# 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 difference between baryons and mesons is not understood. The fractal properties and discrete scale invariance model are also used to study nuclei yrast masses as well as excited nuclei level masses of some nuclei. Here also the good agreement between data and fractal property, allows to make some predictions for still unobserved nuclei masses. Fractal properties are also compared to several nuclei data such as : - atomic masses in several columns of the Mendeleev periodic table of elements, - masses of series following $\beta^{+}$ or $\beta^{-}$ disintegrations, - one and two nucleon separation energies, - half-lives of some isotopes, - the four radioactive family periods. Finally, it is shown that the lepton, hadron, and boson masses can be presented in the same frame. This is also partially true for the coupling constants.
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### Citation

B. Tatischeff. What do fractals learn us concerning the masses of fundamental particles, of hadrons, and of nuclei? Concerning also disintegration life-times?. 21st International Baldin Seminar on High Energy Physics Problems : Relativistic Nuclear Physics and Quantum Chromodynamics (ISHEPP 2012), Sep 2012, Dubna, Russia. pp.055, ⟨10.22323/1.173.0055⟩. ⟨in2p3-00869969⟩

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