\bar \Lambda Production inK − p interactions at 32 GeV/c

Antilambda production is studied inK ^? p interactions at 32 GeV/c. Both total and differential cross sections are presented. The inclusive \(\bar \Lambda \) production cross section amounts to 109±7 μb. A remarkable energy dependence is observed, σ( \(\bar \Lambda \) ) increasing by a factor of four between 14.3 and 32 GeV/c. Thep _⊥ ² distribution exhibits an exponential fall-off with a slope of 3.3±0.2 (GeV/c)^?2. Most of the \(\bar \Lambda \) 's are emitted in the forward hemisphere. The invariantx distribution increases between 14.3 and 32 GeV/c. Data are presented for \(\bar \Lambda \) production inK ^- p→Λ \(\bar \Lambda \) +X K ^- p→ \(\bar \Lambda \) K ⁿ +X, andK ^- p→ \(\bar \Lambda \) p+X.     

p¯p Annihilation into two mesons in the quark rearrangement model and the quark annihilation model

The relativistic³ P ₀ model is applied to the \(p\bar p\) annihilation into twoS-wave mesons. We calculate the branching ratios of the \(p\bar p\) annihilation at rest into two mesons in the quark rearrangement model and in the quark annihilation model. In the annihilation model, we project the intermediate \(cq\bar q\) state to eigenstates ofSU (4) with the relative angular momentum of \(cq\bar q\) equals orp. In the rearrangement model, no annihilation occurs from theS-wave \(p\bar p\) and certain branching ratios conflict with the experimental data. Detailed comparison with the experiment needs inclusion ofP-wave mesons in the final state, nevertheless we find that the annihilation model gives qualitatively better results than the rearrangement model. The effect of initial state interaction through \(N\bar \Delta \pm \Delta \bar {\rm N}\) or \(\Delta \bar \Delta \) channels is discussed.     

On the rate of quantum ergodicity I: Upper bounds

One problem in quantum ergodicity is to estimate the rate of decay of the sums $$S_k (\lambda ;A) = \frac{1}{{N(\lambda )}}\sum\limits_{\sqrt {\lambda _j } \leqq \lambda } {\left| {(A\varphi _j ,\varphi _j ) - \bar \sigma _A } \right|^k } $$ on a compact Riemannian manifold (M, g) with ergodic geodesic flow. Here, {λ _j ,? _j } are the spectral data of the Δ of(M, g), A is a 0-th order ψDO, $\bar \sigma _A $ is the (Liouville) average of its principal symbol and $N(\lambda ) = \# \{ j:\sqrt {\lambda _j } \leqq \lambda \} $ . ThatS _k (λ;A)=o(1) is proved in [S, Z.1, CV.1]. Our purpose here is to show thatS _k (λ;A)=O((logλ) ^?k/2 ) on a manifold of (possibly variable) negative curvature. The main new ingredient is the central limit theorem for geodesic flows on such spaces ([R, Si]).     

Brownian motion in a convex ring and quasi-concavity

LetX be the Brownian motion in ? ⁿ and denote by τ _M the first hitting time ofM?? ⁿ . Given convex setsK?L?? ⁿ we prove that all the level sets $$\{ \left( {x,t} \right) \in \mathbb{R}^n \times [0, + \infty [;P_x [\tau _K \leqq t \wedge \tau _{L^c } ] \geqq \lambda \} ,\lambda \in \mathbb{R}$$ are convex.     

An inequality for Hilbert-Schmidt norm

For the absolute value |C|=(C*C)^1/2 and the Hilbert-Schmidt norm ∥C∥_HS=(trC*C)^1/2 of an operatorC, the following inequality is proved for any bounded linear operatorsA andB on a Hilbert space $$|| |A|---|B| ||_{HS} \leqq 2^{1/2} ||A - B||_{HS} $$ . The corresponding inequality for two normal state ? and ψ of a von Neumann algebraM is also proved in the following form: $$d(\varphi ,\psi ) \leqq ||\xi (\varphi ) - \xi (\psi )|| \leqq 2^{1/2} d(\varphi ,\psi )$$ . Here ξ(χ) denotes the unique vector representative of a state χ in a natural positive coneP ^? forM, andd(?, ψ) denotes the Bures distance defined as the infimum (which is also the minimum) of the distance of vector representatives of ? and ψ. In particular, $$||\xi (\varphi _1 ) - \xi (\varphi _2 )|| \leqq 2^{1/2} ||\xi _1 - \xi _2 ||$$ for any vector representatives ξ _j of ? _j ,j=1, 2.     

