Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

Simultaneous measurements of the p+d→(A=3)+π reactions

A stack of annular detectors made of high-purity germanium was used to measure simultaneously pd → ³H π⁺ and pd → ³He π⁰ differential cross sections at beam momenta of 750 MeV/c, 800 MeV/c, and 850 MeV/c over a large angular range. The extracted total cross sections for the pd → ³He π⁰ reactions bridge a gap between near threshold data and those in the resonance region. The ratio of the cross sections for the two reaction channels taken at the same η=p^cm_π/m_π yields 2.11±0.08 indicating that a deviation from isospin symmetry is very small.     

Differential operators and immersions of a Riemann surface into a Grassmannian

We consider equivariant holomorphic immersions of a universal cover of a compact Riemann surface X into a Grassmannian satisfying a nondegeneracy condition. The equivariance condition says that there is a homomorphism ρ of the Galois group to that takes the natural action of the Galois group on to the action of the Galois group on defined using ρ. We prove that the space of such embeddings are in bijective correspondence with the space of all holomorphic differential operators of order two on a rank n vector bundle over X with the property that the symbol of the operator is an isomorphism.     

Investigation of parity mixing in Ta and Lu by measurement of the circular polarization of γ-rays

The circular polarization of the 482 keV γ-radiation of ¹⁸¹Ta and the 343 keV γ-radiation of ¹⁷⁵Lu was measured with a Compton polarimeter. Spurious effects arising from higher order contributions of quantum electrodynamics to the Compton scattering cross section were discovered. The results for the polarization are P = − (4.1±1.3)10⁻⁶ for ¹⁸¹Ta and P = − (1.5±6.0)10⁻⁶ for ¹⁷⁵Lu. These values are corrected for instrument asymmetries, bremsstrahlung and intensity of other lines.     

Double pion photoproduction on the nucleon: study of the isospin channels

A model for the γp → π⁺π⁻p reaction developed earlier is extended to account for all isospin channels. The model includes N, Δ(1232), N^*(1440) and N^*(1520) as intermediate baryonic states and the meson as an intermediate 2π resonance. Although many terms contribute to the cross section, some channels exhibit particular sensitivity to certain mechanisms of resonance excitation or decay and the reactions provide novel information on such mechanisms. In particular the γN → N^*(1520) → Δπ process affects all the channels and is a key ingredient in the interpretation of the data. Comparison is made with all available data and the agreement is good in some channels. The remaining discrepancies in some other channels are discussed.     

π-electroproduction on hydrogen near threshold at four-momentum transfers of 0.2, 0.4 and 0.6 GeV

The reaction e + p → e + π⁰ + p was measured near the one pion threshold, detecting the final electron and proton in coincidence for values of q² = 0.2, 0.4 and 0.6 GeV². The slope of the cross section at threshold is determined. The data are compared with those of the e + p → e + π⁺ + n reaction, measured simultaneously, and with the results of pseudovector Born approximation and with dispersion theoretical calculations.     

Investigation of light scalar resonances a0(980)/ƒ0(980) with ANKE

A program to investigate the light scalar resonances a₀(980)/ƒ₀(980) in hadronic interactions via their decay into the πη and channels has started at the ANKE spectrometer of COSY-Jülich. As the first step the reactions pp → dπ⁺X and pp → dK⁺X have been measured at two energies, T_p = 2.65 GeV and 2.83 GeV. The status of the analysis at T_p = 2.65 GeV is presented. A total cross section of about 50 nb has been determined for the reaction .     

Ising spin glass on a D = 3 hierarchical lattice: Effects of tailed coupling distributions

Within a real-space renormalization-group framework, we approach the cubic lattice through a D = 3 diamond-like hierarchical lattice. The model is a standard, nearest-neighbor, Ising spin glass with coupling constants {J_ij} distributed according to the family of continuous probability distributions P_q(J_ij) ∝ 1/[1 + (q − 1)J_ij²/2J²]^{1/(q − 1)} (if 1 + (q − 1) J_ij²/2J² > 0, and zero otherwise; q ). Such distributions, which arise naturally in the treatment, within the recently proposed nonextensive thermostatistics, of anomalous diffusion, reproduce the usual, Gaussian case, for q → 1. Moreover, they present a second moment J_ij² proportional to (5 − 3q)⁻¹ for q < 5/3, diverging for q ≥ 5/3, but keeping a finite width at midheight. In the limit q → 3, P_q(J_ij) collapses with the abscissa, and so the width at midheight diverges. We compute the q-dependence of the spin-glass critical temperature T_c. We show numerically that T_c does not scale with J_ij^21/2 (contrary to the usual belief), but rather with the width at midheight of P_q(J_ij). Our results suggest that T_c vanishes as −1/q when q → −∞; furthermore, we verified that T_c diverges exponentially when q approaches 3 from below.     

