Sum Rules for the Decay of the Baryon Decuplet into the Baryon and Meson Octets in Broken SU (3) Symmetry

We have investigated the sum rules for the decuplet → octet+octet coupling constants, taking into account the SU(3)-symmetry-breaking interactions to first order. There are seven sum rules for the possible twelve coupling constants. One of these sum rules involves only the coupling constants for the decays $N^{*}\to N\pi$, ${Y_1}^{*}\to \Lambda \pi$, ${Y_1}^{*}\to \Sigma \pi$, and ${\Xi }^{*}\to \Xi \pi$, all of which are experimentally known. We also give the corresponding sum rules for 10* → 8+8 decay.