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QCD Axion Dark Matter with a Small Decay Constant UC Berkeley UC Berkeley Previously Published Works Title QCD Axion Dark Matter with a Small Decay Constant. Permalink https://escholarship.org/uc/item/61f6p95k Journal Physical review letters, 120(21) ISSN 0031-9007 Authors Co, Raymond T Hall, Lawrence J Harigaya, Keisuke Publication Date 2018-05-01 DOI 10.1103/physrevlett.120.211602 Peer reviewed eScholarship.org Powered by the California Digital Library University of California PHYSICAL REVIEW LETTERS 120, 211602 (2018) Editors' Suggestion QCD Axion Dark Matter with a Small Decay Constant Raymond T. Co,1,2,3 Lawrence J. Hall,2,3 and Keisuke Harigaya2,3 1Leinweber Center for Theoretical Physics, University of Michigan, Ann Arbor, Michigan 48109, USA 2Department of Physics, University of California, Berkeley, California 94720, USA 3Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA (Received 20 December 2017; published 23 May 2018) The QCD axion is a good dark matter candidate. The observed dark matter abundance can arise from 11 misalignment or defect mechanisms, which generically require an axion decay constant fa ∼ Oð10 Þ GeV (or higher). We introduce a new cosmological origin for axion dark matter, parametric resonance from 8 11 oscillations of the Peccei-Quinn symmetry breaking field, that requires fa ∼ ð10 –10 Þ GeV. The axions may be warm enough to give deviations from cold dark matter in large scale structure. DOI: 10.1103/PhysRevLett.120.211602 Introduction.—The absence of CP violation from QCD is unstable and decays into axions [10], yielding a dark is a long-standing problem in particle physics [1] and is matter density [11,12] elegantly solved by the Peccei-Quinn (PQ) mechanism 1.19 [2,3] involving a spontaneously broken anomalous sym- 2 fa Ω h j − ≃ 0.04–0.3 : ð2Þ metry. The scheme predicts the existence of a light boson a string DW 1011 GeV [4,5], the axion, which is constrained by data to be extremely light and, hence, is stable on cosmological time These mechanisms most naturally lead to axion dark scales, and a dark matter (DM) candidate. 11 12 matter for fa ∼ ð10 –10 Þ GeV, and the misalignment What cosmological production mechanism yields axions θ mechanism could also yield dark matter for larger fa as mis that account for dark matter? Axions produced from the is reduced. However, axions are not expected to be dark thermal bath have too low an abundance to be dark matter, matter for smaller fa. (The special cases for axion dark and are too hot. Two production mechanisms have been matter with lower fa are as follows. References [13–15] considered; both are IR mechanisms with axions produced study the anharmonicity effects of the axion cosine potential near the QCD phase transition. While they depend on the θ π when mis is tuned to approach , requiring a small inflation PQ symmetry breaking scale, fa, they are insensitive to scale to avoid quantum fluctuations. Reference [16] ana- details of the UV axion theory and dynamics of the PQ lyzes axion production in nonstandard cosmological eras phase transition. (i) Initially, the axion is nearly massless with kinetic energy domination even at temperatures below a θ and takes a generic field value misaligned by angle mis GeV. References [11,17–19] consider topological defects from the vacuum value. Around the QCD phase transition, for a domain wall number larger than unity with an explicit the axion obtains a mass, and the energy density in the PQ breaking, where a fine tuning is required to solve the resulting oscillations account for the dark matter abundance strong CP problem). – [6 8] In this Letter, we introduce a mechanism for UV production of dark matter axions from the early evolution f 1.19 Ω h2j ≃ 0.01θ2 a : ð1Þ of the PQ symmetry breaking field S in a relatively flat a mis mis 1011 GeV potential. We assume S has a large initial value, Si ≫ fa, e.g., from a negative Hubble induced mass during inflation (ii) When PQ symmetry is broken after inflation, cosmic [20]. After S begins oscillating, parametric resonance strings are produced [9]. Domain walls form between these [21,22] creates a huge number of axions. Assuming no strings around the QCD phase transition and, if the domain subsequent entropy production, wall (DW) number is unity, the string-domain wall network 2 1 9 10 2 10 Ω 2 ≃ 0 1 Si TeV GeV ð Þ ah . 