Abstract
The QCD axion serves as a well-motivated dark matter candidate and the misalignment mechanism is known to reproduce the observed abundance with a decay constant fa ≃ \( \mathcal{O} \)(1012) GeV for a misalignment angle θmis ≃ \( \mathcal{O} \)(1). While fa ≪ 1012 GeV is of great experimental interest, the misalignment mechanism requires the axion to be very close to the hilltop, i.e. θmis ≃ π. This particular choice of θmis has been understood as fine-tuning the initial condition. We offer a dynamical explanation for θmis ≃ π in a class of models. The axion dynamically relaxes to the minimum of the potential by virtue of an enhanced mass in the early universe. This minimum is subsequently converted to a hilltop because the CP phase of the theory shifts by π when one contribution becomes subdominant to another with an opposite sign. We demonstrate explicit and viable examples in supersymmetric models where the higher dimensional Higgs coupling with the inflaton naturally achieves both criteria. Associated phenomenology includes a strikingly sharp prediction of 3 × 109 GeV ≲ fa ≲ 1010 GeV and the absence of isocurvature perturbation.
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R.J. Crewther, P. Di Vecchia, G. Veneziano and E. Witten, Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics, Phys. Lett. B 88 (1979) 123 [Erratum ibid. B 91 (1980) 487] [INSPIRE].
C.A. Baker et al., An Improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 97 (2006) 131801 [hep-ex/0602020] [INSPIRE].
G. ’t Hooft, Symmetry Breaking Through Bell-Jackiw Anomalies, Phys. Rev. Lett. 37 (1976) 8 [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
J.R. Ellis and K.A. Olive, Constraints on Light Particles From Supernova SN 1987A, Phys. Lett. B 193 (1987) 525 [INSPIRE].
G. Raffelt and D. Seckel, Bounds on Exotic Particle Interactions from SN1987A, Phys. Rev. Lett. 60 (1988) 1793 [INSPIRE].
M.S. Turner, Axions from SN1987A, Phys. Rev. Lett. 60 (1988) 1797 [INSPIRE].
R. Mayle, J.R. Wilson, J.R. Ellis, K.A. Olive, D.N. Schramm and G. Steigman, Constraints on Axions from SN 1987A, Phys. Lett. B 203 (1988) 188 [INSPIRE].
G.G. Raffelt, Astrophysical axion bounds, in proceedings of the Joint ILIAS-CAST-CERN Axion Training at CERN, Geneva, Switzerland, 30 November–2 December 2005, Lect. Notes Phys. 741 (2008) 51 [hep-ph/0611350] [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the Invisible Axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
R.L. Davis, Cosmic Axions from Cosmic Strings, Phys. Lett. B 180 (1986) 225 [INSPIRE].
M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion dark matter from topological defects, Phys. Rev. D 91 (2015) 065014 [arXiv:1412.0789] [INSPIRE].
V.B. Klaer and G.D. Moore, The dark-matter axion mass, JCAP 11 (2017) 049 [arXiv:1708.07521] [INSPIRE].
M. Gorghetto, E. Hardy and G. Villadoro, Axions from Strings: the Attractive Solution, JHEP 07 (2018) 151 [arXiv:1806.04677] [INSPIRE].
M. Kawasaki, T. Sekiguchi, M. Yamaguchi and J. Yokoyama, Long-term dynamics of cosmological axion strings, Prog. Theor. Exp. Phys. 2018 (2018) 091E01 [arXiv:1806.05566] [INSPIRE].
C.J.A.P. Martins, Scaling properties of cosmological axion strings, Phys. Lett. B 788 (2019) 147 [arXiv:1811.12678] [INSPIRE].
J.K. Vogel et al., IAXO — The International Axion Observatory, in proceedings of the 8th Patras Workshop on Axions, WIMPs and WISPs (AXION-WIMP 2012), Chicago, Illinois, U.S.A., 18–22 July 2012, FERMILAB-PUB-13-699-A (2013) [arXiv:1302.3273] [INSPIRE] and online pdf version at http://lss.fnal.gov/archive/2013/pub/fermilab-pub-13-699-a.pdf.
