Mixing of P wave axial vector resonances

An analysis is given of the mixing of the axial vector kaon resonances by use of new data from SLAC. Mass values, decay widths and branching ratios of the SLAC work may be compatible with SU(3) and/or “pair creation model” classifications for a mixing angle λ ≈ ?35° ± 10°. The mass values and coupling strengths proposed by Basdevant and Berger, from a different parametrization of the same data, can be fitted in an SU(3) and/or broken SU(6)_w model with a larger mixing angle λ ≈ ?80°. Such a mixing would mean that the lower kaonic state is closely related to the 1^+? nonet in contrast to expectations from duality and/or one-gluon exchange mixing schemes. We also discuss the mixing of the charmed D meson states.     

Spontaneous dynamical breaking of gauge symmetry in dual models

The consequences of gauge invariance are re-examined in dual models with unit intercept when the dimension of space-time has the maximum value compatible with the absence of ghosts. In that case, reggeon-reggeon bound states of zero mass are formed already at second order of perturbation theory. Gauge invariance no longer guarantees that the initially massless SU(3) singlet vector meson remains massless, and the mixing between the reggeon and pomeron sectors of the model yields a massive unitary singlet vector meson already at order g². A Lagrangian model which exhibits similar features to the dual situation is discussed.     

The kinematic and symmetry structure of e+e−→hadron pairs

The kinematic singularity and constraint free amplitudes for e⁺e^?→two particles which can have arbitrary spins are obtained in a simple closed form. The relationships of these amplitudes with the usual multipole form factors are given. It is noted that SU(6)_W and tests of ideas based on the Melosh transformation are liberated from their γN and πN arena and can be confronted with arbitrary targets and axcitations. The matrix elements or arbitrary meson pairs are then derived, rates are computed for pseudoscalar and vector meson production, and some tests of symmetry breaking mechanisms proposed. Extension to SU(4)[SU(8)_W] broken in the masses enables estimates of charmed particle production rates to be obtained. General features of πR final states suggest that scaling violation at small x may be connected with threshold phenomena as channels open up. A subtle difference between space-like and time-like regions is highted.     

SU(2) Yang-Mills theory in (1 + 1) dimensions: A finite-lattice approach

Finite-lattice methods are used to calculate the masses of the lowest-lying baryon and meson states in the two-dimensional SU(2) Yang-Mills theory. No sign of a phase transition is seen at non-zero quark mass m. Both the meson and baryon mass vanish at m = 0: this is presumably a “chiral protection” mechanism.     

Pseudoscalars and vector mesons in a unitary and self-consistently broken SU(6) W scheme

We estimate hadronic self-energy effects to “bare” pseudoscalar (P) and vector (V) meson states due to theP→PV→P, P→VV→P, V→ PP→V, V→PV→V andV→VV→V loops. We simulate higher order diagrams by consistently requiring external and internal particles to have the same mass. We find good agreement with all the experimental masses (exceptm _π), widths and mixing angles. The “bare”P andV states are heavy (≈1.26 GeV) and degenerate up to a smallm _s?m_u quark mass difference term. The “bare” coupling constants for thePPV, PVV andVVV vertices obey exact OZI rule and almost exact SU(6) _W symmetry. We use a common cut-off ofk _cm?0.7 GeV/c corresponding to a harmonic oscillator radius of ?0.7 fm for all SU(6) _W related thresholds except for the pion.     

Charmed Mesons in Nuclei with Heavy-Quark Spin Symmetry

We study the properties of charmed pseudoscalar and vector mesons in dense matter within a unitary meson–baryon coupled-channel model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg–Tomozawa Lagrangian to incorporate spin-flavor symmetry and implement a suitable flavor symmetry breaking. Several resonances with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with 1/2⁺ and 3/2⁺ baryons. Those states are then compared to experimental data as well as theoretical models. Next, Pauli-blocking effects and meson self-energies are introduced in a self-consistent manner to obtain the open-charm meson spectral functions in a dense nuclear environment. We finally discuss the formation of D-mesic nuclei.     

