Charm and bottom quark production cross sections near threshold

The cross sections for charm and bottom quark production in the threshold region are discussed. We consider the effects of an all order resummation of initial state soft-plus-virtual gluon radiation on the total cross sections compared to the order $←pha_{s}^{3}$ results.     

Measurement of $D_s ^+$ meson production in Z decays and of the ${⋏r B}_s ^0$ lifetime

$D_s ^+$ mesons produced in Z⁰ → bb? events were separated from the Z⁰ → cc? component using a lifetime tag. Using a sample of 1.5 million hadronic Z decays collected with the Aleph detector the ${?r B}_s ^0$ and $D_s ^+$ yields have been measured: $$?trix {B(b?ghtarrow {?r B}_s ^0)B({?r B}_s ^0?ghtarrow D_s ^+)=0.088pm 0.020(? stat.)? pm 0.020(? syst.)? B(c?ghtarrow D_s ^+)=0.128pm 0.019(? stat.)_{-0.016} ^{+0.019}(? syst.)}$$ The ${?r B}_s ^0$ lifetime was measured in a ${?r B}_s ^0$ enriched sample reconstructing the decay length from the vertex of the $D_s ^+$ with a hadron from the ${?r B}_s ^0$ decay. The result obtained is: $${?u_B}_s=1.61_{-0.29} ^{+0.30}(? stat.)_{-0.16} ^{+0.18}(? syst.) {? ps.}$$     

Regularity for Eigenfunctions of Schr?dinger Operators

We prove a regularity result in weighted Sobolev (or Babu?ka?CKondratiev) spaces for the eigenfunctions of certain Schr?dinger-type operators. Our results apply, in particular, to a non-relativistic Schr?dinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let ${\mathcal{K}_{a}^{m}(\mathbb{R}^{3N},r_S)}$ be the weighted Sobolev space obtained by blowing up the set of singular points of the potential ${V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}}$ , ${x \in \mathbb{R}^{3N}}$ , ${b_j, c_{ij} \in \mathbb{R}}$ . If ${u \in L^2(\mathbb{R}^{3N})}$ satisfies ${(-\Delta + V) u = \lambda u}$ in distribution sense, then ${u \in \mathcal{K}_{a}^{m}}$ for all ${m \in \mathbb{Z}_+}$ and all a ?? 0. Our result extends to the case when b _j and c _ij are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a?<?3/2.     

Signals of left-right supersymmetry in e + e − collisions

We study chargino and neutralino pair production at the Next Linear e⁺ e^? Collider in a supersymmetric left-right model. We investigate on- and off-resonance signals via the processes: $e^{+}e^{-}?ghtarrow {?lde chi}_{1}^{+}{?lde chi}_{1}^{-} ?ghtarrow e^{+}e^{-}+{? p}_{? miss}$ and $e^{+}e^{-}?ghtarrow {?lde chi}_{2}^{0}{?lde chi}_{1}^{0} ?ghtarrow e^{+}e^{-}+{? p}_{? miss}$. These reactions could lead to observable signals as they compare with the background signal from W^± -pair production.     

Measurement of inclusive K*0(892), ϕ(1020) and ${⤪ K}_{2}^{⇒t 0}(1430)$ production in hadronic Z decays DELPHI Collaboration

The inclusive production of the neutral vector mesons K*⁰(892) and ?(1020), and of the tensor meson ${? K}_{2}^{?t 0}(1430)$, in hadronic decays of the Z has been measured by the DELPHI detector at LEP. The average production rates per hadronic Z decay have been determined to be 0.77 ± 0.08 K*⁰(892), 0.104 ± 0.008 ?(1020) and ${? K}_{2}^{?t 0}(1430)$. The ratio of the tensor-to-vector meson production yields, $«ngle {? K}_{2}^{?t 0}(1430)»ngle$, is smaller than the 〈f₂(1270)〉/〈ρ⁰(770)〉 and $«ngle f_{2}^{?ime}(1525)»ngle$ ratios measured by DELPHI. The production rates and differential cross sections are compared with the predictions of JETSET 7.4 tuned to the DELPHI data and of HERWIG 5.8. The K*⁰(892) and ?(1020) data are compatible with model predictions, but a large disagreement is observed for the ${? K}_{2}^{?t 0}(1430)$.     

First observation of a particle-antiparticle asymmetry in the decay of neutral kaons into π0π0

CP violation has been observed as a time-dependent rate asymmetry between the decays ${?erline K}^0 ?ghtarrow ?^{0} ?^{0}$ and K⁰ → π⁰π{0}, where the neutral kaons are produced with definite and individually known strangeness in ${?r p}p ?ghtarrow{?erline K}^0 K^+?^- $ or p?p → K⁰ K^? π⁺. A special technique for the data analysis has been developed. The values obtained for ?₀₀ and ¦ η₀₀¦ are in agreement with those of previous measurements of CP violation.     

