annealed at about 300 °C, and it disappears in the film annealed at 350 °C. Annealing of the Fe-Ti-N films shows no structural changes between room temperature (RT) and 500 °C. The saturation magnetization 4πM_S and coercivity H_c of the Fe-N films change drastically with the annealing temperature T_a, whereas those of the Fe-Ti-N films do not change with T_a up to 500 °C. These results indicate that the additon of Ti may improve the thermal stability of Fe-N films. Recieved: 6 Juli 1998 / Accepted: 19 Oktober 1998 / Published online: 10 March 1999