On the comparison of forward pion-nucleon dispersion relations with experiments

Abstract

In a previous paper it was shown that it is possible to construct some tests of forward dispersion relations which are independent of the high-energy behaviour of the total cross-sections. The present paper contains an investigation of the dependence of these tests on the threshold parameters (f2 and the scattering lengths). It is well known that the threshold parameters are not very well determined experimentally. Therefore, in order that our tests are reliable, it is necessary that they are practically independent of the threshold parameters. It turns out that there exist two tests of the forward dispersion relations which are practically independent of the actual values of the threshold parameters. This result yields the most critical test of forward dispersion relations (i.e. essentially local commutativity, Lorentz invariance and unitarity) proposed up to now. In the spirit of the previous work it is then shown that the two threshold parametersf2 andTS(m) can be determined by a method which is independent of the high-energy behaviour of the total cross-sections. Finally, it is shown that the existing experimental data indicate thatσA(E)=1/2(σ−(E)−σ+(E)) might change its sign somewhere between 20 GeV and 50 GeV. In an Appendix a discussion of the comparison of sum rules of the Khuri-Kinoshita-Martin type with experiments is given. It turns out that the sum rules of this type are much weaker than the tests discussed in the present paper.