Some comments on the branching ratios for \bar n p annihilation into ππ, K \bar K, and πη channels

We present some remarks on the $\bar n$ p partial branching ratios in flight at low momenta of antineutrons measured by the OBELIX Collaboration. A comparison is made to the known branching ratios from the p $\bar p$ -atomic states. The branching ratio for the reaction $\bar n$ p → π⁺π⁰ is found to be suppressed in comparison to what follows from the p $\bar p$ data. It is also shown that there is no so-called dynamical I=0 amplitude suppression for the process N $\bar N$ → K $\bar K$ .     

Fragmentation production of Ωccc baryons at LHC energies

Within the nonrelativistic quark-diquark model for heavy baryons, the fragmentation functions for the transitions of a c-quark and a doubly charmed vector diquark into an Ω_ccc baryon are calculated in the leading order of perturbative QCD. The cross section for Ω _ccc production in high-energy hadron interactions is estimated. It is assumed that Ω_ccc baryons are formed via the fragmentation of a c quark or a vector (cc) diquark produced in the partonic subprocesses gg → c $\bar c$ , q $\bar q$ → c $\bar c$ , gg → (cc)+ $\bar c$ + $\bar c$ , and q $\bar q$ → (cc)+ $\bar c$ + $\bar c$ .     

Strong magnetic fields,Dirichlet boundaries,and spectral gaps

We consider magnetic Schrödinger operators $$H(\lambda \vec a) = ( - i\nabla - \lambda \vec a(x))^2$$ inL ₂(R ⁿ ), where $\vec a \in C^1 (R^n ;R^n )$ and λεR. LettingM={x;B(x)=0}, whereB is the magnetic field associated with $\vec a$ , and $M_{\vec a} = \{ x;\vec a(x) = 0\}$ , we prove that $H(\lambda \vec a)$ converges to the (Dirichlet) Laplacian on the closed setM in the strong resolvent sense, as λ→∞,provided the set $M\backslash M_{\vec a}$ has measure zero. In various situations, which include the case of periodic fields, we even obtain norm resolvent convergence (again under the condition that $M\backslash M_{\vec a}$ has measure zero). As a consequence, if we are given a periodic fieldB where the regions withB=0 have non-empty interior and are enclosed by the region withB≠0, magnetic wells will be created when λ is large, opening up gaps in the spectrum of $H(\lambda \vec a)$ . We finally address the question of absolute continuity of $\vec a$ for periodic $H(\vec a)$ .     

A review of spin Hamiltonian forms for various point-group site symmetries

A review has been made of the spin Hamiltonian forms for all the 32 point groups, including linear magnetic field-dependent terms in spin operators $\hat O_1^m $ , $\hat O_3^m $ , $\hat O_5^m $ , $\hat O_1^m $ , $\hat O_3^m $ , and $\hat O_5^m $ . All spin operators, as well as their matrix elements, to be used in constructing spin Hamiltonian matrices, have been listed. The various point group aggregates for distinct spin-Hamiltonian forms have been classified. In addition, descent of symmetry point groups, useful for studying structural phase transitions, have been indicated.     

On AB Bond Percolation on the Square Lattice and AB Site Percolation on Its Line Graph

We prove that AB site percolation occurs on the line graph of the square lattice when $p \in (1 - \sqrt {1 - p_c } ,\sqrt {1 - p_c } )$ , where p _c is the critical probability for site percolation in $\mathbb{Z}^2$ . Also, we prove that AB bond percolation does not occur on $\mathbb{Z}^2$ for p = $\frac{1}{2}$ .     

Singular $$ \mathcal{R}$$ -Matrices and Drinfeld's Comultiplication

We compute the $\mathcal{R}$ -matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for ${\text{U}}_q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ . This $\mathcal{R}$ -matrix contains terms proportional to the δ-function. We construct the algebra $A\left( \mathcal{R} \right)$ generated by the elements of the matrices L^±(z) with relations determined by $\mathcal{R}$ . In the category of highest-weight representations, there is a Hopf algebra isomorphism between $A\left( \mathcal{R} \right)$ and an extension $\overline {\text{U}} _q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ of Drinfeld's algebra.     

Strange and non-strange (Anti-) baryon production at 200 A GeV/c

Rapidity distributions of net hyperons $\left( {\Lambda - \bar \Lambda } \right)$ are compared to distributions of participant protons $\left( {p - \bar p} \right)$ . Strangeness production (mean multiplicities of produced Λ/Σ⁰ hyperons and $\left\langle {K + \bar K} \right\rangle $ in central nucleusnucleus collisions is shown for different collision systems at different energies. An enhanced production of $\bar \Lambda $ compared to $\bar p$ is observed at 200 GeV per nucleon.     

Alternative technique for Standard Model estimation of the rare kaon decay branchings \left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM}

We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ _t≡V _tdV _ts ^* of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? _K|, the CP-violating parameter describing K mixing, and a _ψ,K , the CP-violating asymmetry in B _d ⁰ → J/ψK ⁰ decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V _cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ _t with additional data from $\Delta m_{B_d } $ and |V _ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ .     

