Two-Variable Expansions andp¯n→3πAnnihilations at Rest

Abstract

The experimental Dalitz plot for $\overline{p}n\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ annihilations at rest is analyzed, using previously suggested two-variable expansions of decay amplitudes, based on the representation theory of the group O(4). A fair fit to the Dalitz plot is obtained by minimizing the ${\ensuremath{\chi}}^{2}$ function, assuming that the annihilation proceeds from a protium state of definite (but unspecified) angular momentum $J$ (or from several such states). Fits with 2, 4, 6, and 9 free parameters are considered, the values of the parameters are essentially stable with respect to the "cutoff" of the expansion, and the solutions are unique. The fit is purely kinematical, in that no assumptions are made about the initial and final state or the annihilation dynamics. An analysis of the contribution of various parts of the Dalitz plot to the over-all ${\ensuremath{\chi}}^{2}$ suggests that the fit would be considerably improved by including, e.g., $\ensuremath{\rho}$- and $f$-meson final-state resonances explicitly. We compare the O(4) expansions with a power-series expansion in Dalitz-Fabri variables and also with various models that have been recently applied, in particular the Veneziano model and its generalizations and various final-state-interaction models.