Some studies of the interactions of elementary particles

Abstract

A model f o r the pion-production amplitude is developed in which it is possible to calculate the total and differential cross-sections for different assumed forms of the pion-pion 1 = 0, s-wave amplitude. The two final state pions in the processπ p →π (^+)π η are considered as an I = 0, scalar, spin-zero system ʚ with a continuous mass spectrum - the 'mass' "being the di-pion invariant mass; and the model consists of assuming the peripheral interaction for all partial waves other than that corresponding to the S-wave ʚ final state. For this 'lowest' partial wave, a phenomenological form is derived by assuming that of the three particles in the final state, only the two pions, in an I = 0 S-wave, provide an important final state interaction. If the further assumption is made that this final state interaction can be 'factored' from the rest of the amplitude, then an I = 0, S-wave pion-pion phase-shift with a negative scattering length and which turns up through zero is found to reproduce quite well the pion production differential cross-section data. It is also shown from this model that almost any low-energy pion-pion interaction could be compatible with the low-energy total production cross-sections. Corroboration for this type of phase-shift is sought in the pion-nucleon partial wave 'discrepancy' analysis. By increasing the parameterisation of the pion-pion amplitude in this analysis, such a 'turn-over' type of phase-shift is found as well as a very negative solution with a large negative scattering length, and no turn ever, and the solutions previously found from this analysis with positive scattering lengths. The very negative solution is rejected as being incompatible with the pion production differential distributions calculated from our model. The ABC effect is discussed in terms of the two enhancement factors usually assumed for this analysis. It is shown that for a phase-shift which passes through zero, these two factors are not equivalent and it is not clear which - if either -should be used. The possibility of a CDD pole in the 1 = 0, s-wave pion-pion partial wave has recently been suggested. Both the model proposed for the pion-production amplitude, and the 'discrepancy' analysis are adapted to incorporate this possibility. It is found that at least three types of resonating phase-shifts - two similar to those found by Lovelace et al and one similar to that obtained by Wolf - could be compatible with the low-energy pion-production and pion-nucleon scattering data. Finally, a survey is given of the other methods f o r obtaining the form of the low-energy pion-pion interaction. By discussing the possible sources of error inherent in these calculations, some fairly general conclusions are drawn and compared with the results of the above analyses.