16 ; 3 10 GeV mS;i fa Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. where m is the initial S mass. Unlike (1) and (2), the abun- Further distribution of this work must maintain attribution to S;i the author(s) and the published article’s title, journal citation, dance grows at low fa and sufficient dark matter can be obtai- 3 8 11 and DOI. Funded by SCOAP . ned for 10 GeV <fa < 10 GeV. Several experimental 0031-9007=18=120(21)=211602(7) 211602-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 120, 211602 (2018) efforts are ongoing for axions with small f , including IAXO p ðTÞ m à a a ≃ 0.5 × S ; ð8Þ [23,24] and TASTE [25] for solar axions, Orpheus [26] and 1=3 ðΓ Þ1=2 s ÃMPl MADMAX [27] for halo axions, and ARIADNE [28,29] for axion mediated CP-violating forces. See Refs. [30–32] for assuming that axions are produced with momenta other proposals. Helioscopes will explore the lower end of ∼m ðSÃÞ ≡ m Ã. Axions are colder for a larger Γà since this range, and it is worth noting that our mechanism allows S S they receive more redshifting after production. Given the values of f even below 108 GeV, which are also consistent a recent constraint on the warmness of dark matter (see, e.g., with the supernova bound [33–37] if there is a mild [38,39]), we require that the axion velocity is smaller than cancellation in the axion-nucleon coupling. 10−3 at a temperature of 1 eV, In our mechanism, axions are initially produced with momenta of the order mS;i. After subsequent redshifting, ð Þ 109 the axion velocity at a temperature of 1 eV is pa T −6 GeV ≲ 6 × 10 ; ð9Þ T T¼1 eV fa 1 j ∼ 10−4 mS;i 2 fa ð Þ va eV × 6 9 : 4 10 GeV 10 GeV placing a lower bound on ΓÃ. Let us assume that saxion to axion conversion occurs Γ ∼ 3 2 For a sufficiently large mS;i, the axion is warm. via a perturbative decay rate of à mSà =Sþ , where — Axion production by oscillating PQ field. The axion Sþ ¼ maxðSÃ;faÞ. The number density and momenta of mass is [4] the axions are given by 9 10 GeV 2 3 ¼ 6 ð Þ n SÃSþ p Sþ ma meV : 5 a ∼ ; a ∼ : ð10Þ fa s 7=2 3=2 s1=3 1=2 1=2 mSà MPl mSà MPl The axion number density na0 that explains the observed ρ ≃ 0 4 dark matter abundance, DM=s . eV, is One can verify that the bound from coldness, (9), and the abundance requirement, (6), are incompatible with each other for any ðSÃ;m Þ, for all f larger than the exper- na0 fa Sà a Y ≡ ≃ 70 ; ð6Þ 8 a0 s 109 GeV imental lower bound of 10 GeV. Parametric resonance.—In fact, the production rate is where s is the entropy density of the Universe. The required typically much larger than the perturbative decay rate. The 8 Ya is much larger than thermal for all fa ≥ 10 GeV, so saxion couples to the axion through the potential of the PQ axions must be produced nonthermally. breaking field, so that the axion mass oscillates. Axion The radial direction of the PQ symmetry breaking field, modes with nonzero momenta, which we call fluctuations, which we call the saxion, S, (following terminology of grow rapidly by parametric resonance [21,22] from initial supersymmetric theories) is taken to have a large initial seeds set by quantum fluctuations. The axion momentum is field value. As the Hubble scale H becomes smaller than typically of the order mS. The energy of the fluctuations the saxion mass, the saxion beginspffiffiffiffiffiffiffiffiffiffiffiffi coherent zero-mode grows exponentially and, at some point, typically soon after 00 oscillations begin, becomes comparable to that of the saxion oscillations. The mass mSðSÞ ≡ V ðSÞ is generally S dependent and differs from the vacuum value. For a wide oscillation. At this stage, the back reaction on the saxion is range of potentials VðSÞ, the saxion yield is conserved with non-negligible and parametric resonance ceases. Because of the initial value efficient scattering between the oscillating saxion field and the axion fluctuations, the entire zero-mode energy of the 2 saxion is converted into comparable saxion and axion nS Si Y ≡ ∼ Y ∼ ; ð7Þ fluctuations, YS ∼ Ya ∼ YS , given in Eq. (7). S s Si 1=2 3=2 i mS;i MPl The evolution of the fluctuations after this stage is model dependent, and a model-by-model lattice simulation is ≃ in a radiation-dominated universe, where MPl needed to rigorously follow the dynamics. In this Letter, 2.41018 GeV. A result for the matter-dominated case can we consider the case where the comoving momentum and be straightforwardly derived. Suppose that this saxion yield number density of the fluctuations are approximately is converted into axions, e.g., by decay. For fa ≪ conserved, so that the axion yield is comparable to that Si <MPl, the dark matter axion yield of Eq.
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