Pion - Pion Scattering Information

We show how the reaction e-e’+ n-n’y can be used to study the dipion system in states of even charge conjugation (and even angular momentum). In particular, its utility for experimentally investigating an I = 0, J = 0 resonance (e-meson) is discussed in detail. (Submitted to Phys. Rev. ) * Work supported by the U. S. Atomic Energy Commission. t N. S. F. Graduate Fellow. To lowest order in the fine structure constant Q!, the reaction (H, any neutral hadronic system) e+ e’-II produces only final states with charge conjugation (C) odd and angular momentum (J) equal to one. This property is one of the primary advantages of electron-positron colliding beam experiments; i. e. , it allows the careful experimental study of a specific hadronic’channel. Already this reaction has yielded beautiful results on the pion’ and-kaon’ form factors as well as the three-pion final state. ~3 However, this property is at the same time one of the limitations of electron-positron storage rings; since one would also like to investigate experimentally other hadronic channels. In a previous note ,4 we showed how one could use reactions of the form em+efH+Y, where Y is a hard photon, to study hadronic systems with even-C. Although the hadrons H may emerge from this reaction with either even-or odd-C, quantum + electrodynamics plus knowledge of the cross section for e+ e -H allows one to remove the odd-C contribution. Consequently, the effects of the production of hadronic states with even-l: can be isolated and studied in a model-independentway. We have illustrated’ the method of analysis by considering the reaction + e-+e 4.2~~+r++y. In this expanded discussion we will present the details of the analysis and consider further experimental problems and theoretical implications. The outline of the paper is as follows: In Section I we summarize the theoretical predictions and experimental results bearing on the existence of an I = 0, J = Odipion resonance (the f-meson). Jn Section II we discuss the kinematics of the reaction being considered. We include here abrief discussion of how such an experiment may be analyzed and discuss some features of the Dalitz plot. In Section III a particular model for estimating the order of magnitude of the contribution from the e-meson