Three-body decay of the d* dibaryon

Abstract

Under certain circumstances, a three-body decay width can be approximated by an integral involving a product of two off-shell two-body decay widths. This ``angle-average'' approximation is used to calculate the $\pi NN$ decay width of the $d^*(J^\pi=3^+, T=0)$ dibaryon in a simple $\Delta^2$ model for the most important Feynman diagrams describing pion emissions with baryon-baryon recoil and meson retardation. The decay width is found to be about 0.006 (0.07, 0.5) MeV at the $d^*$ mass of 2065 (2100, 2150) MeV for input dynamics derived from the Full Bonn potential. The smallness of this width is qualitatively understood as the result of the three-body decay being ``third forbidden''. The concept of $\ell$ forbiddenness and the threshold behavior of a three-body decay are further studied in connection with the $\pi NN$ decay of the dibaryon $d'(J^\pi=0^-, T=0 or 2)$ where the idea of unfavorness has to be introduced. The implications of these results are briefly discussed.