  Weakly nonlocal (WNL) Quantum Field Theories (QFT's) may define a new class
of UV-completions in particle physics and gravity, without introducing any new
elementary particle. One problematic issue is how to realize spontaneous
symmetry breaking without introducing an infinite tower of ghosts in the
perturbative spectrum. In this article, a WNL extension of the Standard Model
(SM) is proposed: the Fuzzy Standard Model (FSM). It is a smooth deformation of
the SM based on covariant star-products of fields. This new formalism realizes
electroweak symmetry breaking without ghosts at tree-level. We give evidences
that the FSM exhibit Vainshtein screening, aka classicalization, in the
deep-UV. This could solve the electroweak hierarchy problem if it occurs at the
TeV-scale.
