Time-delay, energy-continuum, and systematics of particles

Abstract

Finding systematics in the mass-lifetime data for all the hadrons has been an outstanding problem. In this work, we show that the product of mass and lifetime for unstable particles is very well-approximated by \hbar 2^n/n where n is an integer specific for a particle. In doing so, we have employed a relation between time-delay and resonances. The energy-continuum has been treated in a way to take advantage of Cantor's mathematical work on continuum. Thus, even though the resonances are designated by complex energy variables where ordering is not possible, in terms of stability, the index n labels these resonances; larger the n, more stable a resonance is.