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

Bruno Machet

Published 2012-07-17, updated 2012-11-29Version 3

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.