Abstract
We present a new solution to the hierarchy problem utilizing nonlinearly realized discrete symmetries. The cancellations occur due to a discrete symmetry that is realized as a shift symmetry on the scalar and as an exchange symmetry on the particles with which the scalar interacts. We show how this mechanism can be used to solve the little hierarchy problem as well as give rise to light axions.
Highlights
Introduction.—In this Letter, we describe a new mechanism for obtaining a scalar that is parametrically lighter than the UV cutoff of the theory
This mechanism involves a discrete ZN symmetry that is nonlinearly realized on a scalar as a shift symmetry and manifests as an exchange symmetry on the N copies of particles with which it interacts. (Because of the presence of additional discrete symmetries, the ZN symmetry may be enhanced to a DN symmetry.) This approach allows one to obtain a hierarchy between the mass of the scalar and the UV cutoff that is exponential in N, meaning that N 1⁄4 3 already solves most problems
We first consider an explicit example of a Yukawa coupling between a scalar and a fermion
Summary
The cancellations occur due to a discrete symmetry that is realized as a shift symmetry on the scalar and as an exchange symmetry on the particles with which the scalar interacts We show how this mechanism can be used to solve the little hierarchy problem as well as give rise to light axions. Introduction.—In this Letter, we describe a new mechanism for obtaining a scalar that is parametrically lighter than the UV cutoff of the theory This mechanism involves a discrete ZN symmetry that is nonlinearly realized on a scalar as a shift symmetry and manifests as an exchange symmetry on the N copies of particles with which it interacts. This Lagrangian describes a scalar φ coupled to fermions with a Yukawa coupling ∼ε=f. There is a stronger version of the above cancellation, which is that for all integer m with N > m ≥ 0, sinm φ f þ
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