Chapter 4.3.1 - Rigorous Consequences of Analyticity and Unitarity

Abstract

Pion–Pion scattering is the simplest strong interaction process. The exact results are therefore obtained from the principles of axiomatic field theory. These include the impressive results on axiomatic analyticity domains and on absolute bounds on ππ amplitudes in terms of pion-mass alone. The analyticity domains imply the Roy equations, which are integral equations involving the physical region partial waves. The Roy equations allow the calculations of the lowest partial waves up to c.m. energy 0.8 GeV to within small uncertainties in terms of the available data. The chapter reviews the exact results for ππ scattering in the axiomatic field theory framework and some of their phenomenological applications. Neglecting the mass difference among the pions, and neglecting all electromagnetic effects, π+, π-, and π0 have a common mass lower than the mass of any other particle. Assuming also the experimental fact that pions have no bound states, the next lowest mass state with the G parity of one pion is the three-pion state, and the next lowest mass state with the G parity of two pions is the four-pion state. These facts lead to simple and powerful results on the ππ analyticity domain.