Isospin Degeneracy and Veneziano Representation in Pion-Nucleon Scattering

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It is shown that when the Regge trajectories of πN resonances are rotated to have the universal slope with the centers of rotation being identified with the ground state points on the parent trajectories, they exhibit the isospin degeneracies in a special pattern in which the parent trajectories and even some of the first daughters are not degenerate; no clear evidence is found for the exchange degeneracy. By starting from this pattern of the trajectories, we reconstruct a Veneziano representation for πN scattering with many beta-function terms giving correlations among leading and nonleading trajectories. Veneziano's subsidiary conditions are assumed in order to get definite signatures in the s- and u-channel trajectories, which state that sums of trajectory functions in the a, t and u channels be equal to integers; we assume the conditions among the trajectories passing through the nucleon, Δ(1236), ρ meson, and among those through the nucleon, N(1520;D_<13>), f meson. Because of these conditions, the number of possible beta-function terms are greatly reduced and we take all possible terms. It is found that residues of top-ranking trajectories have rather simple structures due to our isospin degeneracy pattern. We get certain correlations among these residues in the s-channel low-energy region, and get a definite prediction for the s-pole residue of the B^<(-)> amplitude; the results are in good agreement with experimental data. Good results are also obtained for the forward charge-exchange differential cross sections; we have terms which choose the Gell-Mann mechanism or the Mandelstam-Wang mechanism for the dip. Our model, however, gives too large cross sections for large angle and bachward scattering.
理論物理学刊行会の論文
1972-01-25

Isospin Degeneracy and Veneziano Representation in Pion-Nucleon Scattering

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