Influence of Bose-Einstein Statistics on the Antiproton-Proton Annihilation Process

TLDR

Angular distributions of π mesons in antiproton–proton annihilation deviate from predictions of the conventional Fermi statistical model. The study aims to investigate whether a modified statistical model incorporating Bose–Einstein symmetrization can explain these deviations. The authors modify the transition‑rate assumption by expressing the probability of finding N free π mesons in terms of charge‑symmetrized wave functions, and discuss the justification of this approach. The symmetrized model qualitatively reproduces the observed angular correlations when the interaction volume radius lies between one‑half and three‑fourths of the pion Compton wavelength, though quantitative agreement remains limited and highlights the potential importance of Bose–Einstein effects.

Abstract

Recent observations of angular distributions of $\ensuremath{\pi}$ mesons in $\overline{p}\ensuremath{-}p$ annihilation indicate a deviation from the predictions of the usual Fermi statistical model. In order to shed light on these phenomena, a modification of the statistical model is studied. We retain the assumption that the transition rate into a given final state is proportional to the probability of finding $N$ free $\ensuremath{\pi}$ mesons in the reaction volume, but express this probability in terms of wave functions symmetrized with respect to particles of like charge. The justification of this assumption is discussed. The model reproduces the experimental results qualitatively, provided the radius of the interaction volume is between one-half and three-fourths of the pion Compton wavelength; the dependence of angular correlation effects on the value of the radius is rather sensitive. Quantitatively, there seems to remain some discrepancy, but we cannot say whether this is due to experimental uncertainties or to some other dynamic effects. In the absence of information on $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interactions and of a fully satisfactory explanation of the mean pion multiplicity for annihilation, we wish to emphasize the preliminary nature of our results. We consider them, however, as an indication that the symmetrization effects discussed here may well play a major role in the analysis of angular distributions. It is pointed out that in this respect the energy dependence of the angular correlations may provide valuable clues for the validity of our model.