Long Distance Contribution to \(s \to d\gamma\) and Implications for \(\Omega^-\to \Xi ^-\gamma, B_s \to B_d^\gamma\) and \(b \to s\gamma\)

We estimate the long distance (LD) contribution to the magnetic part of the \(s \to d\gamma\) transition using the Vector Meson Dominance approximation \((V=\rho,\omega,\psi_i)\). We find that this contribution may be significantly larger than the short distance (SD) contribution to \(s \to d\gamma\) and could possibly saturate the present experimental upper bound on the \(\Omega^-\to \Xi^-\gamma\) decay rate, \(\Gamma^{\rm MAX}_{\Omega^-\to \Xi^-\gamma} \simeq 3.7\times10^{-9}\)eV. For the decay \(B_s \to B^*_d\gamma\), which is driven by \(s \to d\gamma\) as well, we obtain an upper bound on the branching ratio \(BR(B_s \to B_d^*\gamma)