E. Armengaud et al., Conceptual Design of the International Axion Observatory (IAXO), 2014 JINST 9 T05002 [arXiv:1401.3233] [INSPIRE].
TASTE collaboration, Towards a medium-scale axion helioscope and haloscope, 2017 JINST 12 P11019 [arXiv:1706.09378] [INSPIRE].
G. Rybka, A. Wagner, A. Brill, K. Ramos, R. Percival and K. Patel, Search for dark matter axions with the Orpheus experiment, Phys. Rev. D 91 (2015) 011701 [arXiv:1403.3121] [INSPIRE].
MADMAX Working Group, Dielectric Haloscopes: A New Way to Detect Axion Dark Matter, Phys. Rev. Lett. 118 (2017) 091801 [arXiv:1611.05865] [INSPIRE].
A. Arvanitaki and A.A. Geraci, Resonantly Detecting Axion-Mediated Forces with Nuclear Magnetic Resonance, Phys. Rev. Lett. 113 (2014) 161801 [arXiv:1403.1290] [INSPIRE].
ARIADNE collaboration, Progress on the ARIADNE axion experiment, in proceedings of the 2nd Workshop on Microwave Cavities and Detectors for Axion Research, Livermore, California, U.S.A., 10–13 January 2017, Springer Proc. Phys. 211 (2018) 151 [arXiv:1710.05413] [INSPIRE].
P. Sikivie, Axion Dark Matter Detection using Atomic Transitions, Phys. Rev. Lett. 113 (2014) 201301 [arXiv:1409.2806] [INSPIRE].
A. Arvanitaki, S. Dimopoulos and K. Van Tilburg, Resonant absorption of bosonic dark matter in molecules, Phys. Rev. X 8 (2018) 041001 [arXiv:1709.05354] [INSPIRE].
M. Baryakhtar, J. Huang and R. Lasenby, Axion and hidden photon dark matter detection with multilayer optical haloscopes, Phys. Rev. D 98 (2018) 035006 [arXiv:1803.11455] [INSPIRE].
ADMX collaboration, A Search for Invisible Axion Dark Matter with the Axion Dark Matter Experiment, Phys. Rev. Lett. 120 (2018) 151301 [arXiv:1804.05750] [INSPIRE].
R.T. Co, L.J. Hall and K. Harigaya, QCD Axion Dark Matter with a Small Decay Constant, Phys. Rev. Lett. 120 (2018) 211602 [arXiv:1711.10486] [INSPIRE].
T. Hiramatsu, M. Kawasaki and K. Saikawa, Evolution of String-Wall Networks and Axionic Domain Wall Problem, JCAP 08 (2011) 030 [arXiv:1012.4558] [INSPIRE].
T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion cosmology with long-lived domain walls, JCAP 01 (2013) 001 [arXiv:1207.3166] [INSPIRE].
K. Harigaya and M. Kawasaki, QCD axion dark matter from long-lived domain walls during matter domination, Phys. Lett. B 782 (2018) 1 [arXiv:1802.00579] [INSPIRE].
M.S. Turner, Cosmic and Local Mass Density of Invisible Axions, Phys. Rev. D 33 (1986) 889 [INSPIRE].
D.H. Lyth, Axions and inflation: Sitting in the vacuum, Phys. Rev. D 45 (1992) 3394 [INSPIRE].
K. Strobl and T.J. Weiler, Anharmonic evolution of the cosmic axion density spectrum, Phys. Rev. D 50 (1994) 7690 [astro-ph/9405028] [INSPIRE].
K.J. Bae, J.-H. Huh and J.E. Kim, Update of axion CDM energy, JCAP 09 (2008) 005 [arXiv:0806.0497] [INSPIRE].
L. Visinelli and P. Gondolo, Dark Matter Axions Revisited, Phys. Rev. D 80 (2009) 035024 [arXiv:0903.4377] [INSPIRE].
G.R. Dvali, Removing the cosmological bound on the axion scale, hep-ph/9505253 [INSPIRE].
T. Banks and M. Dine, The Cosmology of string theoretic axions, Nucl. Phys. B 505 (1997) 445 [hep-th/9608197] [INSPIRE].
K. Choi, H.B. Kim and J.E. Kim, Axion cosmology with a stronger QCD in the early universe, Nucl. Phys. B 490 (1997) 349 [hep-ph/9606372] [INSPIRE].
