Pion Phase-Shift Information from $K_{\ell 4}$ Decays

摘要: The structure of the ${K}_{l4}$ decay spectrum is displayed in its full generality as a function complete set five kinematic variables; polarization effects are part similarly described. nontrivial dynamical aspects reside certain form factors, which depend on only three variables. It shown that, with large cuts at two remaining variables, measurement alone suffices to overdetermine factors. On standard assumptions, these factors carry information relating phase shifts for pion-pion scattering. an important practical matter extract something this under conditions limited statistics, where spectra have be treated partially integrated form. We find that can accomplished, surprising economy, energy-dependent phase-shift difference ${\ensuremath{\delta}}_{s}\ensuremath{-}{\ensuremath{\delta}}_{p}$, single additional assumption dipion system produced chiefly $s$- and $p$-wave states. emerges from intensity ${K}_{e4}$ decay, again ${K}_{\ensuremath{\mu}4}$ being functions Moreover, variables simple therefore relatively undemanding statistical sense.