The goofy-symmetric Standard Model and the Hierarchy Problem

TL;DR

This paper explores a novel 'goofy' symmetry in the Standard Model that could naturally forbid the Higgs mass term, offering an alternative approach to addressing the hierarchy problem and suggesting new avenues for symmetry breaking and dark matter candidates.

Contribution

It extends goofy symmetries to the Standard Model, showing they can forbid the Higgs mass term and provide new mechanisms for electroweak symmetry breaking.

Findings

Goofy symmetry can make the SM action symmetric if the Higgs mass term vanishes.

Extensions of the SM with goofy symmetry are constrained but can include dark matter candidates.

Spontaneous breaking of goofy symmetry can produce a viable Higgs mass.

Abstract

A new class of so-called "goofy" symmetries has been shown to lead to renormalization-group stable relations between parameters in two-Higgs-Doublet Models, not known before. In this work we investigate goofy transformations in the Standard Model (SM), extending them to the fermion sector. We show that the SM action is goofy "symmetric", if the Higgs mass term vanishes, while other SM interactions are allowed. Goofy symmetry could thus add another option to the very few means to successfully forbid the Higgs mass term, providing an alternative to conformal symmetry or shift symmetry. We further consider how electroweak symmetry breaking can be realized in the goofy symmetric SM via higher dimensional operators or an extended scalar sector. A viable Higgs mass can be obtained via spontaneous breaking of goofy symmetry, which can be realized via operators that would not be allowed by shift symmetry or conformal symmetry. We find that goofy-symmetric extensions of the SM are strongly constrained, but offer for example a straightforward dark matter candidate.