Daily Archives: June 15, 2008

Koide Splittings and heavy quarkonium

Work on my paper on the Koide formula continues. I’m in the meson section. Things are going okay, but…., so many mesons, so little time. Here’s a short description of some coincidences in the heavy mesons. I already put up a formula for the angular excitations of the pions on physics forums.

The bound states of hydrogen are, to lowest order, described by spherical harmonics, \psi_{nlm} . The energy levels of these wave functions depend only on n . The energies of these wave functions depend only on $n$, they are approximately -13.6/n^2 electron volts. Since the energies do not depend on l or m, the energy states are degenerate. However some of these degeneracies are split at higher orders.

At the lowest order, one ignores the spins of the proton and electron. Taking these into account we find a spin-spin effect. When the electron and proton spins are parallel, the energy is slightly different from when they are anti-parallel.

In the preon model I’m working on, the electron/muon/tau, and the neutrinos are composed of three preons each. The preons come in two types, charge Q = \pm 1/3 and neutral. Naturally, the electron has three charged preons while the neutrino has three neutral preons. The three generations of charged and neutral leptons follow two slightly different forms:
Koide formulas for the leptons

The quarks, having charges between 0 and \pm 1v, are supposed to be composed of a mixture of charged and neutral preons. The masses of the quarks cannot be determined experimentally because colored states never appear alone. The simplest particles made from quarks are the mesons, which are composed of a quark and an antiquark. And the simplest mesons are the q-qbar mesons, where the quark and the anti-quark are of the same type. In such a q-qbar meson, there is a mixture of neutral and charged preons and we can expect the same sort of interactions between these preons as breaks the degeneracy in the hydrogen atom.
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