Ghost-free Electroweak Symmetry Breaking with Weakly Nonlocal Interactions

Abstract: 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 exhibits Vainshtein screening, aka classicalization, in the deep-UV. This could solve the electroweak hierarchy problem if it occurs at the TeV-scale.