An analysis of pion-nucleon scattering at intermediate and high energies

Abstract

A phenomenological analysis of pion nucleon scattering at intermediate and high energies is presented. The intermediate energy range (2-5 GeV) is discussed in terms of a 'new' phase shift analysis which has been constructed from a series of single energy fits to an energy dependent model partial wave analysis. This 'new' phase shift solution exhibits a similar resonance structure to the energy dependent model but enjoys a much better fit to the scattering data, comparable with previous single energy analyses. We discuss the difficulties encountered in previous single energy analyses and illustrate the advantages and feasibility of the energy dependent analysis in which the partial waves satisfy the required smoothness criteria, by construction. The high energy scattering data is discussed with reference to the Regge pole model and we exploit the analytic properties of the scattering amplitudes by the use of the Continuous Moment Sum Rules (C.M.S,R,), The sum rules provide a set of ' consistency equations between the high energy Regge parameters and the low and intermediate energy data which is represented by the phase shifts. In previous analyses of the C.M.S.R., the energy at which they are evaluated has been taken as 2 GeV which corresponded to the maximum energy of available phase shift data. 2 GeV is a long way from the region where we expect the Regge representation to be valid and the saturation of the C.M.S.R. with only those trajectories identified in the high energy region is not obvious, since we may expect lower lying trajectories to be important at these energies. We construct the CM.S.R. at a higher cut off (5 GeV) from the 'new' phase shift solution and compare the results from a simultaneous analysis of the scattering data and C.M.S.R. at the two cut offs. Several differences are apparent between the two analysis in particular we show that it is not possible to construct the A’¯ and B+ atamplitudes at 2 GeV via the C.M.S.R without considering trajectories other than those identified in the high energy scattering region. We present evidence for a new vacuum trajectory which we associate with the n(_0+) (700) meson and this single vacuum trajectory alone constructs the amplitudes b+ at high energies. The total cross-section data is adequately described by the three trajectories P,P' and ρ in the energy range 5-20 GeV but the extrpolations of their contributions to the energy range (20-70 GeV) does not exhibit the energy dependence of the recent Serpukhov pio-nucleon total cross-section data. There have beenseveral models to account for this apparent change in behaviour at 20 GeV which involve the addition of further contributions to the conventional Regge pole term and all these models give an adequate description of the total cross-section data over the whole energy range, which is not surprising considering their increased parameter freedom. We consider two different possibilities of asymptopia which involve the addition of multi-pomeron cuts and dipole contributions respectively to the P,P', ρ Regge poles and we increase our information input to the analysis by the use of the F.E.S.R. as a series of constrait equations on the parameters of the fit. We show that the size of the multi-pomeron cuts identified from the scattering data and the C.M.S.R. are incompatible where as a dipole solution satisfies both the scattering data and C.M.S.R., we consider the possibility of pomeranchuk theorem violation by the inclusion of an odd-signature dipole like term in the amplitude A'¯ but we are unable to reach a decisive conclusion on the possible violation because of the large experimental errors on the Serpukhov data.