Abstract
Cosmological relaxation of the electroweak scale is an attractive scenario addressing the gauge hierarchy problem. Its main actor, the relaxion, is a light spin-zero field which dynamically relaxes the Higgs mass with respect to its natural large value. We show that the relaxion is generically stabilized at a special position in the field space, which leads to suppression of its mass and potentially unnatural values for the model’s effective low-energy couplings. In particular, we find that the relaxion mixing with the Higgs can be several orders of magnitude above its naive naturalness bound. Low energy observers may thus find the relaxion theory being fine-tuned although the relaxion scenario itself is constructed in a technically natural way. More generally, we identify the lower and upper bounds on the mixing angle. We examine the experimental implications of the above observations at the luminosity and precision frontiers. A particular attention is given to the impressive ability of future nuclear clocks to search for rapidly oscillating scalar ultra-light dark matter, where the future projected sensitivity is presented.
Highlights
DM model seems to prefer rapidly oscillating frequencies which pose both challenging and exciting [10,11,12,13] quest for variety of precision-front experiments
The squared relaxion mass is naturally suppressed by δ, no matter what periodic backreaction potential we impose for the relaxion scenario, as long as the change of the backreaction potential is controlled by the same δ
We have examined the dynamics of cosmological relaxion around the local minima
Summary
The above simple and rather naive way to estimate the relaxion mass and couplings requires a more careful look. Due to the incremental change of the Higgs mass, after the first minimum is reached, the backreaction potential barely grows above the value needed to compensate the linear slope — at most by a δ2 fraction — and quickly drops This behaviour is schematically shown in the left panel of figure 1. Low energy observers may find this theory fine-tuned since the cosmological relaxation scenario allows relaxion mixing angle and mass such that the radiative correction to the mass could be larger than the tree level contribution To see this point, suppose that one has measured the relaxion mass and mixing angle corresponding to the latter maximum value, given in eq (2.4), so that the relative size of the quantum correction is (see section 4). We discuss the available constraints from currently available atomic clock systems and provide some projection for the sensitivity of future nuclear clock
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