A road to an elementary particle physics model with no Higgs -- I

This is the first of two companion papers where we prove that the recently discovered non perturbative mechanism capable of giving mass to elementary fermions, in the presence of weak interactions can also generate a mass for the $W$, and can thus be used as a viable alternative to the Higgs scenario. The non perturbative fermion and $W$ masses have the form $m_f\sim C_f(\alpha)\Lambda_{RGI}$ and $M_W\sim g_wc_w(\alpha)\Lambda_{RGI}$ with $C_f(\alpha)$ and $c_w(\alpha)$ functions of the gauge couplings, $g_w$ the weak coupling and $\Lambda_{RGI}$ the RGI scale of the theory. These parametric structures imply that a realistic model must include a new sector of massive fermions (Tera-fermions) subjected, besides Standard Model interactions, to some kind of super-strong gauge interactions (Tera-interactions) so that the RGI scale of the full theory, $\Lambda_T$, will be in the few TeV region. The extension of the model by introducing hypercharge and particles singlets under strong interactions (leptons and Tera-leptons) is the focus of the companion paper, where we also discuss some phenomenological implications of this approach. One can show that, upon integrating out the (heavy) Tera-degrees of freedom, the resulting low energy effective Lagrangian closely resembles the Standard Model Lagrangian. The argument rests on the conjecture that the 125 GeV resonance detected at LHC is a $W^+W^-/ZZ$ composite state, bound by Tera-particle exchanges, and not an elementary object. Although we restrict to the one family case, neglecting weak isospin splitting, this scheme has a certain number of merits with respect to the Standard Model. It offers a radical solution of the Higgs mass tuning problem as there is no Higgs. It allows identifying $\Lambda_T$ as the electroweak scale. It helps reducing the number of Standard Model parameters as elementary particle masses are determined by the dynamics.