## Koide Mass Equations for Hadrons

**Authors:** C. A. Brannen

Koide's mass formula relates the masses of the charged leptons. It is related to the
discrete Fourier transform. We analyze bound states of colored particles and show that
they come in triplets also related by the discrete Fourier transform. Mutually unbiased
bases are used in quantum information theory to generalize the Heisenberg uncertainty
principle to finite Hilbert spaces. The simplest complete set of mutually unbiased bases
is that of 2 dimensional Hilbert space. This set is compactly described using the Pauli
SU(2) spin matrices. We propose that the six mutually unbiased basis states be used
to represent the six color states R, G, B, R-bar, G-bar, and B-bar. Interactions between the colors
are defined by the transition amplitudes between the corresponding Pauli spin states.
We solve this model and show that we obtain two different results depending on the
Berry-Pancharatnam (topological) phase that, in turn, depends on whether the states
involved are singlets or doublets under SU(2). A postdiction of the lepton masses is
not convincing, so we apply the same method to hadron excitations and find that their
discrete Fourier transforms follow similar mass relations. We give 39 mass fits for 137
hadrons.

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 24 Apr 2009

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