How fast can an unstable particle decay into two final states and be observed

Abstract

We investigate unstable hadrons (resonances) which mainly decay into two final states in a very short time. We estimate how far at most these two final states can travel away from each other in the half-life of the initial unstable hadron. As examples, this distance is about 2.5 fm for rho -> pi pi, 1.8 fm for Delta -> N pi, and 0.6 fm for f_0(500) -> pi pi. We calculate this distance for altogether 181 hadrons, among all the 324 ones listed in PDG2012 together with Zc(3900) and Zc(4025). We find it is around one femtometer for many hadrons, which is of the same order of magnitude as the hadronic radii. We also estimate this distance for altogether 15 unstable nuclei. We find it is about several femtometers for some of them, which is of the same order of magnitude as the nuclear radii. For example, it is about six femtometers for O12 -> N11 p.