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.     

A Level 1 Large-Deviation Principle for the Autocovariances of Uniquely Ergodic Transformations with Additive Noise

A large-deviation principle (LDP) at level 1 for random means of the type $$M_n \equiv \frac{1}{n}\sum\limits_{j = 0}^{n - 1} {Z_j Z_{j + 1} ,{\text{ }}n = 1,2,...}$$ is established. The random process {Z _n} _n≥0 is given by Z _n = Φ(X _n) + ξ _n , n = 0, 1, 2,..., where {X _n} _n≥0 and {ξ _n} _n≥0 are independent random sequences: the former is a stationary process defined by X _n = T ⁿ(X ₀), X ₀ is uniformly distributed on the circle S ¹, T: S ¹ → S ¹ is a continuous, uniquely ergodic transformation preserving the Lebesgue measure on S ¹, and {ξ_n} _n≥0 is a random sequence of independent and identically distributed random variables on S ¹; Φ is a continuous real function. The LDP at level 1 for the means M _n is obtained by using the level 2 LDP for the Markov process {V _n = (X _n, ξ _n , ξ _n+1)} _n≥0 and the contraction principle. For establishing this level 2 LDP, one can consider a more general setting: T: [0, 1) → [0, 1) is a measure-preserving Lebesgue measure, $\Phi :\left[ {0,\left. 1 \right)} \right. \to \mathbb{R}$ is a real measurable function, and ξ _n are independent and identically distributed random variables on $\mathbb{R}$ (for instance, they could have a Gaussian distribution with mean zero and variance σ²). The analogous result for the case of autocovariance of order k is also true.     

Multi-quark structure ofU(3.1)

We interpret the recently observedU(3.1) mesons with the \(\Lambda \bar p\) + pions decays as the bound state of \(\Lambda ,\bar p\) andX ₀(1480). TheX ₀(1480) is a mesonium with \(Q^2 \bar Q^2 \) structures observed in γγ reactions and \(\bar pn\) annihilations. With this interpretation, we can understand its decay modes. Furthermore, we predict the ratio of \(\sigma (\Lambda \bar p\pi ^ + \pi ^ - )/\sigma (\Lambda \bar p\pi ^ + \pi ^ + )\) to be ?3.1 for centrally produced events and that the width of \(U^ - (\Lambda \bar p\pi ^ + \pi ^ - )\) to be greater than that of \(U^ + (\Lambda \bar p\pi ^ + \pi ^ + )\) . Both predictions seem to be in reasonable accord with the available data. We call for the detection of the \(\Lambda \bar p\pi ^ - \pi ^ - \) mode to verify the present interpretation.     

Phenomenology of composite colored weak bosons

In composite models of quarks, leptons and weak bosons whereW-constituents are colored objects, color octet partners ofW ^± andZ ⁰ are predicted. We study in detail the phenomenology of these particles. Independent of the specific model one expects a color octet isotriplet of vector bosons (W ₈ ^± ,Z ₈ ⁰ ) with mass in the range of 100–200 GeV, and a color octet isosinglet vector bosonV ₈ ⁰ with substantially larger mass, due to mixing with the gluon. Moreover, relatively light color octet excitations of the leptons appear, while the existence of “color exotic” partners of the quarks is model dependent. These particles decay mainly into a lepton (quark) and a gluon. We construct the couplings ofW ₈ ^± ,Z ₈ ⁰ andV ₈ ⁰ to ordinary and “color exotic” fermions. The signals of color octet weak bosons in low energy weak reactions are explored in detail. The production cross section ofW ₈ ^± (Z ₈ ⁰ ) in hadron-hadron collisions is calculated for \(0.54TeV \leqq \sqrt s \leqq 20TeV\) . Various decay modes of colored weak bosons are studied. The most prominent decay signatures ofW ₈ ^± andZ ₈ ⁰ are events of the type (l ^+-: charged lepton;j: hadronic jet; : missing transverse momentum). The present CERN \(p\bar p\) collider data on such events are discussed in the light ofW ₈ ^± andZ ₈ ⁰ decays. If colored weak bosons are not found with a mass less than ～250 GeV composite model building will be strongly restricted.     

