Is there a 2++ glueball at 1410 MeV?

A glueball component of theJ ^PC =2⁺⁺ q \(\bar q\) isoscalar states is discussed within a simple mass mixing model. As the third isoscalar necessarily present in theq \(\bar q\) ?gg mixing scheme we assumeG(1410) recently claimed by ACCMOR Collaboration in the π^? p→K _s ⁰ K _s ⁰ n data. The hypothesis is found to be compatible with the available experimental data, including two-photon decay widths and radiativeJ/ψ decays.     

Inclusive production ofK s 0 , K s 0 K s 0 andK *±(892) in\bar pp interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c

InclusiveK _s ⁰ andK _s ⁰ K _s ⁰ production in \(\bar pp\) interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c are studied. Cross sections ofK _s ⁰ , K _s ⁰ K _s ⁰ andK ^*±(892) are presented for each incident momentum. The production ofK _s ⁰ andK ^*±(892) through annihilation process is investigated. It is found that the annihilation process is dominant but decreases with incident momentum. The annihilation process is compared withe ⁺ e ^? interactions. Remarkable similarity between them is found in the \({{x_0 = 2E(K_s^0 )} \mathord{\left/ {\vphantom {{x_0 = 2E(K_s^0 )} {\sqrt s }}} \right. \kern-0em} {\sqrt s }}\) distribution. Events with two detectedK _s ⁰ 's are analyzed. The result shows theK _s ⁰ K _s ⁰ pairs are produced in the central region of c.m. system and there is a clearS ^* signal in theK _s ⁰ K _s ⁰ effective mass distribution.     

Mixing of intermediate bosons with Q\bar Q bound states

We discuss the effects of a close degeneracy between theZ ⁰ and vectorQ \(\bar Q\) bound states; large mixing effects can appear modifying mainly theQ \(\bar Q\) states (widths and couplings) and leading to curious structures inside theZ peak.     

On some properties of the neutron in the statistical model

Using the statistical model to arrive at |ψ(r)|² the square modulus of theS state wavefunction of the neutron, the electric dipole moment |d _n ^e | of the neutron as well as its baryon number violating lifetime have been estimated. The baryon asymmetry of the universe depending on |d _n ^e | has also been studied in this context.     

The ππ S-wave in the 1 to 2 GeV region from a ππ,\bar K K and ρρ(ωω) coupled channel model

A simpleππ, $\bar K$ K, andρρ(ωω) fully coupled channel model is proposed to predict the isoscalarS-wave phase shifts and inelasticities forππ scattering in the 1.0 to 2.0 GeV region. TheS- matrix is required to exhibit poles corresponding to the established isoscalarJ ^π=0⁺ resonancesf ₀(975),f ₀(1400), andf ₀(1710). A dominant feature of the experimentalππ inelasticity is the clear opening of the $\bar K$ K channel near 1 GeV, and the opening of another channel in the 1.4–1.5 GeV region. The success of our model in predicting this observed dramatic energy dependence indicates that the effect of multipion channels is adequately described by theππ coupling to the $\bar K$ K channel, theρρ(4π) andωω(6π) channels.     

Conserved-vector-current hypothesis and the\bar v_e e^ - \to \pi ^ - \pi ^0 process

Based on the conserved-vector-current (CVC) hypothesis and a four-ρ-resonance unitary and analytic VMD model of the pion electromagnetic form factor, theσ _tot(E _v ^lab ) and dσdE _π ^lab of the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) process are predicted theoretically for the first time. Their experimental approval could verify the CVC hypothesis for all energies above the two-pion threshold. Since, unlike the electromagnetic e⁺e^?→π⁺π^? process, there is no isoscalar vector-meson contribution to the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) reaction, accurate measurements of theσ _tot(E _v ^lab ) that moreover is strengthened with energyE _v ^lab linearly could solve now a widely discussed problem of the mass specification of the first excited state of theρ(770) meson. As a by-product, an equality \(\sigma _{tot} (\bar v_e e^ - \to \pi ^ - \pi ^0 ) = \sigma _{tot} (e^ + e^ - \to \pi ^ - \pi ^0 )\) is predicted for \(\sqrt s \approx 70 GeV\) .     

