Two types of hadrons

Resonances and enhancements in meson–meson scattering can be divided into two classes distinguished by their behavior as the number of colors (N_c) in QCD becomes large: The first are ordinary mesons that become stable as N_c→∞. This class includes textbook mesons as well as glueballs and hybrids. The second class, extraordinary mesons, are enhancements that disappear as N_c→∞; they subside into the hadronic continuum. This class includes indistinct and controversial objects that have been classified as mesons or meson–meson molecules. Peláez's study of the N_c dependence of unitarized chiral dynamics illustrates both classes: the p-wave ππ and Kπ resonances, the ρ(770) and K^*(892), behave as ordinary mesons; the s-wave ππ and Kπ enhancements, the σ(600) and κ(800), behave like extraordinary mesons. Ordinary mesons resemble Feshbach resonances while extraordinary mesons look more like effects due to potentials in meson–meson scattering channels. I build and explore toy models along these lines. Finally I discuss some related dynamical issues affecting the interpretation of extraordinary mesons.     

Non-Abelian duality from vortex moduli: A dual model of color-confinement

It is argued that the dual transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G→H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The transformation law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v₁v₂) , under an unbroken, exact color-flavor diagonal symmetry . The transformation property among the regular monopoles characterized by π₂(G/H), follows from that among the non-Abelian vortices with flux quantized according to π₁(H), via the isomorphism π₁(G)π₁(H)/π₂(G/H). Our idea is tested against the concrete models—softly-broken supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v₁v₂Λ) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v₁,v₂Λ).     

Algebraic Bethe ansatz for invariant integrable models: Compact and non-compact applications

We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U_q[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact model starting from systems with finite degrees of freedom.     

Critical Casimir amplitudes for n-component models with -symmetry breaking quadratic boundary terms

Euclidean n-component ⁴ theories whose Hamiltonians are O(n) symmetric except for quadratic symmetry breaking boundary terms are studied in the film geometry . The boundary terms imply the Robin boundary conditions at the boundary planes at z=0 and at z=L. Particular attention is paid to the cases in which m_j of the n variables associated with plane take the special value corresponding to critical enhancement while the remaining ones are larger and hence subcritically enhanced. Under these conditions, the semi-infinite system with boundary plane has a multicritical surface–bulk point, called m_j-special, at which an O(m_j) symmetric critical surface phase coexists with the O(n) symmetric bulk phase, provided d is sufficiently large. The L-dependent part of the reduced free energy per cross-section area behaves asymptotically as Δ_C/L^d−1 as L→∞ at the bulk critical point. The Casimir amplitudes Δ_C are determined for small =4−d in the general case where m_c,c components _α are critically enhanced at both boundary planes, m_c,D+m_D,c components are enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at the respective other, and the remaining m_D,D components satisfy asymptotic Dirichlet boundary conditions at both . Whenever m_c,c>0, the corresponding small- expansions involve, besides integer powers of , also fractional powers ^k/2 with k3 modulo powers of logarithms. Results to order ^3/2 are given for general values of m_c,c, m_c,D+m_D,c, and m_D,D. These are used to estimate the Casimir amplitudes Δ_C of the three-dimensional Heisenberg systems with surface spin anisotropies for the cases with (m_c,c,m_c,D+m_D,c)=(1,0), (0,1), and (1,1).     

Observation of the quantum Hall effect in cleaved InAs surfaces

We have performed the in-plane magnetotransport measurements on the two-dimensional electron gas at the cleaved p-InAs (1 1 0) surface by deposition of Ag. The surface electron density N_s is determined from the Hall coefficient at . The coverage dependence of N_s is well explained by the assumption that each adsorbed Ag atom denotes one electron into InAs until the surface Fermi level reaches the adsorbate-induced donor level. The electron mobility μ is about and does not show a clear dependence on the coverage over . In the high-magnetic field regime of B>1/μ, Shubnikov–de Hass oscillations were observed. A beating pattern due to the strong spin–orbit interaction appears for high N_s. For lower N_s of , an apparent quantum Hall plateau for ν=4 and vanishing of the longitudinal resistivity were observed around .     

Resonant Auger decay study of core-excited OCS

The present work aims at characterizing short-lived C1s⁽⁻¹⁾π^*(1) core-excited states of the OCS molecule based on the analysis of the vibrational fine structure and lineshape profiles of the high-resolution resonant Auger decay spectra recorded at the excitation energies along the C1s→π^* resonance in the binding energy region 15–19 eV. Very different behavior in terms of lineshape and resonant enhancement is observed for the , and final states. This is explained by (1) the variation in the C–O bond lengths for the states involved in the electronic relaxation and (2) different contributions in terms of Mulliken population to the molecular orbitals determining the electronic character of the corresponding states. Since the final-state geometries are known from a number of previous experiments and ab initio calculations, the geometry of the C1s⁽⁻¹⁾π^*(1) intermediate states can be predicted in analogy with e.g. the N₂, CO₂ and N₂O molecules.     

Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing

This work focuses on one-dimensional (1D) quasi-periodically forced nonlinear wave equations. This means studying with Dirichlet boundary conditions, where ε is a small positive parameter, (t) is a real analytic quasi-periodic function in t with frequency vector ω=(ω₁,ω₂…,ω_m) and the nonlinearity h is a real analytic odd function of the form It is shown that, under a suitable hypothesis on (t) and h, there are many quasi-periodic solutions for the above equation via KAM theory.     

The polarised valence quark distribution from semi-inclusive DIS

The semi-inclusive difference asymmetry A^h+−h− for hadrons of opposite charge has been measured by the COMPASS experiment at CERN. The data were collected in the years 2002–2004 using a 160 GeV polarised muon beam scattered off a large polarised ⁶LiD target in the kinematic range 0.006<x<0.7 and 1<Q²<100 (GeV/c)². In leading order QCD (LO) the deuteron asymmetry A^h+−h− measures the valence quark polarisation and provides an evaluation of the first moment of Δu_v+Δd_v which is found to be equal to 0.40±0.07(stat.)±0.06(syst.) over the measured range of x at Q²=10 (GeV/c)². When combined with the first moment of previously measured on the same data, this result favours a non-symmetric polarisation of light quarks at a confidence level of two standard deviations, in contrast to the often assumed symmetric scenario .     

Structure of light hypernuclei

The structure of light hypernuclei with strangeness S=−1 and −2 is investigated with the microscopic cluster model and the Gaussian expansion method (GEM). We emphasize that the cluster picture as well as the mean-field picture is invaluable to understand the structure of Λ hypernuclei, Σ hypernuclei and double Λ hypernuclei. A variety of aspects of Λ hypernuclei is demonstrated through a systematic study of p-shell hypernuclei (,, , , , , ) and sd-shell ones (, ): for example, the appearance of genuine hypernuclear states with new spatial symmetry which cannot be seen in ordinary nuclei, the glue-like role of the Λ particle which shrinks the size of nuclear core and thus reduces the B(E2) value, and the halo and skin structures in and etc. The typical light hypernucleus is thoroughly investigated, including its production, structure and decay. Precise three-body and four-body calculations of , and using GEM provide important information on the spin structure of the underlying ΛN interaction, by comparing with recent experimental data from γ-ray hypernuclear spectroscopy. The Λ–Σ coupling effect is studied in and . The binding mechanism of is discussed together with the possible existence of , emphasizing the fact that the study of is useful for extracting information on the ΣN interaction differing from that from . A systematic study of double-Λ hypernuclei, constrained by the NAGARA data () within a four-body cluster model indicates that the recently observed Demachi–Yanagi event can be interpreted as the 2⁺ state of . The effect of hyperon mixing in and is investigated using one-boson-exchange potentials and quark-cluster-model interactions for the S=−2 sector. A close relation between nuclear deep hole states and hypernuclei is discussed, emphasizing the selection rule for fragmentation of the s-hole in light nuclei, which is promising for understanding the production mechanism of double-Λ and twin-Λ hypernuclei via Ξ-atomic capture.     

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f₀ and a₀ resonances. The ππ → ππ, phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π⁰η and mass distributions in the T = 1 channel. Furthermore, the total and partial strong decay widths of the f₀ and a₀ resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below GeV.     

High-resolution infrared and theoretical study of four fundamental bands of gaseous 1,3,4-oxadiazole between 800 and 1600 cm

The Fourier transform infrared spectrum of gaseous 1,3,4-oxadiazole, C₂H₂N₂O, has been recorded in the 800–1600 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. The four fundamental bands ν₉(B₁; 852.5 cm⁻¹), ν₁₄(B₂; 1078.5 cm⁻¹), ν₄(A₁; 1092.6 cm⁻¹), and ν₂(A₁; 1534.9 cm⁻¹) are analyzed by the standard Watson model. Ground state rotational and quartic centrifugal distortion constants are obtained from a simultaneous fit of ground state combination differences from three of these bands and previous microwave transitions. Upper state spectroscopic constants are obtained for all four bands from single band fits using the Watson model. The ν₄ and ν₁₄ bands form a c-Coriolis interacting dyad, and the two bands are analyzed simultaneously by a model including first and second order Coriolis resonance using the ab initio predicted Coriolis coupling constant . An extended local resonance in ν₂ is explained as higher order b-Coriolis type resonance with ν₆ + ν₁₀, which is further perturbed globally by the ν₁₅ + ν₁₀ level. A fit of selected low-J transitions to a triad model including ν₂(A₁), ν₆ + ν₁₀(B₁), and ν₁₅ + ν₁₀(A₂) using an ab initio calculated Coriolis coupling constant is performed.The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration–rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.     

