Model Of Baryons Research Articles

S-wave non-leptonic hyperon decays and models of baryons

S-wave non-leptonic hyperon decays via a current × current, V-A primary Hamiltonian are investigated in three non-relativistic bound-state models of baryons: a quark model, a three-triplet model, and a quartet model. Our main dynamical assumptions are: (i) The S-wave decays are due to a pion emission accompanied by both a single- (constituent) particle and a two-particle transition with the other particles in the baryon bound state not being affected. (ii) The recoil energy-momentum of the particles taking part in the pion emission can be neglected and the pion is emitted with zero energy-momentum. (iii) All the particles are in S-states. Under these assumptions we get the following main results: (i) The amplitudes satisfy the same sum rules as those obtained by the current-algebra-PCAC method. An illustrative argument is given to show why we get this ‘coincidence’. (ii) The single particle transition involves no 27 tensor of SU(3) and gives no contribution to the decay Σ + → n + π +. (iii) A necessary and sufficient condition for the suppression of the 27 part of the two-particle transition and of the decay Σ + → n + π + is found. (iv) In order to fit the experimental results the contribution from the two-particle transition must be substantial in the quark and three-triplet models and must dominate the contribution from the single-particle transition in the quartet model.

S-wave nonleptonic hyperon decays and models of baryons

S-wave nonleptonic hyperon decays and models of baryons

The baryon model as a tetrahedron of quarks and one antiquark

The baryon model as a tetrahedron of quarks and one antiquark

Dynamical Model for Baryon Resonances

We propose a nonrelativistic three-quark (Q) model of baryons and their resonances with the assumptions of (i) parastatistics which, in constrast to Fermi statistics, allows totally symmetric wave functions, and (ii) operation of Q-Q forces of the factorable type in s and p waves which facilitate an exact solution of the three-body problem. It is found that the s-wave force gives rise to a strong attraction in a spatially symmetric (S) state of L=0, but repulsion in a mixed-symmetric (M) state. This provides a natural dynamical realization of the 56 representation of SU(6) for the familiar octet and decuplet of baryons. The same s-wave force also predicts a set of negative-parity resonances but these are of much too high energy to be of any physical consequence. The p-wave force leads to a set of negative-parity L=1 resonances via strong attraction in M-type spatial states of L=1, thus making up the representation (70,3) of SU(6)×O(3). A p-wave spin-orbit Q-Q force splits these states in a manner which fits in rather well with Dalitz's recent analysis of experimental data for the negative-parity baryonic resonances. Finally, the p-wave force generates a strong attraction in a spatially antisymemtric state (A) of even parity and L=1, giving rise to the representation (20,3) of SU(6)×O(3), of which the lowest states are an octet and a singlet of J P =1/2 + , the central mass of each lying lower than the corresponding lowest mass multiplet of negative parity. This provides a natural explanation of the so-called Roper resonance (at 1450 MeV), and in addition, strongly predicts an even-parity singlet of a mass lower than the Y 0 ∗ (1405). The distinction between Fermi statistics and paraststistics is discussed in the context of the above results, and it is argued that while Fermi statistics could in principle generate negative-parity L=1 resonances (via M functions), it could not possibly account for the 56 of baryons, since with Q-Q forces alone,the A function of L=0 that should go with it has a strongly repulsive kernel.

Bootstrap Model of Baryons with Nondegenerate Mesons

A static bootstrap model of baryons including $N$, ${N}^{*}$, $\ensuremath{\Sigma}$, $\ensuremath{\Lambda}$, $Y_{1}^{*}$, $\ensuremath{\pi}$, and $K$ is considered. The mass difference between the mesons is treated as a parameter. We find one solution which produces strong attractions in several channels expected to be free from bound states, and which therefore seems not self-consistent. Besides, the mass spectrum of this solution differs from the experimental results. It is concluded that the heavier baryons ($\ensuremath{\Xi}$, ${\ensuremath{\Xi}}^{*}$, and $\ensuremath{\Omega}$), and perhaps also the $\ensuremath{\eta}$, are necessary for self-consistency.

