APS : Sliding Naturalness: New Solution to the Strong-$CP$ and Electroweak-Hierarchy Problems

Tito D'Agnolo, Raffaele; Teresi, Daniele

doi:10.1103/PhysRevLett.128.021803

Article
Report number	arXiv:2106.04591 ; CERN-TH-2021-055
Title	Sliding Naturalness: New Solution to the Strong-$CP$ and Electroweak-Hierarchy Problems
Author(s)	Tito D'Agnolo, Raffaele (IPhT, Saclay) ; Teresi, Daniele (CERN)
Publication	2022-01-12
Imprint	2021-06-08
Number of pages	6
Note	9 pages, 3 figures. Version published on PRL
In:	Phys. Rev. Lett. 128 (2022) 021803
DOI	10.1103/PhysRevLett.128.021803 (publication)
Subject category	hep-ph ; Particle Physics - Phenomenology ; Astrophysics and Astronomy ; Particle Physics - Experiment ; Particle Physics - Theory
Abstract	We present a novel framework to solve simultaneously the electroweak hierarchy problem and the strong-CP problem. A small but finite Higgs vacuum expectation value and a small $\theta$-angle are selected after the QCD phase transition, without relying on the Peccei-Quinn mechanism or other traditional solutions. We predict a distinctive pattern of correlated signals at hadronic EDM, fuzzy dark matter and axion experiments.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2022-2025 authors (License: CC BY 4.0), sponsored by SCOAP³

$Cartoon of the basic mechanism: a landscape of Higgs masses and QCD $\theta$-angles is populated early in the history of the Universe. All patches with Higgs vev and $\theta$ far from the observed ones crunch after the QCD phase transition. The only universes that survive until today and grow to cosmological sizes are those with $\langle h \rangle \simeq v$ and $\theta \lesssim 10^{-10}$.$ $Example potentials $V(\phi_\pm)$ that select the weak scale. If $\langle h \rangle \gtrsim v$ the local minimum of $V(\phi_-)$ is destabilized (left panel), so that the field rolls down towards its deep global minimum (not shown in the plot) and the Universe rapidly crunches. Conversely, the local minimum of $V(\phi_+)$ is generated only if $\langle h \rangle \gtrsim v$ and $\theta \lesssim \theta_{\rm max}$.$ $Parameter space for which $\phi_+$ constitutes the totality of DM of the Universe, as function of the $\phi_+$ mass and the $\theta$-angle today. Bounds~\cite{Abel:2020gbr} and future prospects~\cite{Abel:2018yeo,SNSnEDM,Filippone:2018vxf} from hadronic EDM searches are shown. New ideas involving molecular compounds could further improve the red dashed line~\cite{Hutzler:2020lmj, PhysRevA.100.032514, doi:10.1063/1.5098540, PhysRevC.94.025501, Yu:2020wtz}. We also plot constraints on fuzzy DM from Lyman-$\alpha$ forest~\cite{Leong:2018opi, Irsic:2017yje, Kobayashi:2017jcf, Armengaud:2017nkf, Bozek:2014uqa, Zhang:2017chj}, measurements of the subhalo mass function~\cite{Schutz:2020jox} and the Eridanus II dwarf galaxy~\cite{Marsh:2018zyw}. Tensions in the fit to other dwarf galaxies point to a similar constraint as Eridanus~\cite{Safarzadeh:2019sre, Bar:2018acw}. We shade the area where multiple observations disfavor the corresponding DM mass hypotheses~\cite{Hui:2016ltb}. The dashed lines correspond to the potential sensitivity from future observations in 21 cm cosmology (HERA)~\cite{Munoz:2019hjh} and by the Vera Rubin Observatory~\cite{Drlica-Wagner:2019xan}.$ Show more plots

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