Recent soft-core baryon–baryon interactions

Recent results obtained with the extended-soft-core (ESC) interactions are presented. In a unified manner the ESC-model describes nucleon–nucleon (NN), hyperon–nucleon (YN), and hyperon–hyperon (YY), using (broken) SU_F(3)-symmetry. In the ESC approach to baryon–baryon (BB) the dynamics is derived from (i) one-boson-exchanges (OBE), (ii) two-meson-exchanges (TME), and (iii) meson-pair-exchanges (MPE). Special features are the inclusion of the axial-vector meson potentials, and a zero in the scalar-meson form-factors. With these ingredients a rather flexible dynamical framework is constructed. Namely, it appeared feasible to keep the parameters of the model rather close to the predictions of the quark-pair-creation model (QPC). This is the case for the meson–baryon coupling constants and the F/(F+D)-ratios as well. The NN, YN, and YY results for this model are rather promising. Here, we report on a recently obtained version, called ESC04. Also, we present the first results with the next version, called ESC06, where we explore the inclusion of the second nonets for the pseudoscalar, vector, and scalar mesons, which have masses approximately in the interval . In the -picture these mesons are the radially excited states, with principal quantum number N=2, of the low lying meson nonets for M1 GeV. This improves the Σ-well-depth considerably.     

Observation of γ-delayed 3α breakup of the 15.11 and 12.71 MeV states in C

The reactions at 4.9 MeV and at 8.5 MeV have been used to investigate the γ decay of states in ¹²C. By measuring the four-body final state in complete kinematics we are able to detect γ transitions indirectly. We find γ transitions from the 15.11 MeV state in ¹²C to the 12.71, 11.83, 10.3 and 7.65 MeV states followed by their breakup into three α particles. The relative γ-ray branching ratios obtained are (1.2±0.3), (0.32±0.12), (1.4±0.2) and (4.4±0.8)%, respectively, with the remaining (92.7±1.0)% of the γ decays going to the bound states. We obtain Γ_α/Γ=(2.8±1.2)% for the isospin-forbidden α decay of the 15.11 MeV state. From the 12.71 MeV state we find γ transitions to the 10.3 and 7.65 MeV states. The relative γ-ray branching ratios are and , respectively, with the remaining of the γ decays going to the bound states. Finally, we discuss the relation between the β decay of ¹²N and ¹²B to states in ¹²C and the γ decay of the 15.11 MeV analog in ¹²C to the same states.     

Counting BPS operators in SYM

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free super-Yang–Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of super-Yang–Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free super-Yang–Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.     

Effects of time reversal symmetry on phonons in sapphire substrate for ZnO and GaN

Vibrational states in a crystal are classified according to the irreducible representations (irreps) of the corresponding factor group . The wave vector k runs over the entire Brillouin zone (BZ). For trigonal BZs, the factor groups are determined by the symmetry points Γ, F, L, T, and the symmetry lines Λ, Σ, Y. When the irreps are complex, the time reversal symmetry has to be taken into account. Using the Frobenuis–Schur criterion adapted to space groups with real and complex irreps, we have investigated high symmetry points and lines of the phonons in trigonal crystals: Cr₂O₃,Fe₂O₃,Ti₂O₃,V ₂O₃,FeCO₃,CaCO₃,CdCO₃,MgCO₃,MnCO₃,NaCO₃ and ZnCO₃, with the common space group (). We have found several phonons which are influenced by the time reversal symmetry. Therefore, an extra degeneracy of phonons arises. The theoretical results are also compared with available experimental data.     

Absolute photoionization cross sections with ultra-high energy resolution for Ar, Kr, Xe and N2 in inner-shell ionization regions

The high-resolution absolute photoionization cross sections for Ar, Kr, Xe and N₂ in the inner-shell ionization region have been measured using a multi-electrode ion chamber and monochromatized synchrotron radiation. The energy ranges of the incident photons for the target gases were as follows: Ar: 242–252 eV (2p Rydberg excitation), Kr: 1650–1770 eV (near the 2p ionization thresholds), Xe: 665–720 eV (near the 3d ionization thresholds) and 880–1010 eV (near the 3p ionization thresholds), N₂: 400–425 eV (N 1s excitation and ionization). It is the first time to measure the absolute ionization cross sections of Ar, Kr, Xe and N₂ over the present energy ranges with the energy resolution of over 10,000. The natural lifetime widths of , , and resonances for Ar, resonance for Xe, and resonance for N₂ have been obtained based on the cross sections determined. The ionization energies into the Ar⁺ (), Ar⁺ () and Xe⁺ () ionic states are also determined using the Rydberg formula.     

Unfamiliar integrals and motions down the ‘plug-hole’ potential

The orbits in the potentials ψ=−CzR⁻²+ζ(R), (ζ arbitrary) have integrals E, and . Thus the z-velocity is proportional to the number of turns made around the axis! The Poisson Bracket [h,I] is not zero so Liouville’s integrability theorem does not apply. Starting from the self-similar potential with ζ∝R⁻¹, we find some orbits that spiral around cones and explore general orbits in this strange system.