Coupled-Channels Approach and Simple Models in the Theory of Exotic Atom Formation

Atomic collisions of slow negative particles X ^? (μ^?, $\bar p$ , etc.) are considered using coupled channels semiclassical approximation that takes into account 2- and 3-particle channels. Analytical expression for differential elastic cross section is proposed. Differential cross section reveals essential quantum interference effects. Inelastic $\bar p$ –Ne and $\bar p$ –Ar cross sections are considered using model potentials.     

Resonance studies at STAR

Preliminary results from measurements of resonances (K ^*0(892), $\overline {K*^0 } (892)$ , Φ(1020), and ρ(770)) and weakly decaying particles (Λ(1116), $\bar \Lambda (1116)$ , and K _S ⁰ (498)) are presented. The measurements are performed at mid-rapidity by the STAR detector in $\sqrt {s_{NN} } = 130$ GeV Au?Au collisions at RHIC. The ratios K ^*0/h?, $\overline {K*^0 } /K$ , and $\bar \Lambda /\Lambda $ are compared to measurements at different energies and colliding systems. Estimates of thermal parameters, such as temperature and baryon chemical potential, are also presented.     

Effects of scalar and pseudoscalar Higgs bosons in the process e^ + e^ - \to b\bar bv\bar v at the LEP II collider

The possibility of setting constraints on the couplings of the scalar or pseudoscalar Higgs boson to b quarks on the basis of data on the process $e^ + e^ - \to b\bar bv\bar v$ at the LEP II collider is investigated. The mixing of the scalar and the hypothetical pseudoscalar Higgs boson in the $Hb\bar b$ vertex is parametrized in the form $\frac{{m_b }}{v}(a + i\gamma _5 b)$ . An analysis of the differential distributions for the process $e^ + e^ - \to b\bar bv\bar v$ reveals that the contribution of the fusion subprocess WW → H in the channel involving an electron neutrino enhances the sensitivity of data to the parameters under analysis. It is shown that the LEP II data at $\sqrt s = 200$ GeV and $\smallint \mathcal{L}dt = 600 pb^{ - 1} $ per experiment would make it possible to constrain the parameters Δa = a ? 1 and b as follows: ?0.75 ≤ Δa ≤ 1.4 at b = 0 and free Δa and ?0.97 ≤ b ≤ 0.97 at Δa = 0 and free b.     

Factorization of Combinatorial R Matrices and Associated Cellular Automata

Solvable vertex models in statistical mechanics give rise to soliton cellular automata at q=0 in a ferromagnetic regime. By means of the crystal base theory we study a class of such automata associated with non-exceptional quantum affine algebras U′ $_q$ ( $\widehat {\mathfrak{g}}$ $_n$ ). Let B $_l$ be the crystal of the U′ $_q$ ( $\widehat {\mathfrak{g}}$ $_n$ )-module corresponding to the l-fold symmetric fusion of the vector representation. For any crystal of the form B = $B_{l_1 }$ ? ...? $B_{l_N }$ , we prove that the combinatorial R matrix B $_M$ ?B $\widetilde \to$ B?B $_M$ is factorized into a product of Weyl group operators in a certain domain if M is sufficiently large. It implies the factorization of certain transfer matrix at q=0, hence the time evolution in the associated cellular automata. The result generalizes the ball-moving algorithm in the box-ball systems.     

Powerful dynamical neutrino source with a hard spectrum

A powerful dynamical neutrino source with a hard spectrum obtained via the (n, γ) activation of ⁷Li and a subsequent β^? decay (T _1/2=0.84 s) of ⁸Li with the emission of high-energy $\tilde \nu _e$ (up to 13 MeV) is discussed. In the dynamical system, lithium is pumped over in a closed cycle through a converter near the reactor core and further to a remote $\tilde \nu _e$ detector. It is shown that, owing to a large growth of the hardness of the total $\tilde \nu _e$ spectrum, the cross section for the interaction with a deuteron can strongly increase both in the neutral ( $\tilde \nu _e + d \uparrow n + p + \tilde \nu _e$ ) and in the charged ( $\tilde \nu _e + d \uparrow n + n + e^ +$ ) channel in relation to the analogous cross sections in the reactor $\tilde \nu _e$ spectrum.     

Correlations in ternary fission

An experiment investigating correlations in ternary fission of²³³U induced by cold polarized neutrons was performed at the high flux reactor of the ILL in Grenoble (France). With the experimental setup, Left—Right and time reversal symmetry violating and conserving correlations between neutron spin $\hat \sigma $ , neutron momentum $\hat p_n $ , momenta of fission fragments $\hat p_f $ and ternary particles $\hat p_t $ could be investigated.     