A Possible Scheme for the Nonleptonic Decays of Hyperons. II

Nonleptonic decays of hyperons are discussed in the unitary symmetrical [x o] composite model for baryons, where x and (} are triplet spinor and scalar (or pseudo-scalar) fields respectively. The decays are assumed to occur through two different mechanisms jj~o+n, x~x and jj~jj, x~x+n. Several relations among the decay amplitudes, including the wellknown Sugawara-Lee relation for the parity violating part and a new sum rule 2P(S_ -)

Quadrilocal Model of Baryons and Unitary Symmetry

A unified theory of baryons is proposed based on a spinor wave equation that depends on four space-time points or equivalently on the center of mass and three relative-coordinate vectors. The associated subsidiary condition and the structure of the mass operator are such that the four-point association is maintained within a small region of Minkowski space-time with characteristic length and that the theory has $U(9)$ symmetry in the full symmetry limit. By the couplings of internal motions this symmetry is reduced to the direct product of the usual unitary-spin group $U(3)$ and the other unitary group $U{(3)}^{\ensuremath{'}}$ characteristic of spherical-oscillator-type motions, and then this latter is further reduced to simple rotational invariance. Baryonic states are assigned to the 165-dimensional irreducible representation (IR) of the $U(9)$ corresponding to the first excited shell with respect to the oscillatory motions of relative coordinates. These states are subgrouped according to the IR of the usual $\mathrm{SU}(3)$ and to the eigenvalue of the relative angular momentum. Identifications with known levels are then made. The whole treatment is carried out covariantly, and minimum violation of causality is implied inside the particle.

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 $\mathrm{SU}(3)$.

Unitary symmetry and Regge poles

A unitary symmetry model of composite baryons and mesons is proposed. The method of summation of asymptotic contributions from Cutkosky diagrams is used for calculating the Regge trajectories of composite particles.

Spin and Unitary-Spin Independence in a Paraquark Model of Baryons and Mesons

Spin and Unitary-Spin Independence in a Paraquark Model of Baryons and Mesons

Shell Model of Baryons

Received 20 October 1964DOI:https://doi.org/10.1103/PhysRevLett.13.592©1964 American Physical Society

Three-Body Leptonic Decays of K-Mesons and Hyperons

A method of treating weak interaction processes involving composite particles is formulated on the basis of the theory of bound states of quantum field theory. The method is applied to the analysis of the decay ⁠. And it is shown that under a possible set of assumptions ξ-value of this decay must like between -1 and +1 irrespective of the structure of π and K-meson. Then the method is applied to the leptonic decays of hyperons and it is shown that if we take -baryon model for hyperons there is a possibility of understanding the smallness of the decay rates compared to the ones expected from the universal coupling theory.

Three Body Problem and a Model of Baryons

Relations among the masses of the S U 3 multiplets are derived assuming the existence of the `quarks' of M. Gell-Mann.

Oscillator model for particles underlying unitary symmetry

1. For a unified description of elementary particles YUKAWA was early led to a relativistic harmonic-oscillator model in the framework of bi-local theory (1), which introduces, besides the usual external co-ordinates X~ and their conjugate momentum components P~, the internal space-time co-ordinates x~ and their conjugates p~. Recently he made a new development of the theory (~) by showing tha t it could imply certain internal quantum number such as isospin. On the other hand different oscillator schemes for particles have been set forth (~-5) to directly account for supermult iplet structures and mass rules for particles. In par t icular in ref. (~) i t was pointed out tha t the Ua symmetry, originally proposed from the s tandpoint of the Sakata model (6), could be interpreted in terms of an oscilla tor model for particles, and it Was remarked tha t the reason why the threedimensional uni tary symmetry should operate could be tr ivial ly understood, according to this kind of model, as ' the direct consequence of the dimensionality of the physical space itself. By combining both viewpoints we introduce in this note the basic assmnption (~) ( r : 1, 2, 3) exist, instead of a single x~ tha t three internal co-ordinate vectors x~ of Yt~KAWA, and show tha t this extended model provides a new basis underlying the Ua or SU a symmetry which has recently proved more and more successful for strongly interact ing particles (6.s). Indeed our theory presents a unified model for baryons and their excitations since all baryonic states belonging to various possible supermultiplets can be regarded as different oscillator levels of tha t same system, each of which is specified by the set of appropriate quantum numbers tha t include the usual ones. The immediate prediction of our model is the existence of specific