Thep - \bar p decays ofP-wave quarkonium and the helicity characteristics of massless QCD

We consider the exclusive \(p - \bar p\) decays of the quarkoniumP-states. Due to the helicity conservation of massless QCD the \(p - \bar p\) mode is forbidden in this limit for the¹ P ₁ and the³ P ₀ states. The angular distributions for the decays of the remaining states in the cascade \(^3 S\prime _1 \to \gamma ^3 P_J \to \gamma p\bar p\) are specific to QCD and can serve as a test of the theory. The same is true of the formation process \(p\bar p \to ^3 P_J \to ^3 S_1 \gamma \) . In lowest order QCD we obtain overall branching ratios for charmonium of the order of 10^?4.     

A reanalysis of branching fractions of charmed mesonsD 0,D + andD s +

We combine highly complementary information on branching fractions of charmed mesonsD ⁰,D ⁺ andD _s ⁺ coming from two experiments both yielding doublecharm samples. The NA 32 experiment provided exclusive branching fractions for channels with at least two charged decay products while a recent Mark III paper provides results on inclusive charm decay properties. The knowledge of channels withK ⁰'s in the former is used to recalculate the charged multiplicity distribution in the latter. We obtain 〈n _ch〉=2.25±0.08 forD ⁰, 〈n _ch〉=1.96±0.08 forD ⁺ and 〈n _ch〉=2.41±0.38 forD _s ⁺ . In turn the knowledge of the charged multiplicity improves the overall normalization of exclusive branching fractions. This reanalysis yields model-independent results for charmed mesons. In particular we obtain branching fractions for 16D _s ⁺ decay channels including $$BF(D_s^ + \to \phi \pi ^ + ) = \left( {4.4\begin{array}{*{20}c} { + 2.3} \\ { - 1.8} \\ \end{array} } \right)\% .$$ .     

Topological pomeron andA-universality

The nuclear mass number dependence of inclusive spectra of secondaries with different quantum numbers in the projectile fragmentation region is analysed. We note that in models with topological pomeron, all the particle spectra fall into two main categories. The first one comprises particles which have a common “valence” quark with the projectile, the second one comprises all the other particles built of “sea” quarks. Thus, in the parameterization \(x\frac{{d\sigma }}{{dx}} \propto A^{\alpha (x)} \) the spectra of all “valence” hadrons (p, n, Λ, π^+,0,?,K ⁺, ... in thepA-interaction) atx→1 can be characterized by the single exponent α_υ =α(x?1) which differs slightly from α _s characterizing the spectra of “sea” hadrons ( \(\bar p, \bar \Lambda \) ,K ^?, ... forpA-interactions). This observation is essentially modelindependent and follows only from the topological structure of the pomeron and Gribov's space-time picture of soft hadronic interactions. Deviations from universality due to preasymptotic corrections and coherent particle production processes are estimated.     

Quark-diagram estimates ofCP violation in two-body baryonicB_d^0 - \bar B_d^0 decays

CP violation in partial-decay-rate asymmetries are examined for some two-body baryonic decays of \(B_d^0 - \bar B_d^0 \) system. We discuss two feasible experimental circumstances: the symmetrice ⁺ e ^? collisions (i) on theZ ⁰ resonance to produce incoherent \(B_d^0 \bar B_d^0 \) states, and (ii) just above the ?(4S) resonance to produceC=even \(B_d^0 \bar B_d^0 \) states. Using the quark-diagram scheme, we estimate the branching ratios of those decays, and the numbers ofb \(\bar b\) pairs needed for testing theCP-violating effects for 3σ signature. We find that the promising channels may beB _d ⁰ , \(\bar B_d^0 \to p\bar p\) , \(\Delta ^ + \bar \Delta ^ - \) , \(p\bar \Delta ^ - \) , \(\Delta ^ + \bar p\) , \(n\bar n\) , \(\Delta ^0 \bar \Delta ^0 \) , \(n\bar \Delta ^0 \) , \(\Delta ^0 \bar n\) , \(\Sigma _c^ + \bar \Sigma _c^ - \) , \(\Lambda _c^ + \bar \Lambda _c^ - \) , \(\Sigma _c^ + \bar \Lambda _c^ - \) , \(\Lambda _c^ + \bar \Sigma _c^ - \) , \(\Sigma _c^0 \bar \Sigma _c^0 \) , \(\Xi _c^0 \bar \Xi _c^0 \) , which should be interesting for experimental observation.     

