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2nd Generation Fermion Masses

The second generation fermion particles correspond to pairs of octonions. There are 8^2 = 64 such pairs. The pair (1,1) corresponds to the mu-neutrino. The pairs (1,e), (e,1), and (e,e) correspond to the mu. Compare the symmetries of the mu pairs to the symmetries of the first generation fermion particles. The pair (e,e) should correspond to the e electron. The other two mu pairs have a symmetry group S2, which is 1/3 the size of the color symmetry group S3 which gives the up and down quarks their mass of 312.75 MeV. Therefore the mass of the mu should be the sum of the (e,e) electron mass and the (1,e)(e,1) symmetry mass, which is 1/3 of the up or down quark mass.

Therefore, M(mu) = 104.76 MeV.

Note that all pairs corresponding to the mu and the mu-neutrino are colorless.

The strange quark corresponds to the 9 pairs (1,ie), (1,je), (1,ke), (ie,1), (je,1), (ke,1), (ie,ie), (je,je), and (ke,ke).

The red strange quark is defined as the three pairs (1,ie), (ie,1), and (ie,ie), because ie is the red down quark. Its mass should be the sum of two parts: the (ie,ie) red down quark mass, 312.75 MeV, and the product of the symmetry part of the µ mass, 104.25 MeV, times the graviton factor.

Unlike the first generation situation, massive second and third generation leptons can be taken, by both of the colorless gravitons that may carry electric charge, into massive particles.

Therefore the graviton factor for the second and third generations is 6/2 = 3.

Therefore the symmetry part of the mu mass times the graviton factor 3 is 312.75 MeV, and the red strange quark constituent mass is ms = 312.75 MeV + 312.75 MeV = 625.5 MeV.

The blue strange quarks correspond to the three pairs involving je, the green strange quarks correspond to the three pairs involving ke, and their masses are determined similarly.

Note particularly that pairs of the type (ie,je), (je,ke), etc., do not correspond to the strange quark, but to the charm quark, because the octonionic products of such octonionic pairs as (ie,je), (je,ke), etc., are of the type -k, -i, etc., that correspond to the charm quark.

The charm quark corresponds to the other 51 pairs. Therefore, the mass of the red charm quark should be the sum of two parts:

the (i,i) red up quark mass, 312.75 MeV; and

the product of the symmetry part of the strange quark mass, 312.75 MeV, and the charm to strange octonion number factor 51/9, which product is 1,772.25 MeV.

Therefore the red charm quark constituent mass is mc = 312.75 MeV + 1,772.25 MeV = 2.085 GeV.

The blue and green charm quarks are defined similarly, and their masses are calculated similarly. Therefore

Smf2 = 4(mµ + 3ms + 3mc) = = 4(0.10476 + 3&endash;0.6255 + 3&endash;2.085) Gev = 32.94504 GeV.


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