Demonstration of the origins of cooperativity within SU2×L 6 mapping over\left\{ {I\tilde H_\upsilon } \right\} Liouvillian carrier subspaces characterising the MQ-NMR cluster [A]6(L 6) and its\{ |kq\upsilon :[\tilde \lambda ] > > \} tensorial bases

The fundamental mappings over carrier subspace and substructures associated with \(\{ |kq\upsilon > > \} \) augmented spin algebras of Liouville space, and their mapping onto a subduced symmetry, are derived for [A]₆(L ₆) spin clusters within the combinatorial context of Rota-Cayley algebra over a field. Use of suitable lexical sets of combinatorialp-tuples (number partitions) over {|IM(M ₁?M _n )>}M, followed by the subsequent use ofL _n inner tensor product (ITP) algebra, allows the substructure of Liouville space to be derived. For SU2×L ₆ mapping over the simply-reducible \(\left\{ {I\tilde H_\upsilon } \right\}\) carrier subspaces, the \(D^k \left( {\tilde U} \right) \times \tilde \Gamma ^{\left[ {\tilde \lambda } \right]} \left( \upsilon \right)\) (L ₆) dual irreps, also arise as a consequence of the Liouville space recoupling termsv≡{k ₁?k _n } being distinct labels for \(\left\{ {I\tilde H_\upsilon } \right\}\) which are themselves amenible to combinatorial analysis within the concept of Rota-Cayley algebra. Hence, theL _n -induced symmetry aspects of multiquantum NMR density matrix formalisms and their dual \(\{ |kq\upsilon :[\tilde \lambda ] > > \} \) tensorial bases of spin cluster problems are derived and the nature of the cooperative, aspect between the individual symmetries comprising the duality is demonstrated, i.e. in the context of the operator bases of Liouville space. These practical arguments correlate, well with those based on an augmented boson pattern algebra derived from a Heisenburg algebra for superoperators, ?_±,?₀. An earlier, treatment of conventional Hilbert space SU2×L ₆ dualitycould only be realised in terms of standard SU2 boson algebra. Since the recoupling Rota-‘field’v for Liouville space is an explicit aspect of the dual mapping, a direct demonstration of cooperativity exists.     

Invariant states and conditional expectations of the anticommutation relations

The groupG of unitary elements of a maximal abelian von Neumann algebra on a separable, complex Hilbert spaceH acts as a group of automorphisms on the CAR algebraA(H) overH. It is shown that the set ofG-invariant states is a simplex, isomorphic to the set of regular probability measures on aw*-compact setS ofG-invariant generalized free states. The GNS Hilbert space induced by an arbitraryG-invariant state onA(H) supports a *-representation ofC(S); the canonical map ofA(H) intoC(S) can then be locally implemented by a normal,G-invariant conditional expectation.     

BFKL Pomeron in the reaction γ ⊥ * (Q 2)p→ρ ⊥ 0 p at large Q 2 and W

The reaction γ _⊥ ^* (Q ²)p→ρ _⊥ ⁰ p has been studied at large Q ² and W ²/Q ² and low momentum transfers to the nucleon, k _⊥ ² —that is, in the region where the Pomeron exchange mechanism is operative. At sufficiently large Q ², the Pomeron interacts with quarks occurring at small distances, whereby the hard component of the Pomeron is separated, so that the process is governed by the Pomeron of perturbative QCD (BFKL Pomeron). Our calculations indicate that, in vector-meson electroproduction at low k _⊥ ² , the perturbative regime cannot set in fast because, for Q ²≤100 GeV² and, accordingly, for W ²/Q ²≤10⁷, comparatively large distances of $\rho _{q\bar q} > 0.2$ fm are important.     

The spectral class of the quantum-mechanical harmonic oscillator

The purpose of this paper is to study the so-calledspectral class Q of anharmonic oscillatorsQ=?D ²+q having the same spectrum λ _n =2n (n≧0) as the harmonic oscillatorQ ⁰=?D ²+x ²?1. Thenorming constants \(t_n = \mathop {\lim }\limits_{x \uparrow \infty } \ell g[( - 1)^n {{e_n (x)} \mathord{\left/ {\vphantom {{e_n (x)} {e_n }}} \right. \kern-0em} {e_n }}( - x)]\) of the eigenfunctions ofQ form a complete set of coordinates inQ in terms of which the potential may be expressed asq=x ²?1?2D ² ?g? with $$\theta = \det \left[ {\delta _{ij} + (e^{ti} - 1)\int\limits_x^\infty {e_i^0 e_j^0 :0 \leqq i,j,< \infty } } \right],$$ e _n ⁰ being then ^th eigenfunctionQ ⁰. The spectrum and norming constants are canonically conjugate relative to the bracket [F, G]=∫ΔFDΔGdx,to wit: [λ _i , λj=0, [t _i, 2λ _j ]=1 or 0 according to whetheri=j or not, and [t _i,t _j]=0. This prompts an investigation of the symplectic geometry ofQ. The function ? is related to the theta function of a singular algebraic curve. Numerical results are also presented.     

Study of the iterations of a mapping associated to a spin glass model

We study the iterations of the mapping $$\mathcal{N}[F(s)] = \frac{{(F(s))^2 - (F(0))^2 }}{s} + (F(0))^2 ,$$ with the constraintsF(1)=1,F(s)=∑a _nsⁿ,a _n≧0, and find that, except ifF(s)≡s,N[F(s)] approaches either 0 or 1 for |s|<1 ask→∞.     