Measurement of QED structure functions of the photon using azimuthal correlations at LEP

We have studied azimuthal correlations in singly-tagged e⁺e^? → e⁺e^?μ⁺μ^? events at an average Q ² of 5.2 GeV². The data were taken with the OPAL detector at LEP at e⁺e^? centre-of-mass energies close to the Z⁰ mass, with an integrated luminosity of approximately 100 pb^?1. The azimuthal correlations are used to extract the ratio $F_{B}^{αmma}/F_{2}^{αmma}$ of the QED structure functions $F_{B}^{αmma}(x,Q^{2})$ and $F_{2}^{αmma}(x,Q^{2})$ of the photon. In leading order and neglecting the muon mass $F_{B}^{αmma}$ is expected to be identical to the longitudinal structure function $F_{L}^{αmma}$. The measurement of $F_{B}^{αmma}/F_{2}^{αmma}$ is found to be significantly different from zero and to be consistent with the QED prediction.     

Absence of symmetry breaking forN-vector spin glass models in two dimensions

We prove the absence of continuous symmetry breaking at arbitrary temperatures for two-dimensionalN-vector spin glass models with Hamilton function $$H = - \sum\limits_{i,j} {J(i,j)\left| {i - j} \right|^{ - 2 - \varepsilon } S_i \cdot S_j ,} \varepsilon > 0$$ whereJ (i, j) has mean 0 and variance 1, for alli, j. We comment on the role of boundary conditions in spin glasses and on their critical behaviour in high dimensions.     

Separable coordinates for four-dimensional Riemannian spaces

We present a complete list of all separable coordinate systems for the equations and with special emphasis on nonorthogonal coordinates. Applications to general relativity theory are indicated.     

On the classification of multidimensionally consistent 3D maps

We classify multidimensionally consistent maps given by (formal or convergent) series of the following kind:

$$\begin{aligned} T_k x_{ij}=x_{ij} + \sum _{m=2}^\infty A_{ij ; \, k}^{(m)}(x_{ij},x_{ik},x_{jk}), \end{aligned}$$

where \(A_{ij;\, k}^{(m)}\) are homogeneous polynomials of degree m of their respective arguments. The result of our classification is that the only non-trivial multidimensionally consistent map in this class is given by the well-known symmetric discrete Darboux system

$$\begin{aligned} T_k x_{ij}=\frac{x_{ij}+x_{ik}x_{jk}}{\sqrt{1-x_{ik}^2}\sqrt{1-x_{jk}^2}}. \end{aligned}$$

     

No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics

Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s and Bob’s spins are identified as $A_{ij}$ and $B_{ij}$ , even though their distributions are determined by, respectively, $\alpha _{i}$ alone and $\beta _{j}$ alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins $A_{ij},B_{ij}$ across all values of $\alpha _{i},\beta _{j}$ are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs $\left( A_{ij},A_{ij'}\right) $ and $\left( B_{ij},B_{i'j}\right) $ with $\alpha _{i}\not =\alpha _{i'}$ and $\beta _{j}\not =\beta _{j'}$ (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of $A_{ij}\not =A_{ij'}$ and $B_{ij}\not =B_{i'j}$ ). Thus, one can achieve a complete KPT characterization of the Bell-type inequalities, or Tsirelson’s inequalities, by specifying the distributions of probabilistic connections compatible with those and only those spin pairs $\left( A_{ij},B_{ij}\right) $ that are subject to these inequalities. We show, however, that quantum-mechanical (QM) constraints are special. No-forcing theorem says that if a set of probabilistic connections is not compatible with correlations violating QM, then it is compatible only with the classical–mechanical correlations. No-matching theorem says that there are no subsets of the spin variables $A_{ij},B_{ij}$ whose distributions can be fixed to be compatible with and only with QM-compliant correlations.     

Remarks on the charged multiplicity of hadronic Z0(91) decays

The charged multiplicity distribution of hadronic decays of Z ⁰ from LEP and those of inclusive $e^{+}+e^{-}?ghtarrow h{?erline h} at E_{? cm}=14 {? to} 60 {? GeV}$ at E _cm = 14 to 61 GeV are analyzed using a Poisson-type distribution for photon statistics, due to Scully-Lamb. Its two parameters are expressed in terms of 〈n〉 and f ₂ = 〈n(n ? 1)〉 ? 〈n〉² of the data in order to perform no-free-parameter fits. It is found that f₂ behaves like $E_{? cm}^{a}$ with a = 2.01 ± 0.11, whereas C ₂ = 〈n ²〉/〈n〉² ～ E _cm with ΔC ₂/ΔE _cm = (1.81 ± 0.14)·10^?3.     

Radiative B* meson decays in QCD sum rules

The decay constant g _B* of the B* mesons and the transition amplitudes of the radiative decays $B_{a}^{?t}?ghtarrow B_{a}αmma$are calculated in the frame-work of QCD sum rules. It is shown that the decay rates B* → Bγ are one order smaller than the corresponding D* meson decays.     

Photoproduction of jets and the virtual structure of the photon

We compute the ratio between the direct and the resolved photon components of single jet and dijet production in ep collisions for the kinematical range covered by the most recent ZEUS data. We analyse the phenomenological consequences of different models for the structure of virtual photons in these observables and compare them with the available data. We also comment on the correlation between the so-called $x_{αmma}^{? obs}$ and the ‘true’ x_γ, that can be inferred from the data.     

