Nuclear, Particle, Astroparticle and Cosmology (NUPAC) Seminars
A Study of Mass Matrices with Permutational Symmetry for Quark and Lepton Families
Presented by Dr. Richard Holmes (Boeing)
The most general class of mass matrices consistent with permutational symmetry and 3 generations of particles is studied. It is found that 3 Hermitian, permutationally-symmetric matrices and their complex conjugates can match exactly the 3 masses in a particle family. The 3 matrices have eigenstates that are found to be isomorphic to QCD color in the quark families. Upon integration of these matrices with Dirac's equation, it is shown that there is always one pure-mass Dirac solution for each particle within a family. For the electron family, these pure-mass states can be identified with the electron, muon and tau particles. For the remaining two solutions, bound states of composite mass arise. These bound states match the behavior of Pontecorvo oscillations in the neutrino family. Further, these bound states are shown to match the behavior of bound quarks, quantitatively obtaining the well-known quark potential -a/r + br with b accurate to 5% in an
initial calculation of Yang-Mills potentials. Given complete permutational symmetry and three QCD colors, it is shown that 3 generations of particles are required. The PMNS and CKM matrices can be fit exactly and uniquely assuming color is conserved. A physical interpretation is provided for this fit.
The mass matrices are equivalent to a solid-state physics Hamiltonian of three potential wells in a ring and the consequences of this are explored. Of the 26 input parameters of the Standard Model, 23 can be fit with an accuracy of 1.2% or better, with semi-quantitative physical explanations.
2:00 pm, Tuesday, August 28, 2018
PAIS-2540, PAIS
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