Regge Poles and Finite-Energy Sum Rules for Kaon-Nucleon Scattering
- 25 November 1968
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 175 (5), 1774-1794
- https://doi.org/10.1103/physrev.175.1774
Abstract
Generalized finite-energy sum rules (FESR) for kaon-nucleon scattering are evaluated to determine the dependence and other properties of the relevant Regge-exchange amplitudes: , , , , and . The FESR's have been evaluated (a) with the available phase-shift analyses for the low-energy system as input and (b) in the resonance-saturation approximation with all the appropriate resonances of which is known. For the system, the phase-shift analysis of Lea et al. has been used; for the system, the multichannel effective-range analysis of Kim, and the resonance-plus-background analysis of Armenteros et al. Matching energies of GeV and GeV have been used for the cases (a) and (b), respectively. In terms of the definite helicity flip amplitudes, (which is the full forward amplitude at ) and , we find that assuming the contribution to be known, the non-spin-flip contributions for the various Regge poles are similar to those deduced from high-energy fits; however, the spin-flip contributions of the high-energy fits are inconsistent with our FESR results. For example, the factorization ratio () for the , , , and contributions, where is , is found to have the opposite sign to that used in previous high-energy fits. As far as our results go, the FESR's are consistent with the usual explanation of the crossover phenomenon in terms of a single genuine Regge pole, though we cannot regard this conclusion as very strong, because of the poor available input data. We find no evidence of a wrong-signature nonsense zero in for ; we find for . There is some evidence for an exchange degeneracy between the and the for this ratio, because we also find evidence for . There is some evidence for the no-compensation mechanism for the , with at , which, however, would make the and trajectories quite nondegenerate. For the , we find , which would be expected if the were degenerate with the . Our determination of the signs of the spin-flip amplitudes allows us to predict the polarizations semiquantitatively; our results agree with the available polarization data, while the previous Regge models gave the wrong sign of this polarization. Our new signs for the amplitudes also improve the agreement of the conventional Regge model with the available charge-exchange cross section without invoking a contribution. On the basis of getting good agreement between the FESR results and the Regge expectations, we are able to choose a particular set of low-energy input data as our favored one: We prefer Kim's coupling constants and for the Born terms, a negligible coupling (as also found by Kim), and the nonresonant-type solution IV for the phase-shift analysis. We have also considered FESR's for amplitudes with the wrong crossing properties, generalizing the Schwarz superconvergence relations. A simple model to remove the infinities expected in the case of Schwarz FESR's is seen to be in good agreement with the low-energy data, at least at .
Keywords
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