A Classical Analogue to the Standard Model, Chapters 4-11: Particle generations and masses; curved spacetimes and gravitation; heavy weak bosons

Abstract

The ${\mathbb{C}}^{\wedge 18}$ analogue model contains counterparts to the particle spectrum and interactions of the Standard Model, and has only three tunable parameters. As the structure of this model is highly constrained, predictive relationships between constants may be obtained. In Chapters 4-6, the masses of the tau, the $W$ and $Z$ bosons, and a Higgs-like scalar boson are calculated as functions of $\alpha$, $m_e$, and $m_{\mu }$. They are shown to be $1.776867413(43)$ GeV/$c^2$, $80.3587(22)$ GeV/$c^2$, $91.1877(35)$ GeV/$c^2$, and $125.1261(48)$ GeV/$c^2$ respectively, with no free fitting parameters. All are within $0.1\sigma$ of the observed values of $1.77686(12)$ GeV/$c^2$, $80.360(16)$ GeV/$c^2$, $91.1876(21)$ GeV/$c^2$, and $125.11(11)$ GeV/$c^2$ respectively. In Chapter 7 the final ungauged freedom of the ${\mathbb{C}}^{\wedge 18}$ model is used to eliminate the right-handed weak interaction, while simultaneously introducing space-time curvature and a gravitational interaction emulating general relativity. The value of Newton's constant is then calculated from $\alpha$, $m_e$, and $m_{\mu }$, yielding $G_N=6.67426(230)\times 10^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$, which is in agreement with the observed value of $G_N=6.67430(15)\times 10^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$ with tension less than $0.1{\sigma }_{\exp }$. This persistent consistency with experiment suggests the existence of a unifying relationship between lepton generations, gravitation, and the electroweak mass scale. In the Classical Analogue to the Standard Model this unification arises from an underlying construction from coloured preons, with the low-energy residuals of the preon binding interactions corresponding to the strong nuclear force.

arXiv comment201 pages, 46 figures. Updated calculation of Higgs boson mass (0.1% correction; Secs. 5:3.3 & 6:4.5). Added some initial discussion of Higgs interactions in CASMIR (Ch. 11)