WeakΔI=12Rule and the Dynamical Higgs Mechanism

Abstract

We show that the weak $\Delta I=\frac{1}{2}$ rule, $\frac{{m_W}^2}{{m_Z}^2}={cos}^2\theta$, in an $\mathrm{S}{\mathrm{U}}_L\mathrm{}\left(2\right)\mathrm{}\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauge model can be obtained from a dynamical Higgs mechanism. This is independent of weak isospin breaking in the fermion mass spectrum. A consequence of this mechanism is a sum rule which implies the existence of heavy quarks or leptons with ultraviolet masses comparable to the $W$ and $Z$ weak boson masses, ∼30-100 GeV.