Eine scheinbare Abschwächung der Lokalitätsbedingung. II

If for a relativistic field theory the expectation values of the commutator (Ω|[A (x),A(y)]|Ω) vanish in space-like direction like exp {? const|(x-y ²|^α/2#x007D; with α>1 for sufficiently many vectors Ω, it follows thatA(x) is a local field. Or more precisely: For a hermitean, scalar, tempered fieldA(x) the locality axiom can be replaced by the following conditions 1. For any natural numbern there exist a) a configurationX(n): $$X_1 ,...,X_{n - 1} X_1^i = \cdot \cdot \cdot = X_{n - 1}^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^1 - X_{i + 1}^1 )} \right]^2 + \left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^2 - X_{i + 1}^2 )} \right]^2 > 0\) for all λ _i ≧0i=1,...,n?2, \(\sum\limits_{i = 1}^{n - 2} {\lambda _i > 0} \) , b) neighbourhoods of theX _i 's:U _i (X _i )?R ⁴ i=1,...,n?1 (in the euclidean topology ofR ⁴) and c) a real number α>1 such that for all points (x):x ₁, ...,x _n?1:x _i ∈U _i (X _r ) there are positive constantsC ⁽ⁿ⁾{(x)},h ⁽ⁿ⁾{(x)} with: $$\left| {\left\langle {\left[ {A(x_1 )...A(x_{n - 1} ),A(x_n )} \right]} \right\rangle } \right|< C^{(n)} \left\{ {(x)} \right\}\exp \left\{ { - h^{(n)} \left\{ {(x)} \right\}r^\alpha } \right\}forx_n = \left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ r \\ \end{array} } \right),r > 1.$$ 2. For any natural numbern there exist a) a configurationY(n): $$Y_2 ,Y_3 ,...,Y_n Y_3^i = \cdot \cdot \cdot = Y_n^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^1 - Y_{i{\text{ + 1}}}^{\text{1}} } )} \right]^2 + \left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^2 - Y_{i{\text{ + 1}}}^{\text{2}} } )} \right]^2 > 0\) for all μ _i ≧0,i=3, ...,n?1, \(\sum\limits_{i = 3}^{n - 1} {\mu _i > 0} \) , b) neighbourhoods of theY _i 's:V _i(Y _i )?R ⁴ i=2, ...,n (in the euclidean topology ofR ⁴) and c) a real number β>1 such that for all points (y):y ₂, ...,y _n y _i ∈V _i (Y _i there are positive constantsC _(n){(y)},h _(n){(y)} and a real number γ_(n){(y)∈a closed subset ofR?{0}?{1} with: γ_(n){(y)}\y ₂,y ₃, ...,y _n totally space-like in the order 2, 3, ...,n and $$\left| {\left\langle {\left[ {A(x_1 ),A(x_2 )} \right]A(y_3 )...A(y_n )} \right\rangle } \right|< C_{(n)} \left\{ {(y)} \right\}\exp \left\{ { - h_{(n)} \left\{ {(y)} \right\}r^\beta } \right\}$$ for \(x_1 = \gamma _{(n)} \left\{ {(y)} \right\}r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right),x_2 = y_2 - [1 - \gamma _{(n)} \{ (y)\} ]r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right)\) and for sufficiently large values ofr.     

