Showing papers on "Mass formula published in 1969"
TL;DR: In this paper, a simple nonperturbative model is used to estimate corrections to the first-order perturbation-theory formula for the isobaric multiplet masses.
Abstract: A simple nonperturbative model is used to estimate corrections to the first-order perturbation-theory formula for the isobaric multiplet masses. The leading-order correction to the equation, which is proportional to $T_{z}^{}{}_{}{}^{3}$, is found to be much smaller than expected from second-order perturbation arguments and from limits set by experiments.
20 citations
TL;DR: In this article, the quadratic isobaric multiplet mass equation was replaced by an expression which is quartic in T z if the electrostatic interaction is treated in second-order perturbation theory.
18 citations
TL;DR: In this paper, a phenomenological spinor theory is developed which incorporates SU3 symmetry in the form of octet spinor fields rather than triplet quark fields, which allows the use of more conventional procedures in attacking the dynamical problem.
Abstract: A phenomenological spinor theory is developed which incorporatesSU3 symmetry in the form of octet spinor fields rather than triplet quark fields. This allows the use of more conventional procedures in attacking the dynamical problem. A development of such aSU3 theory based on Weyl spinors proves too restrictive, since, in particular, it is unable to produce a nontrivialF/D ratio for the 0−-boson-octet-baryon interaction in the lowest approximation. Hence the main emphasis is based on theories involving Dirac spinor fields. It is demonstrated that in the octet formulation the Weyl-typeV−A interaction is the only four-spinor interaction which has exactlySU3×SU3 as maximal internal symmetry group (besides the two gauge groups). TheSU3×SU3 invariant interactions involving Dirac-scalar terms have higher symmetry. For theories involving among others a scalar interaction an appropriate regularization procedure allows one to formulate the continuity equations for the currents in the conventional form. Mass values and coupling constants for the simplest baryon and boson multiplets can be calculated in terms of one free regularization constant. There exists a uniquely determinedSU3-breaking four-spinor interaction which is proportional to an octet operator and does not mixSU3 multiplets. The formalism is exemplified in some preliminary models.
11 citations
TL;DR: In this paper, the group dynamical prescriptions for constructing conserved currents of baryons of fixed internal quantum numbers are extended as to apply to the whole SU(3) octet of weak and electromagnetic curents.
Abstract: The group dynamical prescriptions for constructing conserved currents of baryons of fixed internal quantum numbers are extended as to apply to the whole SU(3) octet of weak and electromagnetic curents
6 citations
TL;DR: In this article, a new mass formula is presented which has a form different from those so far proposed, and the production mechanism of mesons is described in detail in § 4.
Abstract: In the present paper a new mass formula is presented which has a form different from those so far proposed. After giving experimental data and pheno menological rules which suggest a composite structure of hadrons in § 2, we shall derive the mass formula and discuss its physical implications in § 3:. As an ap plication of the mass formula, the production mechanism· of mesons will be de scribed in § 4.
6 citations
4 citations
TL;DR: In this article, the semi-empirical mass formula was extended to include different radii for the proton and neutron distributions, and the radii were determined by minimising the energy.
4 citations
TL;DR: In this paper, Mass Formulae for M = 0 and M = 1 Toller families are derived using the standard tools of the S-matrix theory, and they are shown to be equivalent to
Abstract: «Mass formulae» forM=0 andM=1 Toller families are derived using the standard tools of theS-matrix theory.
4 citations
3 citations
TL;DR: In this article, a simple mass formula for the SU3 multiplets in anSU6 representation is suggested, on the basis of the physical masses of the particles, and the mesic states are classified into mesic and non-mesic states.
Abstract: Classification of the mesic states into theSU3 multiplets occurring in the first two members of the most degenerate Feynman series is made. On the basis of the physical masses of the particles, a simple mass formula for theSU3 multiplets in anSU6 representation is suggested.
3 citations
TL;DR: In this article, it was shown that singularities at t = 0 in the Regge amplitude for unequal mass, spinless particle scattering can be cancelled by a single series of daughters, provided that the k th daughter trajectory α k ( t ) is given implicity as a function of k and t by an expansion of a certain form.