Spin and torsion in general relativity: I. Foundations

From physical arguments space-time is assumed to possess a connection \(\Gamma _{ij}^k = \left\{ {\begin{array}{*{20}c} k \\ {ij} \\ \end{array} } \right\} + S_{ij}^{ k} - S_{j i}^{ k} + S_{ ij}^k = \left\{ {\begin{array}{*{20}c} k \\ {ij} \\ \end{array} } \right\} - K_{ij}^{ k} \) . \(\left\{ {\begin{array}{*{20}c} k \\ {ij} \\ \end{array} } \right\}\) is Christoffel's symbol built up from the metric g _ij and already appearing in General Relativity (GR). Cartan's torsion tensor \(S_{ij} ^k = \tfrac{1}{2}(\Gamma _{ij}^k - \Gamma _{ji}^k )\) and the contortion tensor K _ij ^k , in contrast to the theory presented here, both vanish identically in conventional GR. Using the connection introduced above in this series of articles, we will discuss the consequences for GR in the framework of a consistent formalism. There emerges a theory describing, in a unified way, gravitation and a very weak spin-spin contact interaction. In section 1 we start with the well-known dynamical definition of the energy-momentum tensor σ ^ij ～ δ?/δg _ij , where ? represents the Lagrangian density of matter (section1.1). In sections1.2,3 we will show that due to geometrical reasons, the connection assumed above leads to a dynamical definition of the spin-angular momentum tensor according to τ^k _ji ～ δ?/δK _ij ^k . In section1.4, by an ideal experiment, it will become clear that spin prohibits the introduction of an instantaneous rest system and thereby of a geodesic coordinate system. Among other things in section1.5 there are some remarks about the rôle torsion played in former physical theories. In section 2 we sketch the content of the theory. As in GR, the action function is the sum of the material and the field action function (sections2.1,2). The extension of GR consists in the introduction of torsion S _ij ^k as a new field. By variation of the action function with respect to metric and torsion we obtain the field equations in a general form (section2.3). They are also valid for matter described by spinors; in this case, however, one has to introduce tetrads as anholonomic coordinates and slightly to generalize the dynamical definition of energy-momentum (sections2.4,5).     

J/Ψ and Ψ′ production in hadronic Z0 decays

The production of Jψ mesons in Z⁰ decays is studied using 3.6 million hadronic events recorded by the OPAL detector at LEP. The inclusive Z⁰ to Jψ and b-quark to Jψ branching ratios are measured from the total yield of Jψ mesons, identified from their decays into lepton pairs. The Jψ momentum distribution is used to study the fragmentation of b-quarks. The production rate of ψ′ mesons, identified from their decays into a Jψ and a π⁺π^? pair, is measured as well. The following results are obtained: ${Br(Z^{0}?ghtarrow {? J}/?i X)=(3.9pm 0.2pm 0.3)cdot 10^{-3} {? and} ?op Br(Z^0?ghtarrow ?i ^?ime X)=(1.6pm 0.3pm 0.2)cdot 10^{-3}, }$ where the first error is statistical and the second systematic. Finally the Jψ sample is used to reconstruct exclusive b-hadron decays and calculate the corresponding b-hadron branching ratios and masses.     

QED interconnection effects on W momentum distributions at LEP 2

The process ${? e}^{+}{? e}^{-}?ghtarrow {? W}^{+}{? W}^{-}?ghtarrow {? f}_{1}{?erline {? f}}_{2}{? f}_{3}{?erline {? f}}_{4}$ contains charges in the initial, intermediate and final stages. This gives a rich selection of possible QED interconnection effects. Coulomb interaction is the simplest of these, and can thus be used to explore consequences. We study a number of experimental observables, with emphasis on those related to the W momentum distribution. Second-order Coulomb effects are shown to be practically negligible. The limited LEP 2 statistics will not allow detailed tests, so any theory uncertainty will be reflected in the systematic error on the W mass. Currently the uncertainty from this source may be as high as 20 MeV.     

Collective Dand Structures in Doubly Odd 136La Nucleus

Using heavy-ion nuclear reaction and in-beam γ-ray spectroscopy technique,high spin states of ¹³⁶La have been studied. The nuclear reaction used is ¹³⁰Te(¹¹B,5n) with a beam energy 60MeV. The level scheme with three collective band structures has been updated with spin up to 20h. The collective backbending has been observed in $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band. According to the TRS calculations,this backbending is due to the alignment of a pair of h_11/2 neutrons. The signature splitting and inversion for the $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band were also discussed. Other two bands based on $12^-$ and $16^+$ levels were proposed as oblate deformation with $\gamma\approx -60^\circ$. They most probably originate from four- and six- quasiparticle configurations, that is,$\uppi h_{11/2}\otimes\upnu g_{7/2} h_{11/2}^2$ and $\uppi g_{7/2}\otimes\upnu g_{7/2}^2 d_{5/2}h_{11/2}^2$ respectively.