Nuclear bound states of ω mesons

Models based on chiral SU(3)_l ⊗ SU(3)_r symmetry and vector meson dominance suggest an attractive potential for the ω meson in a nuclear medium. We discuss the feasibility of producing nuclear bound states of ω mesons using (d, ³He) and pion induced reactions on selected nuclear targets.     

Gluonium and the 0++ spectrum

We suggest that the σ (broad ππ s-wave states below 1 GeV) and the S¹(0.98) can be interpreted by a mixing between a scalar gluonium and an SU(2) singlet meson with a mixing angle of the order of 14°–19°. The decays of the σ and of the S¹ into a pseudoscalar pair are shown to be dominated by their gluon component. In this way, one expects a universal coupling of the σ and of the S¹ to ππ and KK?. The above scheme is confronted to the ψ-decays and to some scattering data. A radial excitation assignment of the G(1.6) is discussed.     

Axial vector meson production

Recently available differential cross section and density matrix information on π^?p → B^?p at 4 GeV/c are successfully described in terms of t channel exchanges and s channel absorptive effects. The s channel helicity amplitude which is dominant at small |t| (zero net helicity flip ω exchange) is found to have a zero at ?t = 0.2 GeV². SU(3) and higher symmetries are used to predict cross sections for further axial vector meson production processes, in particular non-diffractive A₁ production. The importance of these processes with regard to Regge phenomenology and meson spectroscopy is emphasized.     

Bare current-quark masses,inelastic reactions and light-cone algebra

Relations connecting the effective bare current-quark masses with asymptotic meson-nucleon and lepton-nucleon scattering are derived by making use of the extended light-cone algebra which includes commutators of pseudoscalar densities. The commutators are relevant to meson-nucleon scattering amplitudes since the pseudoscalar densities act as fields of the (composite) mesons. Assuming pomeron-exchanged Regge behaviour, sufficient analyticity in the meson mass-squared variable is established to obtain finite-mass dispersion and superconvergence relations. Making additionally certain other reasonable assumptions, we are then able to show how these relations yield testable connections among the asymptotic πN and KN total cross sections, the structure functions of the deep inelastic lepton-nucleon scattering (for the scaling variable, ξ →0) and the bare current-quark masses μ_{p, n, λ} that appear essentially as parametrising the breaking of the chiral SU(3) ? SU(3) symmetry. One interesting consequence of our results is at the Llewellyn-Smith inequality on the said structure functions should be experimentally satisfied as a near equality for ξ → 0, if chiral SU(2) ? SU(2) turns out to be a rather good symmetry of nature. Moreover, taking the specific symmetry breaking model of Gell-Mann Oakes and Renner,we find that μ_{p, n} ≈ 35 MeV and μ_λ ≈ 800 MeV.     

An operatorially solved model of massless two-dimensional quantum chromodynamics

An operator solution is constructed in (1,1) dimensions to the massless quantum chromodynamics of n fermion quarks and n² ? 1 vector boson gluons with local colour SU(n) symmetry. The interacting quark field is a confined SU(n) Thirring field with zero Abelian coupling. The colour gluons are dependent Lie fields obeying the gluon-free fermionic current identity. Explicit local infinitesimal operator colour transformations (with an arbitrary coordinate-independent Lorentz vector coefficient defining the gauge) are given and the requirement of proper colour covariance linked to the vanishing of the coloured quark source currents and hence to the absence of coloured quark-composite states. The status of Noether's theorem is also clarified.     

Mixing of meson isosinglets

The mixing angles for the vector and pseudoscalar meson isosinglets are obtained in a non-relativistic quark model. Schwinger-type mass relations are also obtained for SU(4) and SU(5). Quark contents of different meson isosinglets are computed which agree well with similar estimation of Maki and co-workers and Boal.     

Vector states in e+e− annihilation at 3.9–4.5 GeV

The structure observed at SPEAR in e⁺e^? annihilation in the energy range 3.9–4.5 GeV is explained in an SU(8) × SL(3, R) color quark model. The model can account for the mass differences, total hadronic and leptonic widths, as well as for the rise in, and the magnitude of, R. Main predictions are the SU(3) properties of these states, strong suppression of their decays into the ψ(3.1) and the existence of another vector meson around 6 GeV.     