Resonance structures in the \Lambda \bar \Lambda system

The results of studying the $\Lambda \bar \Lambda $ system produced in the reaction π^? p→ $\Lambda \bar \Lambda $ n at a π^?-meson energy of 40 GeV are reported. Experimental data (～2300 events) were obtained on the ITEP 6-meter spectrometer with a beam of the IHEP U-70 accelerator. The invariant-mass spectra for the events dominated by the singlet or triplet $\Lambda \bar \Lambda $ states were found to differ considerably from each other. The data give evidence for the existence of resonance $\Lambda \bar \Lambda $ states of the system in the mass regions near 2.3, 2.5, and 2.8 GeV.     

Φπ production in\bar pp annihilation from S and P states and in J/ψ decaysannihilation from S and P states and in J/ψ decays

Recent experiments at LEAR have found surprisingly large branching ratios for reactions $\bar NN \to \phi \pi $ from S-wave initial states while noφπ production is observed from P states of the $\bar pp$ system. Also, noφπ is seen in radiative J/ψ decays even though the rate forωπ is substantial. We calculate theφπ production rates for these three cases viaKK* intermediate states and $K\bar K$ rescattering using the dispersion relation technique; we find that the largeφπ rate in $\bar pp$ annihilations from S states can be reproduced with a reasonable cut-off for the dispersion integral; for J/ψ decays the calculatedφπ rate is compatible with the observed upper limit. We would, however, expectφπ to be seen from $\bar pp$ P-states, in contrast to experimental findings. Yet the branching ratio for $\bar pp \to K*\bar K$ via isospinI = 1 of $\bar pp$ ,¹ P ₁ state is not known; and therefore no definite conclusion can be drawn. We also compare the Dalitz plots we obtain for directφ production and forφ production via rescattering. Clear differences between the two theoretical distributions are observed; yet very high precision data would be required to establish the origin — direct production or rescattering — of theφ mesons. This observation supports the use of the isobar model in data analyses.     

The Percolation Transition in the Zero-Temperature Domany Model

We analyze a deterministic cellular automaton σ ^?=(σ ⁿ :n≥0) corresponding to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice $\mathbb{N}$ . The state space $\mathcal{S}_\mathbb{H} = \left\{ { - 1, + 1} \right\}^\mathbb{H}$ consists of assignments of ?1 or +1 to each site of $\mathbb{H}$ and the initial state $\sigma ^0 = \left\{ {\sigma _{^x }^0 } \right\}_{x \in \mathbb{H}}$ is chosen randomly with P(σ ⁰ _x=+1)=p∈[0,1]. The sites of $\mathbb{H}$ are partitioned in two sets $\mathcal{A}$ and $\mathcal{B}$ so that all the neighbors of a site x in $\mathcal{A}$ belong to $\mathcal{B}$ and vice versa, and the discrete time dynamics is such that the σ ^? _x 's with ${x \in \mathcal{A}}$ (respectively, $\mathcal{B}$ ) are updated simultaneously at odd (resp., even) times, making σ ^? _x agree with the majority of its three neighbors. In ref. 1 it was proved that there is a percolation transition at p=1/2 in the percolation models defined by σ ⁿ , for all times n∈[1,∞]. In this paper, we study the nature of that transition and prove that the critical exponents β, ν, and η of the dependent percolation models defined by σ ⁿ , n∈[1,∞], have the same values as for standard two-dimensional independent site percolation (on the triangular lattice).     

Reichenbachian Common Cause Systems

A partition C_{i i∈ I} of a Boolean algebra $\mathcal{S}$ in a probability measure space $(\mathcal{S},p)$ is called a Reichenbachian common cause system for the correlated pair A,B of events in $\mathcal{S}$ if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set I is called the size of the common cause system. It is shown that given any correlation in $(\mathcal{S},p)$ , and given any finite size n>2, the probability space $(\mathcal{S},p)$ can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions of $\mathcal{S}$ contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated.     

From nonassociativity to solutions of the KP hierarchy

A recently observed relation between ‘weakly nonassociative’ algebras $\mathbb{A}$ (for which the associator ( $\mathbb{A},\mathbb{A}^2 ,\mathbb{A}$ ) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus $\mathbb{A}$ ′ of { $\mathbb{A}$ ) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with matrix algebra $\mathbb{A}$ ′, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.     

Phenomenological model for the \overline{{K}}N \rightarrow K \Xi reaction

A phenomenological model for the $ \overline{{K}}$ N $ \rightarrow$ K $ \Xi$ reaction is suggested. The model includes s and u channel exchanges by $ \Lambda$ , $ \Sigma$ , $ \Sigma$ (1385) , and $ \Lambda$ (1520) and s channel exchanges by above-threshold hyperonic resonances. The explicit expression for the propagator for a particle with spin 7/2 is presented. High-mass and high-spin resonances play a significant role in the process. We deal with the whole set of existing experimental data on the cross-sections and polarizations in the energy range from the threshold to 2.8GeV in the center-of-mass system and reach a good agreement with experiments. Applications of the model to other elementary reactions of $ \Xi$ production and to $ \Xi$ hypernuclear spectroscopy are briefly discussed.