Unlocking the Standard Model. II. 1 generation of quarks. Masses and couplings

TL;DR

This paper analyzes a specific Standard Model extension with one fermion generation and two Higgs doublets, determining masses and couplings from low energy physics, and exploring implications for quark masses and Higgs properties.

Contribution

It introduces a model with two parity-transformed Higgs doublets for one fermion generation, deriving all masses and couplings from low energy considerations and analyzing their relationships.

Findings

The Higgs boson $\xi$ has a mass approximately equal to the pion mass.

The light Higgs $\xvarsigma$ has a mass around 34 keV and weak coupling to matter.

The ratio of Higgs masses relates to the weak and chiral scales.

Abstract

We continue investigating the Standard Model for one generation of fermions and two parity-transformed Higgs doublets K and H advocated for in a previous work, using the one-to-one correspondence, demonstrated there, between their components and bilinear quark operators. We show that all masses and couplings, in particular those of the two Higgs bosons $\varsigma$ and $\xi$, are determined by low energy considerations. The mass of the "quasi-standard" Higgs boson, $\xi$, is $m_\xi \approx m_\pi$; it is coupled to u and d quarks with identical strengths. The mass of the lightest one, $\varsigma$, is $m_\varsigma \approx m_\pi \frac{f_\pi}{2\sqrt{2}m_W/g} \approx\ 34\,KeV$; it is very weakly coupled to matter except hadronic matter. The ratio of the two Higgs masses is that of the two scales involved in the problem, the weak scale $\sigma=\frac{2\sqrt{2}m_W}{g}$ and the chiral scale $v=f_\pi$, which are also the respective vacuum expectation values of the two Higgs bosons. They can freely coexist and be accounted for. The dependence of $m_\varsigma$ and $m_\xi$ on $m_\pi$, that is, on quark masses, suggests their evolution when more generations are added. Fermions get their masses from both Higgs multiplets. The theory definitely stays in the perturbative regime.