Corrections of order O(\bar \alpha \bar \alpha _s ) and O(\overline \alpha ^2 ) to the \bar bb-decay width of the neutral Higgs boson

Analytical expressions are presented for contributions of order $O(\overline \alpha \overline \alpha _s )$ and $O(\overline \alpha ^2 )$ to the $\bar bb$ -decay width of the neutral Higgs boson of the standard model of electroweak interactions. The numerical value of the mixed QED and QCD correction of order $O(\overline \alpha \overline \alpha _s )$ is comparable to other computed terms in the perturbation series.     

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.     

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.     

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.     

Dependence of electroweak parameters on the definition of the top-quark mass

The QCD corrections to electroweak parameters depend on the renormalization scheme and scales used to define the top-quark mass. We analyze these dependences for theW-boson mass predicted via Δr to ${\mathcal{O}}(\alpha \alpha _s )$ and ${\mathcal{O}}(\alpha \alpha _s^2 )$ in the on-shell and $\overline {MS} $ schemes. These variations provide us with a hint on the magnitude of the unknown higher-order QCD effects and contribute to the theoretical error of the prediction.     

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.     

Single decay-lepton angular distributions in polarizede + e − →\overline {tt} and simple angular asymmetries as a measure of CP-violating top dipole couplingsand simple angular asymmetries as a measure of CP-violating top dipole couplings

In the presence of an electric dipole coupling of $\overline {tt} $ to a photon, and an analogous ‘weak’ dipole coupling to the Z, CP violation in the process e⁺e^? → $\overline {tt} $ results in modified polarization of the top and the anti-top. This polarization can be analyzed by studying the angular distributions of decay charged leptons when the top or anti-top decays leptonically. Analytic expressions are presented for these distributions when eithert or $\overline t $ decays leptonically, including $\mathcal{O}$ (α_s) QCD corrections in the soft-gluon approximation. The angular distributions are insensitive to anomalous interactions in top decay. Two types of simple CP-violating polar-angle asymmetries and two azimuthal asymmetries, which do not need the full reconstruction of thet or $\overline t $ , are studied. Independent 90% CL limits that may be obtained on the real and imaginary parts of the electric and weak dipole couplings at a linear collider operating at √ s = 500 GeV with integrated luminosity 500 fb^? and also at √s = 1000 GeV with integrated luminosity 1000 fb^? have been evaluated. The effect of longitudinal electron and/or positron beam polarizations has been included.     

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.     

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.     

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 = $\frac{1}{2}$ .     

Superfield effective action within the general chiral superfield model

The chiral superfield model associated with the low-energy limit of superstring theory and characterized by the Kähler and the chiral potential [K(Φ, $\overline \Phi$ ) and W(Φ), respectively] is analyzed. An approach to solving a general problem is developed, and quantum loop corrections at arbitrary K(Φ, $\overline \Phi$ ) and W(Φ) are found. Various aspects of a supergraph technique that are associated with calculating perturbative contributions to the superfield effective action are analyzed. Explicit expressions for the one-and two-loop corrections to the Kähler potential are calculated. The leading two-loop correction to the chiral potential is obtained, and it is shown that, irrespective of the form of K(Φ, $\overline \Phi$ ) and W(Φ), counterterms are not needed for deducing this correction.     

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.     

Mixing and CP violation: fromB^0 - \overline {B^0 } to T^0 - \overline {T^0 }

We extend from \(B^0 - \overline {B^0 } to T^0 - \overline {T^0 } \) the study of neutral pseudoscalar mesons with respect to mixing and CP violation. The possibility of a quite large top quark mass necessitates a more careful computation of the box diagram amplitude. Our result is that, while in \(B^0 - \overline {B^0 } \) systems CP violation is expected to be very small (～10^?6) and mixing quite large (10–20% or more), precisely the opposite occurs for \( T^0 - \overline {T^0 } \) . In particular, CP violation in the \( T_u^0 - \overline {T_u^0 } \) system could be of the same order of magnitude as in the \(K^0 - \overline {K^0 } \) system (～10^?3) while the mixing is totally negligible.     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.     

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 brief review of antimatter production

In this article, we present a brief review of the discoveries of kinds of antimatter particles, including positron ( $ \bar e $ ), antiproton ( $ \bar p $ ), antideuteron ( $ \bar d $ ) and antihelium-3 ( $ ^3 \overline {He} $ ). Special emphasis is put on the discovery of the antihypertriton( $ \frac{3} {\Lambda }\overline H $ ) and antihelium-4 nucleus ( $ ^4 \overline {He} $ , or $ \bar \alpha $ ) which were reported by the RHIC-STAR experiment very recently. In addition, brief discussions about the effort to search for antinuclei in cosmic rays and study of the longtime confinement of the simplest antimatter atom, antihydrogen are also given. Moreover, the production mechanism of anti-light nuclei is introduced.     

57Fe Mössbauer-effect studies of quadrupole splitting distributions in icosahedral Al-TM-Fe quasicrystals

Room temperature⁵⁷Fe Mössbauer effect spectra of several Al-TM-Fe icosahedral quasicrystals are reported. Results of fits to discrete sites and to various distributions of quadrupole splittings are presented. Mean isomer shifts, \(\overline \delta \) , and quadrupole splittings, Δ, are shown to be insensitive to the fitting procedure used. Trends in \(\overline \delta \) and \(\overline \Delta \) for the icosahedral phase may be indicative of a Hume-Rothery stabilization mechanism.     

The tomography of quark-gluon plasma by vector mesons

The fireball formed in a heavy ion collision is characterized by the impact parameter vector $\vec b$ , which is orthogonal to the beam direction and can be determined from the multiplicity and the angular distribution of the reaction products. By appropriate rotations the $\vec b$ vectors of each collision can be oriented into a fixed direction. Using the measured values of the momentum distributions of the vector mesons an integral equation can be formulated for the unknown emission densities $(E_M (\vec r))$ and for the unknown absorption densities $(\Delta \mu _M (\vec r,p))$ of the different vector mesons $M( \equiv \omega ^0 ,\rho ^0 ,\phi ^0 ,\psi ^0 ,\psi ^{0'} ,\Upsilon )$ .     

Equivalent Forms of the Bessis–Moussa–Villani Conjecture

The BMV conjecture for traces, which states that ${\text{Tr}}\;{\text{exp}}\left( {A - \lambda B} \right)$ is the Laplace transform of a positive measure, is shown to be equivalent to two other statements: (i) The polynomial $\lambda \mapsto {\text{Tr}}\;\left( {A + \lambda B} \right)^p$ has only non-negative coefficients for all $A,B \geqslant 0,p \in \mathbb{N}$ and (ii) $\lambda \mapsto {\text{Tr}}\;\left( {A + \lambda B} \right)^{ - p}$ is the Laplace transform of a positive measure for $A,B \geqslant 0,p > 0$ .     

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.