Sliding naturalness: cosmological selection of the weak scale

Abstract

We present a cosmological solution to the electroweak hierarchy problem. After discussing general features of cosmological approaches to naturalness, we extend the Standard Model with two light scalars very weakly coupled to the Higgs and present the mechanism, which we recently introduced in a companion paper to explain jointly the electroweak hierarchy and the strong-CP problem. In this work we show that this solution can be decoupled from the strong-CP problem and discuss its possible implementations and phenomenology. The mechanism works with any standard inflationary sector, it does not require weak-scale inflation or a large number of e-folds, and does not introduce ambiguities related to eternal inflation. The cutoff of the theory can be as large as the Planck scale, both for the Cosmological Constant and for the Higgs sector. Reproducing the observed dark matter relic density fixes the couplings of the two new scalars to the Standard Model, offering a target to future axion or fifth force searches. Depending on the specific interaction of the scalars with the Standard Model, the mechanism either yields rich phenomenology at colliders or provides a novel joint solution to the strong-CP problem. We highlight what predictions are common to most realizations of cosmological selection of the weak scale and will allow to test this general framework in the near future.

Sliding Naturalness

“…( 7)). This will be discussed more extensively in [15]. In conclusion we have an "axion" φ + with a mass-coupling relation identical 1 There is an exception to this argument.…”

“…( 2), as well as including tadpole and cubic terms (with scale M ± ) and possibly cross-interactions. We discuss this in [15].…”

“…All other universes rapidly crunch. We discuss a similar way to select m 2 h independently of θ in a companion paper [15]. Different versions of a crunching mechanism have been advocated to explain the value of the CC in [16] and of m 2 h in [8,9].…”

“…( 2) and can be longer than the inverse of the physical mass of φ + , set by V φH . Then the region m φ+ H(Λ QCD ) becomes allowed [15]. 2) m φ− is taken to be larger than m φ+ , but also universes with h µ B crunch after the QCD phase transition when the destabilizing potential for φ − in Eq.…”

“…Similarly scale invariance could be replaced by supersymmetry. We discuss more general implementations in a companion paper [15].…”