What do fractals learn us concerning the masses of fundamental particles, of hadrons, and of nuclei? Concerning also disintegration life-times?

Abstract

The hadron spectroscopy is studied through the use of fractals and discrete scale invariance (DSI) implying log-periodic corrections to continuous scaling. The masses of mesons and baryons, reported by the Particle Data Group (PDG), agree with (DSI), as well as the masses of exotic narrow mesons, baryons, and dibaryons. Two distributions are systematically studied: first the log of the masses versus the log of their rank, and also the successive mass ratios. Each fitted parameter of the second distributions, as a function of the hadronic masses, displays the same shape for all PDG hadronic families and species. The same parameters allow good fits for the narrow exotic mesons, baryons and dibaryons. When the successive mass ratios between different baryon families are constant, this property is not observed between different meson families. Such observation is studied within the double mass ratios eliminating the quark masses, but the differenc e between baryons and mesons is not