Trying to catch the elusive A and more. Reactions initiated by b-quarks and the Higgs sector of the MSSM

We study the cross sections for the production of neneural, intermediate mass Higgs boson in the process pp→ tq′φ, pp→tW⁻φ and pp→bZ⁰φ in the Minimal Supersymmetric Standard Model (φ = H⁰, h⁰ and A⁰) at Supercollider energies. The additional heavy particles (t, W, Z) in the final state can be used for tagging purposes, increasing the signal to background ratio. These reactions are dominated by bg and bg fusion. Their relevance for Higgs particle searches is discussed taking into account the expected efficiencies and purities for b-tagging. We find that, for tan β = 30, the cross sections for pp → bZ⁰φ are larger than 14 pb, over the whole intemediate range of M_A⁰, for A⁰ and at least one of the other two Higgses. Therefore this reaction is an excellent candidate for the discovery of one or more MSSM Higgs particles.     

The use of QCD in OZI violating radiative decays of vector mesons

The spin parity (J^P) of the hadronic system produced in OZI violating vector decays V → γ + h is analyzed in the lowest order QCD approach. While the predicted rates for 0^± states agree with the data, theoretically unacceptable anomalies occur for even J ≠ 0, P = +1, channels. Experimental consequences are drawn. We argue that the rate for gluon jet emission in V → γ + 2 gluons is substantially smaller than previously stated.     

Predictions for all processes ee → fermions + γ

The complete matrix elements for e⁺e⁻ → 4 and e⁺e⁻ → 4fγy are calculated in the Electroweak Standard Model for polarized massless fermions. The matrix elements for all final states are reduced to a few compact generic functions. Monte Carlo generators for e⁺e⁻ → 4f and e⁺e⁻ → 4fγ are constructed. We compare different treatments of the finite widths of the electroweak gauge bosons; in particular, we include a scheme with a complex gauge-boson mass that obeys all Ward identities. The detailed discussion of numerical results comprises integrated cross sections as well as photon-energy distributions for all different final states.     

Investigation of 1.3 μm emission in Nd-doped bismuth-based oxide glasses

Nd₂O₃-doped 43Bi₂O₃–xB₂O₃–(57−x)SiO₂–1.0Nd₂O₃ (x=57, 47, 39, 28.5, 19.5, 10, 0 mol%) bismuth glasses were prepared by the conventional melt-quenching method, and the Nd³⁺: ⁴F_3/2→⁴I_13/2 fluorescence properties had been studied in an oxide system Bi₂O₃–B₂O₃–SiO₂. The Judd–Ofelt analysis for Nd³⁺ ions in bismuth boron silicate glasses was also performed on the basis of absorption spectrum, and the transition probabilities, excited-state lifetimes, the fluorescence branching ratios, quantum efficiency and the stimulated emission cross-sections of ⁴F_3/2→⁴I_13/2 transition were calculated and discussed. The stimulated emission cross-sections of 1.3 μm were quite large due to a large refractive index of the host. Although the effective bandwidths decreased with increasing SiO₂ content, quantum efficiencies and stimulated emission cross-sections enhanced largely with increasing SiO₂ content.     

On the pp → ppη(η′) reactions near threshold

The production rate for η′ in pp → ppη′ at rest is calculated in a covariant one boson exchange model, previously applied to study π⁰ and η production in NN collisions. The transition amplitudes for the elementary BN → η′N processes with B being the meson exchanged (B = π, σ, η, , ω and a₀) are taken to be the sum of s- and u-channels with a nucleon in the intermediate states, and an a₀ meson pole in a t-channel. The couplings of the η′ to hadrons are a factor 0.4 weaker than the respective η-hadron couplings, as suggested by a quark model and a singlet-octet mixing angle θ = −23°. The model reproduces near threshold cross sections for the quasielastic processes π⁻p → nη(η′) and pp → ppη(η′) reactions.     

The NN → NNη reaction close to threshold

The pp → ppη and np → npη reactions at energies near the η production threshold are studied in a non-relativistic one boson exchange model, where the N^* (1535 MeV) S11 resonance is excited through the exchange of π, η, and ω mesons and subsequently decays into an ηN pair. Energy integrated cross sections and energy spectra of the out going η's are reported. Providing NN and ηN final state interactions are taken into account coherently, the model reproduces both the scale and energy dependence of the cross section for the pp → ppη reactions up to 100 MeV. Final state interaction corrections due to the nucleon-nucleon and meson-nucleon forces influence strongly the scale and shape of the cross sections. The shape of the energy spectra of the outgoing η's provides a clear signature of the ηN force.     

