Low-lying Baryons Research Articles

Baryon resonances in a gluon-perturbed linear potential

A harmonic-oscillator De R\'ujula-Georgi-Glashow model (i.e., a model with harmonic oscillator perturbed by a Fermi-Breit potential) is used to calculate masses of $n=0$ and $n=1$ baryons. It is observed that some of the gross features of the mass spectrum would not be altered by choosing a linear potential rather than the linear harmonic oscillator. Results agree with the presently measured particle masses to within 25% of the mean multiplet splitting and on this basis it is predicted that there is an as-yet-unseen low-lying baryon (${N}_{\frac{1}{2}}^{P=\ensuremath{-}1}$) with mass 1335(\ifmmode\pm\else\textpm\fi{}60) MeV. A number of other predictions are also made; in particular, the decuplet electromagnetic splittings are expected to be reliable.

Universality of hadron form factors abstracted from the parton model

The role played by the orbital angular momentum ${L}_{z}$ in parton models at $P=\ensuremath{\infty}$ is delineated. By postulating similar behavior for the parton wave functions of the low-lying baryons of equal ${L}_{z}$, we are able to relate various of the transition form factors for ${\ensuremath{\gamma}}_{V}N\ensuremath{\rightarrow}{N}^{*}$ to the elastic form factors of the nucleon.

General formulation of pionic decays in the quark model

Predictions for pionic decays of resonances to states in the low-lying baryon 56 or meson 36 supermultiplets are shown to follow from general model-independent algebraic properties. All models in which transition operators change the state of only a single quark allow only two partial waves for the decay pion and give $\mathrm{SU}{(6)}_{W}$ relations between decays in each partial wave, while not necessarily relating different partial waves.

The photoproduction processes {fx377-1}, KΛ, KΣ in a dual model with fixed poles, KΛ, KΣ in a dual model with fixed poles

The photoproduction of pseudoscalar mesons is investigated in the framework of a dualB5-model with fixed and Regge poles. A reasonable fit to the available high-energy forward scattering data is presented which is characterized by essentially three parameters. The values of the Regge residues for natural- and unnatural-parity exchanges agree with the values obtained in other photoproduction models. The photoexcitation features of the low-lying baryon resonances derived from our model are in qualitative agreement with experimental results.

Relationship of Flux Quantization to Charge Quantization and the Electromagnetic Coupling Constant

The concept of a closed quantized flux loop (elementary loop) which avoids the implication of magnetic monopoles is investigated, leading to a theory of a charged lepton (muon or electron). In order to reconstruct a continuous magnetic dipole field of a source lepton, it is assumed that the flux loop adopts a statistical distribution of alternative forms characterized by a complex probability amplitude superposition, in a manner somewhat analogous to the superposition of path histories in Feynman's space-time approach to quantum mechanics. Flux quantization results from the equivalence of a line discontinuity of the phase factor of a $\ensuremath{\psi}$ function of a field lepton (due to its phase multivaluedness by $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}$) to the presence of a line of quantized flux. On the same basis as quantized flux arises from such a singularity of that phase factor, so also an electric field arises when this singularity line is moving. In particular, the source's Coulomb field results from a spinning of the quantized flux loop (about the center of the source) with an angular velocity equal to the Zitterbewegung frequency $\frac{2m{c}^{2}}{\ensuremath{\hbar}}$, if the statistical distribution of flux loopforms properly represents the magnetic dipole field of a muon or of an electron. The reconstruction of the magnetic and electric fields of a charged lepton and the comparison of them with the quantized flux $\frac{\mathrm{hc}}{e}$ gives a numerical estimate of the electromagnetic interaction constant $\frac{{e}^{2}}{\ensuremath{\hbar}c}$, i.e., an understanding of the relationship between $e$ and $\ensuremath{\hbar}$. The energy $m{c}^{2}$ and angular momentum $\frac{\ensuremath{\hbar}}{2}$ may be interpreted as electromagnetic. The theory should work for both muon and electron and is expected to give some insight into the ratio of the masses of these two leptons. A representation of quarks in terms of linked quantized flux loops is suggested to describe a low-lying meson as a linkage of an elementary loop with an antiloop, and a low-lying baryon as three interlinked elementary loops. We are here developing a model approach to problems of structure and conservation laws in particle physics. A more abstract version of a quantized flux theory of particles should be preceded by such an heuristic model.

Representation mixing inU 6,6 and its application to weak and electromagnetic interactions.—II

The recent conjecture by Dashen and Gell-Mann that the low-lying baryon states may not belong to any pure representation but may be in a mixed representation is studied in the context ofU6,6 and various predictions, resulting from such a conjecture, are made and compared with experiment. It is found that an impressive agreement with experiment is obtained if the mixed representations (220,L=1) and (364,L=0) are chosen.

Meson-Baryon Couplings in a Quark Model

The widths for decay of low-lying baryons of negative parity into baryon plus pseudoscalar meson are determined in a quark model and extensively compared with experiment. One conclusion is that Ξ * (1816) is not in an octet with N * (1518), Y 1 * (1660). A second prediction is a kinematical factor in s-wave decay enhancing the decay into high-mass mesons (K and η over η), which provides a qualitative reason for η peaks at threshold. Properties of the many missing baryon resonances are discussed. Channels appropriate for the search for some of these are indicated.

Magnetic Moments of the Strange Baryons and the Algebra of Currents

Using equal-time commutation relations of the axial-vector charges with the isoscalar and isovector electromagnetic current densities, the magnetic moments of the strange members of the baryon octet and the ${\ensuremath{\Sigma}}^{0}\ensuremath{-}\ensuremath{\Lambda}$ transition moment have been calculated in terms of the pseudoscalar-meson photoproduction amplitudes, which are evaluated using low-lying baryon resonant states. The results agree very well with the experimental values available for the ${\ensuremath{\Sigma}}^{+}$ and the $\ensuremath{\Lambda}$ magnetic moments. A comparison is also made with the results of the $\mathrm{SU}(3)$ symmetry.

Three-Triplet Model with DoubleSU(3)Symmetry

With a view to avoiding some of the kinematical and dynamical difficulties involved in the single-triplet quark model, a model for the low-lying baryons and mesons based on three triplets with integral charges is proposed, somewhat similar to the two-triplet model introduced earlier by one of us (Y. N.). It is shown that in a $U(3)$ scheme of triplets with integral charges, one is naturally led to three triplets located symmetrically about the origin of ${I}_{3}\ensuremath{-}Y$ diagram under the constraint that the Nishijima-Gell-Mann relation remains intact. A double $\mathrm{SU}(3)$ symmetry scheme is proposed in which the large mass splittings between different representations are ascribed to one of the $\mathrm{SU}(3)$, while the other $\mathrm{SU}(3)$ is the usual one for the mass splittings within a representation of the first $\mathrm{SU}(3)$.

Mass Rules for Baryons and Resonant States

The formula that expresses the baryon mass in terms of internal quantum numbers is generalized so as to apply to the low-lying baryon resonances. Simple relations that systematize masses of all other known baryon resonant states are also presented. (C.E.S.)

Remarks on the Lowlying Baryon Isobars

Relative energies and widths of low-lying baryon isobars were examined from the point of view of the global symmetry hypothesis. Energy shifts of the hyperon isobars Λ * and Σ * due to the mass differences between the baryons were calculated, independent of the dynamics.