Abstract
We show how the Koide relationships and associated triplet mass matrices can be generalized to derive the observed sum of the free neutron and proton rest masses in terms of the up and down current quark masses and the Fermi vev to six parts in 10,000. This sum can then be solved for the separate neutron and proton masses using the neutron minus proton mass difference derived by the author in a recent, separate paper. The oppositely-signed charges of the up and down quarks are responsible for the appearance of a complex phase exp(iδ) and real rotation angle θ which leads on an independent basis to mass and mixing matrices similar to that of Cabibbo, Kobayashi and Maskawa (CKM). These can then be used to specify the neutron and proton mass relationships to unlimited accuracy using θ as a nucleon fitting angle deduced from empirical data. This fitting angle is then shown to be related to an invariant of the CKM mixing angles within experimental errors. Also developed is a master mass and mixing matrix which may help to interconnect all baryon and quark masses and mixing angles. The Koide generalizations developed here enable these neutron and proton mass relationships to be given a Lagrangian formulation based on neutron and proton field strength tensors that contain vacuum-amplified and current quark wavefunctions and masses. In the course of development, we also uncover new Koide relationships for the neutrinos, the up quarks, and the down quarks.
Highlights
In an earlier paper [1] the author introduced the thesis that baryons are Yang-Mills magnetic monopoles
We show how the Koide relationships and associated triplet mass matrices can be generalized to derive the observed sum of the free neutron and proton rest masses in terms of the up and down current quark masses and the Fermi vev to six parts in 10,000
This sum can be solved for the separate neutron and proton masses using the neutron minus proton mass difference derived by the author in a recent, separate paper
Summary
In an earlier paper [1] the author introduced the thesis that baryons are Yang-Mills magnetic monopoles. In this paper, we combine the author’s previous work in [1,5] as well as [8], using the generalization provided by Koide triplet mass matrices of the form (2.1) below, to deduce the observed rest masses 938.272046 MeV and 939.565379 MeV of the free neutron and proton as a function of the up and down quark masses and electric charges and the Fermi vev. We start by showing how to reformulate the Koide relationships in terms of the statistical variance of the Koide terms across the three generations
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