The Arnol''d cat: Failure of the correspondence principle

The classical Hamiltonian H = p²/2m + ε(q²/2)Σδ[s-(t/T)] has an integrable mapping of the plane, [q_n+1, p_n+1]= [q_n+1+p_n, q_n+2p_n], as its equations of motion. But then by introducing periodic boundary conditions via (mod 1) applied to both q and p variables, the equations of motion become the Arnol'd cat map, [q_n+1, p_n+1] = [q_n + p_n, q_n + 2p_n], (mod 1), revealing it to be one of the simplest fully chaotic systems which can be derived from a Hamiltonian and analyzed. Consequently, we here quantize the Arnol'd cat and examine its quantum motion for signs of chaos using algorithmic complexity as the litmus. Our analysis reveals that the quantum cat is not chaotic in the deep quantum domain nor does it become chaotic in the classical limit as required by the correspondence principle. We therefore conclude that the correspondence principle, as defined herein, fails for the quantum Arnol'd cat.     

The geometry of the SU(2) Kepler problem

The SU(2) Kepler problem is defined and analyzed, which is a Hamiltonian system reduced from the conformal Kepler problem on T^*( ⁸ − {0}) by the use of the symplectic SU(2) action lifted from the SU(2) left action on the SU(2) bundle ⁸ − {0} → ⁵ − {0}. This reduced system has a parameter μ ε su(2) coming from the value of the moment map associated with the symplectic SU(2) action. If μ ≠ 0, the phase space of this system have a bundle structure with base space T^*( ⁵ − {0}) and fibre S². The fibre, a (co)adjoint orbit through μ for SU(2), represents the internal degrees of freedom, called the isospin, of the particle of this system. The SU(2) Kepler problem with μ ≠ 0 is then interpreted as describing the motion of a classical particle with isospin in the Newtonian potential plus a specific repulsive potential together with a Yang-Mills field. This Yang-Mills field is to be referred to as BPST Yang's monopole field in ⁵ − {0};, since it becomes the Belavin-Polyakov-Schwartz-Tyupkin instanton, restricted on S⁴. If μ = 0, the SU(2) Kepler problem reduces to the ordinary Kepler problem. Like the ordinary Kepler problem, the Hamiltonian flows of the SU(2) Kepler problem of negative energy are all closed. It is shown in an explicit manner that the energy manifolds and isoenergetic orbit spaces for the SU(2) Kepler problem of negative energy are both homogeneous manifolds on which SU(4) acts transitively to the right; those homogeneous manifold are classified into two, according as the parameter μ is zero or not. For a certain value of μ, however, they contracts to the manifold which represents the set of all the equilibrium states. The isoenergetic orbit spaces are finally shown to be symplectomorphic to certain Kirillov-Konstant-Souriau coadjoint orbits for U(4), if μ is not the exceptional value mentioned above.     

Interference effects in photoionization of noble gas atoms outer s-subshells

A strong influence of ns²np⁶ → ns²np⁵ εd transition on the outer ns subshell photoionization cross section of noble gas atomsis demonstrated.     

Double charge exchange and one-pion production in π He collisions at 1.7 GeV/c

We present the results of a study of the exclusive reactions π^{+ 4}He → π⁻ 4p (double charge exchange, DCE) and π^{+ 4}He → π⁺ π⁻ 3pn (one-pion production). The experiment was performed with the Oxford/RHEL helium bubble chamber irradiated with a 1.7 GeV/c π⁺ beam. A general review of DCE models is presented and experimental results at other energies are discussed in the light of these models. None of the existing theoretical models is compatible with out data at 1.7 GeV/c. We propose a new mechanism for DCE, involving three nucleons, which reproduces the integrated as well as the differential cross sections. Some consequences for other models are also discussed.     

Final-state hyperon-nucleon interaction in the inclusive K photoproduction from the deuteron

We calculate d(γ, K⁺) inclusive cross sections with the full inclusion of the final ΛN - ΣN interaction. Modern hyperon-nucleon forces and a recently updated production operator for the γ + N → K⁺ + Y process are used. Significant effects of the hyperon-nucleon final-state interaction have been found especially around the K⁺ΣN threshold.     

Orbits for the adjoint coaction on quantum matrices

Conjugation coactions of the quantum general linear group on the algebra of quantum matrices have been introduced in an earlier paper and the coinvariants have been determined. In this paper the notion of orbit is considered via co-orbit maps associated with -points of the space of quantum matrices, mapping the coordinate ring of quantum matrices into the coordinate ring of the quantum general linear group. The co-orbit maps are calculated explicitly for 2×2 quantum matrices. For quantum matrices of arbitrary size, it is shown that when the deformation parameter is transcendental over the base field, then the kernel of the co-orbit map associated with a -point ξ is a right ideal generated by coinvariants, provided that the classical adjoint orbit of ξ is maximal. If ξ is diagonal with pairwise different eigenvalues, then the image of the co-orbit map coincides with the subalgebra of coinvariants with respect to the left coaction of the diagonal quantum subgroup of the quantum general linear group.