Abstract
Relaxion models are an interesting new avenue to explain the radiative stability of the Standard Model scalar sector. They require very large field excursions, which are difficult to generate in a consistent UV completion and to reconcile with the compact field space of the relaxion. We propose an $N$-site model which naturally generates the large decay constant needed to address these issues. Our model offers distinct advantages with respect to previous proposals: the construction involves non-Abelian fields, allowing for controlled high-energy behavior and more model building possibilities, both in particle physics and inflationary models, and also admits a continuum limit when the number of sites is large, which may be interpreted as a warped extra dimension.
Highlights
Large field excursions are known to be an ingredient of slow roll theories of inflation [1,2] and have become a requirement for relaxation solutions to the hierarchy problem of the Standard Model (SM) [3]
Our model generates a potential composed of many oscillatory terms with very different periods [see Eq (9)]; the term with the larger period plays the role of the linear term in Eq (1)
From N fields acquiring expectation values of order f, an effective scale f1 1⁄4 CNf=qN−1 ≫ f [see Eq (10)] is generated and the pNGBs have a compact field space of 2πf1, which allows for large field excursions
Summary
Large field excursions are known to be an ingredient of slow roll theories of inflation [1,2] and have become a requirement for relaxation solutions to the hierarchy problem of the Standard Model (SM) [3]. (ii) Another crucial feature of Eq (1) is the presence of a linear term that explicitly breaks a gauge symmetry (the axion shift symmetry), which is inconsistent with the pNGB nature of the relaxion [9] This second point can be avoided if all operators involving φ are periodic, but with very different periods, and the linear term is nothing but a small region in an oscillation of longer period. An explicit example is proposed in [10] to generate an effective super-Planckian field range, by considering N þ 1 complex scalars with the same decay constant f < MPl. By adding a conveniently chosen breaking term, the global Uð1ÞNþ1 is explicitly broken to Uð1Þ and the remaining pNGB has a decay constant which exponentially depends on the number of fields as F ≫ ecNf, where c ∼ Oð1Þ. For explorations along these lines, see [27,28]
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