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.
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References
S. Dimopoulos and H. Georgi, Softly Broken Supersymmetry and SU(5), Nucl. Phys. B 193 (1981) 150 [INSPIRE].
S. Dimopoulos, S. Raby and F. Wilczek, Supersymmetry and the Scale of Unification, Phys. Rev. D 24 (1981) 1681 [INSPIRE].
J. Bagger and J. Wess, Supersymmetry and supergravity, Princeton University Press, U.S.A. (1983).
S. P. Martin, A supersymmetry primer, Adv. Ser. Direct. High Energy Phys. 18 (1998) 1 [hep-ph/9709356] [INSPIRE].
S. Weinberg, The quantum theory of fields, Vol. 3, Supersymmetry, Cambridge University Press (2013).
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59 (1980) 135 [INSPIRE].
S. Dimopoulos and L. Susskind, Mass Without Scalars, Nucl. Phys. B 155 (1979) 237 [INSPIRE].
H. Terazawa, K. Akama and Y. Chikashige, Unified Model of the Nambu-Jona-Lasinio Type for All Elementary Particle Forces, Phys. Rev. D 15 (1977) 480 [INSPIRE].
D. B. Kaplan and H. Georgi, SU(2) × U(1) Breaking by Vacuum Misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].
D. B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs Scalars, Phys. Lett. B 136 (1984) 187 [INSPIRE].
M. J. Dugan, H. Georgi and D. B. Kaplan, Anatomy of a Composite Higgs Model, Nucl. Phys. B 254 (1985) 299 [INSPIRE].
Z. Chacko, H.-S. Goh and R. Harnik, The Twin Higgs: Natural electroweak breaking from mirror symmetry, Phys. Rev. Lett. 96 (2006) 231802 [hep-ph/0506256] [INSPIRE].
G. Burdman, Z. Chacko, H.-S. Goh and R. Harnik, Folded supersymmetry and the LEP paradox, JHEP 02 (2007) 009 [hep-ph/0609152] [INSPIRE].
M. Farina, D. Pappadopulo and A. Strumia, A modified naturalness principle and its experimental tests, JHEP 08 (2013) 022 [arXiv:1303.7244] [INSPIRE].
A. de Gouvêa, D. Hernandez and T. M. P. Tait, Criteria for Natural Hierarchies, Phys. Rev. D 89 (2014) 115005 [arXiv:1402.2658] [INSPIRE].
T. Hambye, A. Strumia and D. Teresi, Super-cool Dark Matter, JHEP 08 (2018) 188 [arXiv:1805.01473] [INSPIRE].
K. S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
A. Salvio and A. Strumia, Agravity, JHEP 06 (2014) 080 [arXiv:1403.4226] [INSPIRE].
G. F. Giudice, G. Isidori, A. Salvio and A. Strumia, Softened Gravity and the Extension of the Standard Model up to Infinite Energy, JHEP 02 (2015) 137 [arXiv:1412.2769] [INSPIRE].
K. Kannike et al., Dynamically Induced Planck Scale and Inflation, JHEP 05 (2015) 065 [arXiv:1502.01334] [INSPIRE].
A. Salvio and A. Strumia, Agravity up to infinite energy, Eur. Phys. J. C 78 (2018) 124 [arXiv:1705.03896] [INSPIRE].
T. D. Lee and G. C. Wick, Negative Metric and the Unitarity of the S Matrix, Nucl. Phys. B 9 (1969) 209 [INSPIRE].
A. Salvio and A. Strumia, Quantum mechanics of 4-derivative theories, Eur. Phys. J. C 76 (2016) 227 [arXiv:1512.01237] [INSPIRE].
A. Strumia, Interpretation of quantum mechanics with indefinite norm, MDPI Physics 1 (2019) 17 [arXiv:1709.04925].
C. Gross, A. Strumia, D. Teresi and M. Zirilli, Is negative kinetic energy metastable?, Phys. Rev. D 103 (2021) 115025 [arXiv:2007.05541] [INSPIRE].
R. Barbieri and G. F. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].
R. Barbieri and A. Strumia, The ‘LEP paradox’, in 4th Rencontres du Vietnam: Physics at Extreme Energies (Particle Physics and Astrophysics), (2000) [hep-ph/0007265] [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, Viable range of the mass scale of the standard model, Phys. Rev. D 57 (1998) 5480 [hep-ph/9707380] [INSPIRE].
P. W. Graham, D. E. Kaplan and S. Rajendran, Cosmological Relaxation of the Electroweak Scale, Phys. Rev. Lett. 115 (2015) 221801 [arXiv:1504.07551] [INSPIRE].
N. Arkani-Hamed, T. Cohen, R. T. D’Agnolo, A. Hook, H. D. Kim and D. Pinner, Solving the Hierarchy Problem at Reheating with a Large Number of Degrees of Freedom, Phys. Rev. Lett. 117 (2016) 251801 [arXiv:1607.06821] [INSPIRE].