Model of Mesons and Baryons Based on SU3Symmetry

Model of Mesons and Baryons Based on S<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">U</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Symmetry

A schematic model of baryons and mesons

If we assume that the strong interactions of baryons and mesons are correctly described in terms of the broken way, we are tempted to look for some fundamental explanation of the situation. A highly promised approach is the purely dynamical bootstrap model for all the strongly interacting particles within which one may try to derive isotopic spin and strangeness conservation and broken eightfold symmetry from self-consistency alone. Of course, with only strong interactions, the orientation of the asymmetry in the unitary space cannot be specified; one hopes that in some way the selection of specific components of the F-spin by electromagnetism and the weak interactions determines the choice of isotopic spin and hypercharge directions.

Possible Unified Models of Elementary Particles with Two Neutrinos

Possible unified models of elementary particles are discussed assuming the existence of two kinds of neutrino accompanying with electron and muon respectively. The discus­ sions are focused on the Nagoya model which is based on the Sakata model of baryons and mesons and the Gamba-Marshak-Okubo symmetry. In its connection the following assump­ tions are taken: i) Fundamental particles among baryons and mesons have one-to-one correspondence with leptons or their linear combinations. The correspondence is realized through a kind of matter. ii) Basic leptons do not transmute each other by the strong interaction between the fundamental baryons. There are two essentially different types of model. One depends on the existence of two neutrinos which are Dirac particles, and the other is related with two Majorana neutrinos. With regard to the models, the difference between electron and muon and the asymmetry of A-pionic decay are also discussed.

A fundamental particle model (II)

This paper pursues the discussion of a fundamental particle model proposed in a previous paper. The model for baryons and mesons starts from a fundamental non-linear equation of motion for the field operator in the Heisenberg representation, with a formally symmetric self-interaction. Equations of motion are generated for particles and particle interactions from the equation of motion of the field by using the τ-function formalism. The equation of motion of a single baryon is discussed and it is argued that, if one confines the analysis to the mass shells and the asymptotic domain, a solution is found which should be rather accurate. This equation of motion is then completely integrated in momentum space for pseudoscalar, vector and pseudovector self-interaction terms. A new method is discussed for finding the low energy peripheral interaction of two baryons from the fundamental equation, for all three types of self-interaction. The vector and pseudovector types have explicity velocity dependent terms even in the lowest approximation. Possible conflicts between the demands of the low energy interaction of two baryons, and the baryon self-energy problem are discussed. It appears possible that the origin of self-energy lies in a very short range self-interaction. Numerical computations of the baryon self-energy problem are then exhibited for an extensive range of meson mass parameters. Possible cases of self-interaction are discussed which would give the nucleon and Λ-baryon masses, with the basic mass m 0 = 0. In one of these cases it is shown from the numerical results that the ghost mass appearing in the baryon propagator does not satisfy the asymptotic wave equation which the real masses do satisfy. It is further suggested that the leptons and the photon are associated with the notion of saturated compounds in the strong coupling theory. A strong coupling theory would then have the more massive strongly interacting particles, and have the saturated compounds as lighter, weakly interacting particles. A tentative sketch is given of a fundamental theory based on three basic baryons, n, p, Λ in strong self-interaction, in which strongly interacting hyperons and mesons appear as well as weakly interacting leptons and photons.

Some predictions from a composite model of baryons

Baryons are considered as composites of a neutral baryon core plus various mesons. This model makes three specific predictions: 1) The K+-Σ0(Λ0) force should be much more attractive than the K−-Σ0(Λ0) force. 2) Neutral particles should be approximately electrically neutral throughout. 3) At high energies many elementary particle reactions should have characteristic angular distributions.

The Pion-Nucleon S-Wave Scattering, the Structure of the Nucleon and the Composite Model of Baryons and Mesons

The Pion-Nucleon S-Wave Scattering, the Structure of the Nucleon and the Composite Model of Baryons and Mesons