K.S. Jeong and F. Takahashi, Suppressing Isocurvature Perturbations of QCD Axion Dark Matter, Phys. Lett. B 727 (2013) 448 [arXiv:1304.8131] [INSPIRE].
K. Choi, E.J. Chun, S.H. Im and K.S. Jeong, Diluting the inflationary axion fluctuation by a stronger QCD in the early Universe, Phys. Lett. B 750 (2015) 26 [arXiv:1505.00306] [INSPIRE].
R.T. Co, E. Gonzalez and K. Harigaya, Axion Misalignment Driven to the Bottom, JHEP 05 (2019) 162 [arXiv:1812.11186] [INSPIRE].
J.R. Ellis and M.K. Gaillard, Strong and Weak CP-violation, Nucl. Phys. B 150 (1979) 141 [INSPIRE].
I.B. Khriplovich and A.R. Zhitnitsky, What Is the Value of the Neutron Electric Dipole Moment in the Kobayashi-Maskawa Model?, Phys. Lett. B 109 (1982) 490 [INSPIRE].
A.E. Nelson, Naturally Weak CP-violation, Phys. Lett. B 136 (1984) 387 [INSPIRE].
S.M. Barr, Solving the Strong CP Problem Without the Peccei-Quinn Symmetry, Phys. Rev. Lett. 53 (1984) 329 [INSPIRE].
L. Bento, G.C. Branco and P.A. Parada, A Minimal model with natural suppression of strong CP-violation, Phys. Lett. B 267 (1991) 95 [INSPIRE].
G. Hiller and M. Schmaltz, Solving the Strong CP Problem with Supersymmetry, Phys. Lett. B 514 (2001) 263 [hep-ph/0105254] [INSPIRE].
S. Dimopoulos and L.J. Hall, Inflation and Invisible Axions, Phys. Rev. Lett. 60 (1988) 1899 [INSPIRE].
P.W. Graham and A. Scherlis, Stochastic axion scenario, Phys. Rev. D 98 (2018) 035017 [arXiv:1805.07362] [INSPIRE].
F. Takahashi, W. Yin and A.H. Guth, QCD axion window and low-scale inflation, Phys. Rev. D 98 (2018) 015042 [arXiv:1805.08763] [INSPIRE].
O. Wantz and E.P.S. Shellard, Axion Cosmology Revisited, Phys. Rev. D 82 (2010) 123508 [arXiv:0910.1066] [INSPIRE].
P. Petreczky, H.-P. Schadler and S. Sharma, The topological susceptibility in finite temperature QCD and axion cosmology, Phys. Lett. B 762 (2016) 498 [arXiv:1606.03145] [INSPIRE].
S. Borsányi et al., Calculation of the axion mass based on high-temperature lattice quantum chromodynamics, Nature 539 (2016) 69 [arXiv:1606.07494] [INSPIRE].
F. Burger, E.-M. Ilgenfritz, M.P. Lombardo and A. Trunin, Chiral observables and topology in hot QCD with two families of quarks, Phys. Rev. D 98 (2018) 094501 [arXiv:1805.06001] [INSPIRE].
C. Bonati, M. D’Elia, G. Martinelli, F. Negro, F. Sanfilippo and A. Todaro, Topology in full QCD at high temperature: a multicanonical approach, JHEP 11 (2018) 170 [arXiv:1807.07954] [INSPIRE].
M. Gorghetto and G. Villadoro, Topological Susceptibility and QCD Axion Mass: QED and NNLO corrections, JHEP 03 (2019) 033 [arXiv:1812.01008] [INSPIRE].
S. Ipek and T.M.P. Tait, Early Cosmological Period of QCD Confinement, Phys. Rev. Lett. 122 (2019) 112001 [arXiv:1811.00559] [INSPIRE].
T. Higaki, K.S. Jeong and F. Takahashi, Solving the Tension between High-Scale Inflation and Axion Isocurvature Perturbations, Phys. Lett. B 734 (2014) 21 [arXiv:1403.4186] [INSPIRE].
