${\hat{I}}^3{\hat{I}}^3\to \ddot{I}{€}^0\ddot{I}{€}^0$ and $\hat{I}\cdot \to \ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ at $O(p^6)$ in the NJL model

Abstract

We discuss the processes ${\hat{I}}^3{\hat{I}}^3\to \ddot{I}{€}^0\ddot{I}{€}^0$ and $\hat{I}\cdot \to \ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ at $O(p^6)$ in the momentum expansion. The calculation involves tree--level, one--loop and two--loop diagrams of a chiral effective lagrangian which is obtained by a bosonization of the NJL model. The importance of integrating out meson resonances (reduction) is pointed out. Our final results for the total cross section of ${\hat{I}}^3{\hat{I}}^3\to \ddot{I}{€}^0\ddot{I}{€}^0$ are in good agreement with the experimental data of the Crystal Ball Collaboration. For the width of the $\hat{I}\cdot \to \ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3$ decay we obtain the value $0.11$ eV which has to be compared with the experimental value of $(0.84\pm 0.18)$ eV. Alternatively, taking empirical parameters from a vector--meson--dominance model the prediction for the decay width is $0.35$ eV. We present a prediction for the differential decay probability as a function of $m_{{\hat{I}}^3{\hat{I}}^3}^2/m_{\hat{I}}{\cdot }^2$.

16 pages, LaTeX, 2 figures included. Complete Postscript file is available at http://cv.jinr.dubna.su/~lanyov/save/gg-prep.ps