πΛPhase-Shift Information from High-Energy Antineutrino Reactions and fromΞe4Decays

Abstract

Methods are described to obtain the $S$-wave $\pi \Lambda$ phase shift from the processes $\Xi \to \Lambda \pi e\overline{\nu }$ and $\overline{\nu }+N\to \Lambda \pi \overline{\mu }$. Each of these processes is fully specified (for vanishing lepton mass) by a set of sixteen seven-dimensional distributions describing the intensity and the various polarization spectra. From each distribution, nine functions of a single variable, the invariant $\pi \Lambda$ mass, are extracted. Ratios of these functions determine the $S$-wave phase shift, for energies where only $S$- and $P$-wave amplitudes are appreciable and where the $S$ phase shift is the only significant one. For the decays there are 36 independent determinations of this kind. For the reactions there are 8, and these are independent of a detailed knowledge of the incoming $\overline{\nu }$ spectrum. In all instances, knowledge of the polarizations of the parent baryon and of the $\Lambda$ is indispensable. No assumptions on the structure of hadronic form factors are necessary. We do assume that possible deviations from lepton pair locality and from $T$ invariance are insignificant.