Multiquark states and the mixing of scalar meson

In order to describe Kaon-Nucleon scattering data, the mixing of scalar meson σ_0 and σ_8 must be introduced in the chiral SU(3) quark model. Inspired by this, now the mixing of scalar meson is further considered to study some interesting dibaryons in the chiral SU(3) quark model. The results show that the mixing of scalar meson has different effects on these dibaryons.     

Exact SU(n) instantons with cylindrical symmetry

We construct SO(3) symmetric, irreducible instantons in an SU(n) gauge theory. The solutions are symmetric with respect to J = ?ir × ? + T, where T spans the maximal SO(3) subalgebra of SU(n). Our ansatz as well as the resulting self dual equations are closely related to those for monopoles.     

Mixing of meson isosinglets in SU(5) and an extension to SU(N)

The mixing angles of meson isosinglets belonging to the 24-dimensional and singlet representations of SU(5) are calculated under specific assumptions in the non-relativistic quark model. The procedure to extend the scheme to SU(N) has been outlined. The results have been compared with other earlier estimates.     

Axial vector current divergences and the pseudoscalar meson spectrum

The strong anomaly in the axial vector current divergence is simply related to the mass of the ninth pseudoscalar meson in an SU (3) × SU (3) quark model. A discussion is given of the dependence of the pseudoscalar meson masses upon quark masses as well as upon the strong coupling; the SU (3) character of the states is also treated.     

Dark matter from the SU(4) model

The left-right symmetric Pati-Salam model of the unification of quarks and leptons is based on the SU(4) and SU(2)×SU(2) symmetry groups. These groups are naturally extended to include the classification of families of quarks and leptons. We assume that the family group (the group which unites the families) is also the SU(4) group. The properties of the fourth generation of fermions are the same as those of the ordinary-matter fermions in the first three generations except for the family charge of the SU(4)_F group: F=(1/3, 1/3, 1/3, ?1), where F=1/3 for fermions of ordinary matter and F=?1 for the fourth-generation fermions. The difference in F does not allow mixing between ordinary and fourth-generation fermions. Because of the conservation of the Fcharge, the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the fourth generation. As a result, the excess n _B of baryons over antibaryons leads to the excess n_4ν=N?N? of neutrinos over antineutrinos in the fourth generation with n_4ν=n _B . This massive neutrino may form nonbaryonic dark matter. In principle, the mass density of the fourth neutrino n_4νm _N in the Universe can make the main contribution to dark matter, since the lower bound on the neutrino mass m _N from the data on decay of the Z bosons is m _N <m _Z /2. The straightforward prediction of this model leads to the amount of cold dark matter relative to baryons, which is an order of magnitude higher than allowed by observations. This inconsistency may be avoided by nonconservation of the F charge.     

Static hyperon properties in a linearizedSU(3)-Chiral Bag model

We use a linearized Chiral Bag model to describe the strange octet and decuplet baryons. The approach is canonically extended to spontaneously broken chiral SU(3)_L × SU(3)_R, and the corresponding Goldstone Bosons are identified with the pseudoscalar meson octet. We include explicit symmetry breaking corrections both for baryons and mesons. The linearized quark-meson intraction is applied in a self-consistent calculation of the masses and, for Δ, Σ^* and Ξ^*, of the decay widths. Our special interest is in the influence of theK- andη-cloud (in addition to theπ) on hyperon static properties. We show results for radii, masses, decay widths and renormalization constants as obtained by a fit to the experimental hyperon spectra. The effects of theK- andη-mesons are found to be non-negligible, although supressed by symmetry breaking effects. The effective gluon coupling α is reduced in comparison to the SU(2)_L × SU(2)_R case. In addition, we discuss the dependence on the bag constantB. It turns out that the lightest hyperon states, Λ and Σ are well described and stable for B^1/4 < 130 MeV. The heavier strange baryons have stable solutions also for larger values ofB. The bag radii determined at the minimal energies are R₀?1.15 fm for the octet and R₀?1.25 fm for the decuplet baryons.