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(searched for: doi:10.1103/physrev.188.2274)
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L. R. Ram Mohan
Physical Review D, Volume 12, pp 2886-2892; https://doi.org/10.1103/physrevd.12.2886

Abstract:
A nucleon saturation scheme for the algebra of Regge residues and chiral symmetry is studied. A representation of this extended algebra of SU(2) × SU(2) × O(5) includes the nucleon N(940), the Δ(1236), and two other nucleon resonances. The masses for the resonances, the low-energy pionic coupling, and the Regge coupling of the ρ, f, π, and A1 trajectories to the particles present in the scheme are predicted and the results are compared with experimental numbers.
Barry Horwitz
Published: 15 February 1974
Physical Review D, Volume 9, pp 996-1003; https://doi.org/10.1103/physrevd.9.996

Abstract:
Using the technique of Fubini and Furlan we extend the algebraic relations for chiral SU(2)⊗SU(2) obtained by Weinberg to the larger algebra formed by including tensor charges. Hence, we deal with the "good" charges of SU(12). The relations we derive are algebraic conditions for vector-meson-hadron decay amplitudes. These conditions enable one to obtain relation-ships between states of different helicity.
W. Tybor
Published: 1 January 1974
Annalen der Physik, Volume 486, pp 137-142; https://doi.org/10.1002/andp.19744860206

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Milan Noga
Physical Review D, Volume 7, pp 3050-3058; https://doi.org/10.1103/physrevd.7.3050

Abstract:
Consequences of Weinberg's postulative assumption requiring that rapidly growing pole terms which contribute to the forward-scattering amplitude must cancel among themselves and not with the continuum in order to preserve the Regge behavior are examined within the framework of dispersion relations. Twice-subtracted dispersion relations with soft-meson theorems as known subtraction constants are used to determine the transformation properties of the SU(3)⊗SU(3)-symmetry-breaking term in the mass spectrum of hadrons.
J. Cleymans
Published: 1 August 1971
Il Nuovo Cimento A, Volume 4, pp 433-442; https://doi.org/10.1007/bf02731362

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Milan Noga
Physical Review D, Volume 3, pp 3047-3058; https://doi.org/10.1103/physrevd.3.3047

Abstract:
Making use of generally accepted assumptions about the equal-time commutator algebra of axial charges and axial divergences, the spin and helicity dependence of Weinberg's algebraic relations is entirely determined for pions in arbitrary partial waves. It is shown that the algebraic structure of axial-vector coupling matrices may be given by the Lie algebra of the group SO(4,3), and so hadron states must be assigned to unitary representations of this group. Furthermore it is proved that the mass-spectrum operator is given as a sum of a scalar and a component of a 35-dimensional totally antisymmetric irreducible tensor of the group SO(4,3). The general form of the mass spectrum is exhibited as a linear combination of the Clebsch-Gordan coefficients of the group SO(4,3). Application to hadron states of fixed intrinsic quantum numbers leads to the conclusion that mass-squared values of hadrons must be a linear function of spin. This result is a unique and exact consequence of the structure of certain algebraic relations.
A. McDonald, L. R. Ram Mohan
Physical Review D, Volume 3, pp 3076-3078; https://doi.org/10.1103/physrevd.3.3076

Abstract:
The consequences of assuming that there is no isospin T=2 part in the commutator [Q̇5a,Q¨5b] of time derivatives of the axial charges Q5a and Q5b have been investigated. The superconvergence condition derived from this assumption provides constraints on Weinberg's mass matrix. The mixing angles introduced by Weinberg for the π−A1−ρ−σ system of mesons and for the nucleon resonances belonging to the (1, ½) and (½, 0) representations of the chiral group are now determined. When only ρ-wave pion interactions are considered, it is shown that the new constraints on the mass matrix lead to mass degeneracy for the symmetric representations of SU(2)⊗SU(4). The constraints on the spin spectrum derivable from the superconvergence conditions are briefly mentioned.
J. Pasupathy
Physical Review D, Volume 2, pp 357-361; https://doi.org/10.1103/physrevd.2.357

Abstract:
Superconvergence relations are known to obey algebraic equations involving the spin and the mass. States of the same helicity fall into reducible representations of SU(2)⊗SU(2). When the helicity is ±½, the two representations are related both by parity operation and by spin raising or lowering operators in the helicity space. The combination of the two yields sufficient constraints to solve for a number of properties of low-lying resonances, with results in good agreement with experiment.
A. Sudbery
Published: 15 June 1970
Nuclear Physics B, Volume 20, pp 1-13; https://doi.org/10.1016/0550-3213(70)90192-6

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