The octet model and its Clebsch-Gordan coefficients
CERN1
TL;DR: In this article, the Wigner-Eckart theorem is applied to derive a general mass formula for the octets and the Gell-Mann-Okubo mass relation is used to satisfy the mesons.
Abstract: The Clebsch-Gordan (CG) coefficients of SU(3) are derived for the products of the most important irreducible representations. Useful symmetry relations for the CG coefficients are derived. The Wigner-Eckart theorem for this group is given and applied to derive a general mass formula for the octets. The Gell-Mann-Okubo mass relation and a mass relation foi the octets that is very well satisfied by the vector mesons, if one takes as the K/sup */ the 730-Mev (K- pi ) resonance, are given. The Yukawa couplings between baryons and mesons are considered. The mathematical framework of the octet model for strong interactions is examined. (C.E.S.)
Citations
More filters
TL;DR: In this article, the nuclear forces can be derived using effective chiral Lagrangians consistent with the symmetries of QCD, and the status of the calculations for two and three nucleon forces and their applications in few-nucleon systems are reviewed.
Abstract: Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.
1,455 citations
TL;DR: In this article, the results gathered here on simple Lie algebras have been selected with attention to the needs of unified model builders who study Yang-Mills theories based on simple, local symmetry groups that contain as a subgroup the SUw2 × Uw1 × SUc3 symmetry of the standard theory of electromagnetic, weak, and strong interactions.
1,251 citations
University of Sheffield1, University of Warsaw2, Yale University3, CERN4, University of Liverpool5, Lancaster University6, University of Oxford7, Laboratoire d'Annecy-le-Vieux de physique des particules8, RWTH Aachen University9, University of Freiburg10, University of Turin11, Uppsala University12, Max Planck Society13
TL;DR: An investigation of the spin structure of the proton in deep inelastic scattering of polarised muons on polarised protons was performed in this article, where the spin was investigated in the context of the deep scattering process of polarized muons.
813 citations
TL;DR: The generalized parton distribution (GPD) as discussed by the authors was introduced as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom, and has been used for a long time in studies of hadronic structure.
705 citations
TL;DR: In this paper, the authors predict an exotic Z + baryon with spin 1/2, isospin 0 and strangeness + 1 with a relatively low mass of about 1530 MeV and total width of less than 15 MeV.
Abstract: We predict an exotic Z
+ baryon (having spin 1/2, isospin 0 and strangeness +1) with a relatively low mass of about 1530 MeV and total width of less than 15 MeV. It seems that this regionof masses has avoided thorough searches in the past.
621 citations
References
More filters
TL;DR: In this article, it is suggested that the group is in fact U(3)×U(3), exemplified by the symmetrical Sakata model, and the symmetrized Sakata models are used to define the structure of baryons and mesons.
Abstract: The system of strongly interacting particles is discussed, with electromagnetism, weak interactions, and gravitation considered as perturbations. The electric current jα, the weak current Jα, and the gravitational tensor θαβ are all well-defined operators, with finite matrix elements obeying dispersion relations. To the extent that the dispersion relations for matrix elements of these operators between the vacuum and other states are highly convergent and dominated by contributions from intermediate one-meson states, we have relations like the Goldberger-Treiman formula and universality principles like that of Sakurai according to which the ρ meson is coupled approximately to the isotopic spin. Homogeneous linear dispersion relations, even without subtractions, do not suffice to fix the scale of these matrix elements; in particular, for the nonconserved currents, the renormalization factors cannot be calculated, and the universality of strength of the weak interactions is undefined. More information than just the dispersion relations must be supplied, for example, by field-theoretic models; we consider, in fact, the equal-time commutation relations of the various parts of j4 and J4. These nonlinear relations define an algebraic system (or a group) that underlies the structure of baryons and mesons. It is suggested that the group is in fact U(3)×U(3), exemplified by the symmetrical Sakata model. The Hamiltonian density θ44 is not completely invariant under the group; the noninvariant part transforms according to a particular representation of the group; it is possible that this information also is given correctly by the symmetrical Sakata model. Various exact relations among form factors follow from the algebraic structure. In addition, it may be worthwhile to consider the approximate situation in which the strangeness-changing vector currents are conserved and the Hamiltonian is invariant under U(3); we refer to this limiting case as "unitary symmetry." In the limit, the baryons and mesons form degenerate supermultiplets, which break up into isotopic multiplets when the symmetry-breaking term in the Hamiltonian is "turned on." The mesons are expected to form unitary singlets and octets; each octet breaks up into a triplet, a singlet, and a pair of strange doublets. The known pseudoscalar and vector mesons fit this pattern if there exists also an isotopic singlet pseudoscalar meson χ0. If we consider unitary symmetry in the abstract rather than in connection with a field theory, then we find, as an attractive alternative to the Sakata model, the scheme of Ne'eman and Gell-Mann, which we call the "eightfold way"; the baryons N, Λ, Σ, and Ξ form an octet, like the vector and pseudoscalar meson octets, in the limit of unitary symmetry. Although the violations of unitary symmetry must be quite large, there is some hope of relating certain violations to others. As an example of the methods advocated, we present a rough calculation of the rate of K+→μ++ν in terms of that of π+→μ++ν.
1,673 citations
1,451 citations
TL;DR: In this article, a mass formula for particles belonging to the same irreducible representation is derived and compared with experiments, assuming invariance of a theory under three-dimensional unitary group.
Abstract: Assuming invariance of a theory under three-dimensional unitary group, various consequences are investigated. Both the Sakata and Gell-Mann schemes can be treated in this fashion in a simple way. A mass formula for particles belonging to the same irreducible representation is derived and compared with experiments. (auth)
591 citations
TL;DR: In this article, a representation for the baryons and bosons based on the Lie algebra of the 3-dimensional traceless matrices is suggested, which enables us to generate the strong interactions from a gauge invariance principle, involving 8 vector bosons.
542 citations
TL;DR: In this article, the explicit determination of the matrices of the generators of the unitary groups, SUn, is carried out and discussed in two alternative treatments: (a) by purely algebraic infinitesimal methods, and (b) by Young-pattern techniques employing the Schwinger-Bargmann boson operator methods.
Abstract: The explicit determination of the matrices of the generators of the unitary groups, SUn, is carried out and discussed in two alternative treatments: (a) by purely algebraic infinitesimal methods, and (b) by Young‐pattern techniques employing the Schwinger‐Bargmann boson operator methods. The implication of this result for a tableau calculus is discussed and a determination of the [λ] × [1] Wigner coefficient for all SUn is indicated.
370 citations