The goofy-symmetric Standard Model and the Hierarchy Problem

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.