Estimates of general Mayer graphs III: Upper bounds obtained by means of spanningn-trees

We obtain computable upper bounds for any given Mayer graph withn root-points (orn-graph). These are products of integrals of the type \(\left( {\int {\left| {f_L } \right|^{z_{iL} y_i^{ - 1} } dx} } \right)^{yi} \) , where thez _iL andy _i are nonnegative real numbers whose sum overi is equal to 1. As a particular case, we obtain the canonical bounds (see their definition in Section 2.2): $$\left| {\int {\prod\limits_L {f_L \left( {x_i ,x_j } \right)dx_{n + 1} \cdot \cdot \cdot dx_{n + k} } } } \right| \leqslant \prod\limits_L {\left( {\int {\left| {f_L } \right|^{\alpha _L } dx} } \right)^{\alpha _L^{ - 1} } } $$ where theα _L 's satisfy the conditionα _L ≥1 for anyL, and ∑ _L α _L ^?1 =k (k is the number of variables that are integrated over). These bounds are finite for alln-graphs of neutral systems. We obtain also finite bounds for all irreduciblen-graphs of polar systems, and for certainn-graphs occurring in the theory of ionized systems. Finally, we give a sufficient condition for an arbitraryn-graph to be finite.     

K-conversion coefficient of the 53.3 keV transition and\frac{K}{{L + M}}-ratio of the 13.34 keV transition in73Ge

TheK-conversion coefficient of the 53.3 keV transition in⁷³Ge was measured by coincidence techniques to be αk ₁=7.1 ± 0.6 indicating very good agreement with heory forM2-radiation. The \(\frac{K}{{L + M}}\) -ratio of the 13.34 keV transition to the ground state was determined using the same techniques. The resulting value \(\left( {\frac{K}{{L + M}}} \right)_2 \) =0.36 ± 0.03 supports theE2-character of this radiation and therefore a spin assignment of \(\frac{5}{2}\) for the 13.34 keV level. The measured lifetime of this transition (T _1,2=(2.95 ± 0.05) μsec) corresponds to a factor of 15 greater than the Weisskopf estimation for a pureE2-transition. A short discussion of a possible transfer of the collectivity of the⁷²Ge-nucleus to the⁷³Ge-nucleus is given.     

Search for the K L 0 → π0ν \tilde v decay at the INEP U-70 accelerator: The KLOD project

The rare decay K _L ⁰ → π⁰ν $ \tilde v $ branching ratio measurement is one of the clearest Standard Model test. Calculations based on the SM predict Br(K _L ⁰ → π⁰ν $ \tilde v $ ) ≈ 2.8 × 10^?11, but the most accurate experimental value Br(K _L ⁰ → π⁰ν $ \tilde v $ ) < 6.7 × 10^?8 (90% C.L.). We present design of a new experimental setup KLOD (U-70 accelerator, IHEP, Protvino) for K _L ⁰ → π⁰ν $ \tilde v $ branching ratio measurement. Sensitivity of the KLOD experiment will be enough for registration of 2.4 events K _L ⁰ → π⁰ν $ \tilde v $ for every 10 days of the data taking (according to SM predictions).     

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⁺).     

N\bar N annihilation at rest into πππ andK\bar K\pi in the3 P 0 model and selection rules on the πρ,K\bar K* and\bar KK* production

\(N\bar N\) annihilation into three pseudoscalar mesons especially πππ and \(K\bar K\pi \) are studied in the quark pair creation model or the³ P ₀ model in which two \(q\bar q\) pairs are annihilated and two \(q\bar q\) pairs are created with quantum numbers of the vacuum or³ P ₀. The correlations of two pions to form ?,f ₂ and the resonance AX(1565) which is recently found by the ASTERIX group are taken into account. A proper treatment of the symmetry among the three pions in the final state shows that the \({}^{31}S_0 p\bar p\) annihilation into ?π is suppressed in agreement with the experiment. We calculate the cosθ distribution or the distribution of the Dalitz plot as the function of the angle between the direction of emission of one decay pion in the resonance centre of mass and the line of flight of the resonance. The interferences of π⁺ρ⁺, π^?ρ⁺ and π⁰ρ⁰ in the isospin 0 channels and π^±ρ^? and π⁰ f ₂ in the isospin 1 channel reproduce the peaks. The cos θ distribution for the P-wave \(p\bar p\) annihilation into πAX depends strongly on the size of the pion since the amplitude interfers with the π^±ρ^? amplitude which is sensitive to the size of the pion. The same model qualitatively explains the \(p\bar p\) annihilation into \(K\bar K\pi \) in whichK or \(\bar K\) and π are correlated to formK* \(\bar K\) or \(\bar K\) *K final states. We can qualitatively reproduce different patterns of the cos θ distribution for theK ^*+ andK ^*0.