Hamburg 2016 – scientific programme

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T: Fachverband Teilchenphysik

T 93: Andere Gebiete der Theorie

T 93.2: Talk

Thursday, March 3, 2016, 17:00–17:15, VMP6 HS D

On the role of the fine structure constant in the alpha/beta rule for calculation of particle masses. — •Karl Otto Greulich — Fritz Lipmann Institut, Beutenbergstr.11, 07745 Jena

The masses of essentially all elementary particles are given almost exactly by the alpha/beta rule:

m = alpha to power of -n divided by or times beta*27,2 eV/c2

(K.O.Greulich, Spring meeting 2014 German Phys Society T 99.4), i.e. particle masses depend on the fine structure (Sommerfeld) constant alpha = 1/137). This is somewhat surprising since alpha is rather known as a spectroscopic constant than as a mass ratio. One key to understand this is the observation that the Bohr energy is exactly the 1 / alpha fold of the ionization energy of the hydrogen atom (Rydberg energy, 13.6 eV). Thereby the Bohr energy is the de Broglie energy of the electron in the ground state (on the Bohr radius). A second mass * or energy ratio, the ratio between the energy at rest of the electron and the Bohr energy can be derived analytically to be alpha to the power -2. Both results together suggest a general dependence of rest energies or rest masses on alpha. Simply by the hypothesis that this observation can be extrapolated to higher values of n, the alpha / beta rule follows immediately. Only the beta (1 or 1836,12) term has to be added empirically.