Title:

Some studies of the interactions of elementary particles

A model f o r the pionproduction amplitude is developed in which it is possible to calculate the total and differential crosssections for different assumed forms of the pionpion 1 = 0, swave amplitude. The two final state pions in the processπ p →π (^+)π η are considered as an I = 0, scalar, spinzero system ʚ with a continuous mass spectrum  the 'mass' "being the dipion invariant mass; and the model consists of assuming the peripheral interaction for all partial waves other than that corresponding to the Swave 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 Swave, 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, Swave pionpion phaseshift with a negative scattering length and which turns up through zero is found to reproduce quite well the pion production differential crosssection data. It is also shown from this model that almost any lowenergy pionpion interaction could be compatible with the lowenergy total production crosssections. Corroboration for this type of phaseshift is sought in the pionnucleon partial wave 'discrepancy' analysis. By increasing the parameterisation of the pionpion amplitude in this analysis, such a 'turnover' type of phaseshift 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 phaseshift 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, swave pionpion partial wave has recently been suggested. Both the model proposed for the pionproduction amplitude, and the 'discrepancy' analysis are adapted to incorporate this possibility. It is found that at least three types of resonating phaseshifts  two similar to those found by Lovelace et al and one similar to that obtained by Wolf  could be compatible with the lowenergy pionproduction and pionnucleon scattering data. Finally, a survey is given of the other methods f o r obtaining the form of the lowenergy pionpion 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.