TL;DR: In this article, the algebraic formalism of chiral SU(2) is applied to the spectrum of nonstrange mesons and a mass formula valid under general conditions is derived, both with existing data and with current ideas about mass spectra such as rising Regge trajectories, meson towers and the Veneziano representation.
Abstract: The algebraic formalism of chiral $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ recently constructed by Weinberg is applied to the spectrum of nonstrange mesons. A mass formula valid under general conditions is derived. It is shown that some semiquantitative features of the formalism are in good agreement, both with existing data, and with current ideas about mass spectra such as rising Regge trajectories, meson towers, and the Veneziano representation. An attempt to fit known mesons into a coherent supermultiplet structure is described. Some arguments are given as to why this will probably not be possible without further assumptions. It is argued that if the theory is to be useful, it must be cast into a stronger form in which $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ is an approximate symmetry of the spectrum.
TL;DR: In this paper, the authors considered the superconvergent bootstrap, where crossing is imposed by the generalized superconsvergence relations (GSCR) or finite energy sum rules (FESR).
TL;DR: In this paper, deviations from the Gell-Mann-Okubo formula for various multiplets of elementary particles are predicted by saturating an energy-momentum tensor of the Sugawara type by octet states.
Abstract: Deviations from the Gell-Mann---Okubo formula for various multiplets of elementary particles are predicted by saturating an energy-momentum tensor of the Sugawara type by octet states.
TL;DR: In this article, it was shown that in both Tomonaga's intermediate-coupling approximation and North's strong coupling approximation, the Hamiltonian can be written as the sum of two commuting operators, Q and K, each of which also commutes with the Hamiltonians.
Abstract: It is pointed out that in both Tomonaga's intermediate-coupling approximation and North's strong-coupling approximation, the Hamiltonian can be written as the sum of two commuting operators,Q andK, each of which also commutes with the Hamiltonian Furthermore, it is shown thatK2=−Q+ const, whereQ is the total-charge operator for the meson-nucleon system (and consequently its eigenvalues are known) Hence both the strong-coupling and intermediate-coupling approximations lead to the same type of «mass formula»
01 Jan 1969
TL;DR: In this paper, the authors considered the off-mass-shell continuation of the matrix element in which a baryon resonance decays into another baryone resonance with the emission of a single pion, kaon, or η-meson.
Abstract: The off-mass-shell approach to baryon resonances may be considered as a new formulation of bootstrap idea in which the dispersion theory and the current-commutator algebra [1] are incorporated in a systematic and unambiguous manner. We study in this approach the off-mass-shell continuation of the matrix element in which a baryon resonance decays into another baryon resonance with the emission of a single pion, kaon, or η-meson. We study, in particular, the dispersion relation satisfied by the off-mass-shell decay amplitude with respect to the external mass of the baryon resonance. We assume no subtraction in this dispersion relation. We assume, furthermore, that the dispersion relation can be saturated in terms of the baryon resonances, which are assumed in this approach to behave more or less like stable particles. Because of this bootstrap assumption, the above dispersion relation reduces to a set of self-consistency conditions satisfied by the physical decay amplitudes among the baryon resonances.
TL;DR: In this article, a phenomenological effective charge-dependent potential is introduced and its parameters are determined by a least-square analysis based on Coulomb interaction alone after accounting for the neutron-proton mass difference and the residual shifts are attributed to charge dependent effects in the nuclear forces.
Abstract: The masses within an isobaric multiplet are related by the general model-independent mass formula M(A,T,Tz)=a(A,T)+b(A,T)Tz+c(A,T)Tz2. The values of the coefficients b(A,T) and c(A,T) are extracted from experimental data function of mass number for several triplets ranging from A=6 to A=32. Theoretical calculations are made for these coefficients on the basis of Coulomb interaction alone after accounting for the neutron-proton mass difference, and the residual shifts are attributed to charge dependent effects in the nuclear forces. A phenomenological effective charge-dependent potential is introduced and its parameters are determined by a least-square analysis.