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This is the first of two companion papers where we prove that the recentlydiscovered non perturbative mechanism capable of giving mass to elementaryfermions, 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. Thenon perturbative fermion and $W$ masses have the form $m_f\simC_f(\alpha)\Lambda_{RGI}$ and $M_W\sim g_wc_w(\alpha)\Lambda_{RGI}$ with$C_f(\alpha)$ and $c_w(\alpha)$ functions of the gauge couplings, $g_w$ theweak coupling and $\Lambda_{RGI}$ the RGI scale of the theory. These parametricstructures imply that a realistic model must include a new sector of massivefermions (Tera-fermions) subjected, besides Standard Model interactions, tosome kind of super-strong gauge interactions (Tera-interactions) so that theRGI scale of the full theory, $\Lambda_T$, will be in the few TeV region. Theextension of the model by introducing hypercharge and particles singlets understrong interactions (leptons and Tera-leptons) is the focus of the companionpaper, where we also discuss some phenomenological implications of thisapproach. One can show that, upon integrating out the (heavy) Tera-degrees offreedom, the resulting low energy effective Lagrangian closely resembles theStandard Model Lagrangian. The argument rests on the conjecture that the 125GeV resonance detected at LHC is a $W^+W^-/ZZ$ composite state, bound byTera-particle exchanges, and not an elementary object. Although we restrict tothe one family case, neglecting weak isospin splitting, this scheme has acertain number of merits with respect to the Standard Model. It offers aradical solution of the Higgs mass tuning problem as there is no Higgs. Itallows identifying $\Lambda_T$ as the electroweak scale. It helps reducing thenumber of Standard Model parameters as elementary particle masses aredetermined by the dynamics.

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