A Liu-Okubo-type dispersion relation is derived for the crossing-even pion-nucleon forward elastic scattering amplitude T(+). Two subtractions are made, one at the physical scattering threshold and the other at a previously determined zero of T(+) on the imaginary axis of the complex ω (pion lab energy) plane. The dispersion relation is well satisfied over the whole allowed range of the Liu-Okubo parameter. Moreover, it is nearly saturated by low-energy scattering for a considerable range of the parameter. It should thus serve as an extremely sensitive test of the low-energy scattering data when such data become more accurately known.
D. J. George et al., "New Superconvergent Dispersion Relations for the Forward πN Crossing-Even Amplitude," Physical Review, vol. 168, no. 5, pp. 1924-1925, American Physical Society (APS), Apr 1968.
The definitive version is available at https://doi.org/10.1103/PhysRev.168.1924
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© 1968 American Physical Society (APS), All rights reserved.