FastJet user manual

FastJet is a C++ package that provides a broad range of jet finding and analysis tools. It includes efficient native implementations of all widely used 2??1 sequential recombination jet algorithms for pp and e ⁺ e ^? collisions, as well as access to 3rd party jet algorithms through a plugin mechanism, including all currently used cone algorithms. FastJet also provides means to facilitate the manipulation of jet substructure, including some common boosted heavy-object taggers, as well as tools for estimation of pileup and underlying-event noise levels, determination of jet areas and subtraction or suppression of noise in jets.     

A Mermin–Wagner Theorem for Gibbs States on Lorentzian Triangulations

We establish a Mermin–Wagner type theorem for Gibbs states on infinite random Lorentzian triangulations (LT) arising in models of quantum gravity. Such a triangulation is naturally related to the distribution P of a critical Galton–Watson tree, conditional upon non-extinction. At the vertices of the triangles we place classical spins taking values in a torus M of dimension d, with a given group action of a torus G of dimension d′≤d. In the main body of the paper we assume that the spins interact via a two-body nearest-neighbor potential U(x,y) invariant under the action of G. We analyze quenched Gibbs measures generated by U and prove that, for P-almost all Lorentzian triangulations, every such Gibbs measure is G-invariant, which means the absence of spontaneous continuous symmetry-breaking.     

Asymmetry extraction in experiment for measurement of neutron electric form-factor at high momentum transfer

Measurement of the neutron electric form-factor G _E ⁿ for the values of the transferred momentum Q ² = 1.3, 1.7, 2.5, and 3.5 (GeV/c)² has been performed at the Jefferson Laboratory (USA). The experiment used the technique of double polarization where the asymmetry of the quasielastic scattering in the semi-inclusive ³ $ \overrightarrow {He} $ ( $ \vec e $ . e′n)pp reaction is measured. The obtained asymmetry is connected directly with the ratio of electric to magnetic form-factors of the neutron which allows obtaining the former with use of the known values of the latter. This work presents the technique of extraction of the asymmetry from the obtained experimental data.     

Further study of theE/f 1 (1420) meson in central production

We have studied the reactions \(({{\pi ^ + } \mathord{\left/ {\vphantom {{\pi ^ + } p}} \right. \kern-0em} p})p \to ({{\pi ^ + } \mathord{\left/ {\vphantom {{\pi ^ + } p}} \right. \kern-0em} p})(K\bar K\pi )p\) where the \(K\bar K\pi \) system is centrally produced, at 85 GeV/c and 300 GeV/c using the CERN Omega spectrometer. A spin-parity analysis of theK _S ⁰ K ^± π ^? system shows the presence of a strongJ ^PC=1⁺⁺ signal which we identify as theE/f ₁ (1420) meson. We also find evidence for the decayE/f ₁(1420)→K _S ⁰ K _S ⁰ π ⁰ which determines theC-parity of this state to be positive. Alternative explanations of the data have been tested and ruled out. Hence we obtain the quantum numbers of theE/f ₁ (1420) to beI ^G(J^PC)=0⁺(1⁺).     

The penetration parameter λ of the anomalousM1-conversion of the 482 keV transition in181Ta

Byγ- e _K ^? ande _K ^? -γ TDPAC measurements with the 133 keV–482 keV cascade of¹⁸¹Ta in a polycrystalline beryllium matrix theA ₂(e _K ^? )-coefficient of the 482 keV transition was determined as: A₂(482e _K ^? )=?0.095±0.015. The theoretical value is 6.0 times larger. A remeasurement of the E2/M1 mixing ratio of the same transition by integralγ- γ angular correlation measurements with a system of three 20 ccm Ge(Li)-detectors gave the result:δ(482)=4.96±0.25. Theα _K -coefficient was redetermined as:α _K (482)=0.0246±0.0018. From these data the penetration parameter:λ=157±11 is derived and compared with previously published values and theoretical estimates.     

Inclusive production ofK *(892) andΣ(1385) in\bar p p interactions at 3.6 GeV/c and a test of factorization hypothesis

We present a study of the inclusive production ofK ^*(892) and ∑^t+-(1385)+cc at 3.6 GeV/c from \(\bar p\) p interactions. The sensitivity of the exposure is 35.4 events/μb. Longitudinal and transverse momentum distributions are presented. The indirect production ofK _s ⁰ from parentK ^* and that of Λ's from parent Σ(1385) are studied. The shape of thex distribution of Λ's for \(p\xrightarrow{{\bar p}}\Lambda \) are calculated from \(p\xrightarrow{p}\Lambda \) and \(p\xrightarrow{{\pi ^ - }}\Lambda \) and compared with the experimental distributions. The difference of antiparticle production cross-section ofK _s ⁰ in the central region is compared with the expectation from Mueller-Regge formalism.