M. Kawasaki, M. Yamada and T.T. Yanagida, Cosmologically safe QCD axion as a present from extra dimension, Phys. Lett. B 750 (2015) 12 [arXiv:1506.05214] [INSPIRE].
F. Takahashi and M. Yamada, Strongly broken Peccei-Quinn symmetry in the early Universe, JCAP 10 (2015) 010 [arXiv:1507.06387] [INSPIRE].
J. Kearney, N. Orlofsky and A. Pierce, High-Scale Axions without Isocurvature from Inflationary Dynamics, Phys. Rev. D 93 (2016) 095026 [arXiv:1601.03049] [INSPIRE].
M. Kawasaki, F. Takahashi and M. Yamada, Suppressing the QCD Axion Abundance by Hidden Monopoles, Phys. Lett. B 753 (2016) 677 [arXiv:1511.05030] [INSPIRE].
Y. Nomura, S. Rajendran and F. Sanches, Axion Isocurvature and Magnetic Monopoles, Phys. Rev. Lett. 116 (2016) 141803 [arXiv:1511.06347] [INSPIRE].
ACME collaboration, Improved limit on the electric dipole moment of the electron, Nature 562 (2018) 355 [INSPIRE].
C. Cesarotti, Q. Lu, Y. Nakai, A. Parikh and M. Reece, Interpreting the Electron EDM Constraint, arXiv:1810.07736 [INSPIRE].
J.E. Kim, Weak Interaction Singlet and Strong CP Invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can Confinement Ensure Natural CP Invariance of Strong Interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].
A. Manohar and H. Georgi, Chiral Quarks and the Nonrelativistic Quark Model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].
H. Georgi and L. Randall, Flavor Conserving CP-violation in Invisible Axion Models, Nucl. Phys. B 276 (1986) 241 [INSPIRE].
M.A. Luty, Naive dimensional analysis and supersymmetry, Phys. Rev. D 57 (1998) 1531 [hep-ph/9706235] [INSPIRE].
A.G. Cohen, D.B. Kaplan and A.E. Nelson, Counting 4π’s in strongly coupled supersymmetry, Phys. Lett. B 412 (1997) 301 [hep-ph/9706275] [INSPIRE].
D. Bödeker, Moduli decay in the hot early Universe, JCAP 06 (2006) 027 [hep-ph/0605030] [INSPIRE].
K. Mukaida and K. Nakayama, Dynamics of oscillating scalar field in thermal environment, JCAP 01 (2013) 017 [arXiv:1208.3399] [INSPIRE].
K. Harigaya, M. Ibe, K. Schmitz and T.T. Yanagida, Peccei-Quinn Symmetry from Dynamical Supersymmetry Breaking, Phys. Rev. D 92 (2015) 075003 [arXiv:1505.07388] [INSPIRE].
K. Harigaya and J. Leedom, Unified Models of the QCD Axion and Supersymmetry Breaking, Nucl. Phys. B 921 (2017) 507 [arXiv:1702.00401] [INSPIRE].
K. Harigaya and K. Mukaida, Thermalization after/during Reheating, JHEP 05 (2014) 006 [arXiv:1312.3097] [INSPIRE].
I. Affleck, M. Dine and N. Seiberg, Dynamical Supersymmetry Breaking in Supersymmetric QCD, Nucl. Phys. B 241 (1984) 493 [INSPIRE].
E.W. Kolb and I.I. Tkachev, Nonlinear axion dynamics and formation of cosmological pseudosolitons, Phys. Rev. D 49 (1994) 5040 [astro-ph/9311037] [INSPIRE].
E.W. Kolb and I.I. Tkachev, Axion miniclusters and Bose stars, Phys. Rev. Lett. 71 (1993) 3051 [hep-ph/9303313] [INSPIRE].
P.B. Greene, L. Kofman and A.A. Starobinsky, Sine-Gordon parametric resonance, Nucl. Phys. B 543 (1999) 423 [hep-ph/9808477] [INSPIRE].
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Co, R.T., Gonzalez, E. & Harigaya, K. Axion misalignment driven to the hilltop. J. High Energ. Phys. 2019, 163 (2019). https://doi.org/10.1007/JHEP05(2019)163
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DOI: https://doi.org/10.1007/JHEP05(2019)163