G. F. Giudice, A. Kehagias and A. Riotto, The Selfish Higgs, JHEP 10 (2019) 199 [arXiv:1907.05370] [INSPIRE].
A. Strumia and D. Teresi, Relaxing the Higgs mass and its vacuum energy by living at the top of the potential, Phys. Rev. D 101 (2020) 115002 [arXiv:2002.02463] [INSPIRE].
C. Csáki, R. T. D’Agnolo, M. Geller and A. Ismail, Crunching Dilaton, Hidden Naturalness, Phys. Rev. Lett. 126 (2021) 091801 [arXiv:2007.14396] [INSPIRE].
R. Tito D’Agnolo and D. Teresi, Sliding Naturalness, arXiv:2106.04591 [INSPIRE].
I. M. Bloch, C. Csáki, M. Geller and T. Volansky, Crunching away the cosmological constant problem: dynamical selection of a small Λ, JHEP 12 (2020) 191 [arXiv:1912.08840] [INSPIRE].
G. Dvali and A. Vilenkin, Cosmic attractors and gauge hierarchy, Phys. Rev. D 70 (2004) 063501 [hep-th/0304043] [INSPIRE].
G. Dvali, Large hierarchies from attractor vacua, Phys. Rev. D 74 (2006) 025018 [hep-th/0410286] [INSPIRE].
A. Arvanitaki, S. Dimopoulos, V. Gorbenko, J. Huang and K. Van Tilburg, A small weak scale from a small cosmological constant, JHEP 05 (2017) 071 [arXiv:1609.06320] [INSPIRE].
M. Geller, Y. Hochberg and E. Kuflik, Inflating to the Weak Scale, Phys. Rev. Lett. 122 (2019) 191802 [arXiv:1809.07338] [INSPIRE].
C. Cheung and P. Saraswat, Mass Hierarchy and Vacuum Energy, arXiv:1811.12390 [INSPIRE].
N. Arkani-Hamed, R. T. D’Agnolo and H. D. Kim, Weak scale as a trigger, Phys. Rev. D 104 (2021) 095014 [arXiv:2012.04652] [INSPIRE].
G. F. Giudice, M. McCullough and T. You, Self-organised localisation, JHEP 10 (2021) 093 [arXiv:2105.08617] [INSPIRE].
R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].
B. Freivogel, Making predictions in the multiverse, Class. Quant. Grav. 28 (2011) 204007 [arXiv:1105.0244] [INSPIRE].
S. Winitzki, Eternal inflation, World Scientific (2008), [DOI] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive landscapes and new physics at a TeV, hep-th/0501082 [INSPIRE].
P. Ghorbani, A. Strumia and D. Teresi, A landscape for the cosmological constant and the Higgs mass, JHEP 01 (2020) 054 [arXiv:1911.01441] [INSPIRE].
L. J. Hall, D. Pinner and J. T. Ruderman, The Weak Scale from BBN, JHEP 12 (2014) 134 [arXiv:1409.0551] [INSPIRE].
G. D’Amico, A. Strumia, A. Urbano and W. Xue, Direct anthropic bound on the weak scale from supernovæ explosions, Phys. Rev. D 100 (2019) 083013 [arXiv:1906.00986] [INSPIRE].
N. Arkani-Hamed and S. Dimopoulos, Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC, JHEP 06 (2005) 073 [hep-th/0405159] [INSPIRE].
H. Georgi, Generalized dimensional analysis, Phys. Lett. B 298 (1993) 187 [hep-ph/9207278] [INSPIRE].
M. Shifman and A. Vainshtein, (In)dependence of Θ in the Higgs regime without axions, Mod. Phys. Lett. A 32 (2017) 1750084 [arXiv:1701.00467] [INSPIRE].
G. R. Dvali and A. Vilenkin, Field theory models for variable cosmological constant, Phys. Rev. D 64 (2001) 063509 [hep-th/0102142] [INSPIRE].
J. R. Espinosa, C. Grojean, G. Panico, A. Pomarol, O. Pujolàs and G. Servant, Cosmological Higgs-Axion Interplay for a Naturally Small Electroweak Scale, Phys. Rev. Lett. 115 (2015) 251803 [arXiv:1506.09217] [INSPIRE].
H. Beauchesne, E. Bertuzzo and G. Grilli di Cortona, Constraints on the relaxion mechanism with strongly interacting vector-fermions, JHEP 08 (2017) 093 [arXiv:1705.06325] [INSPIRE].
S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys. 61 (1989) 1 [INSPIRE].
L. Hui, J. P. Ostriker, S. Tremaine and E. Witten, Ultralight scalars as cosmological dark matter, Phys. Rev. D 95 (2017) 043541 [arXiv:1610.08297] [INSPIRE].
G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel and H. E. Swanson, Short range tests of the equivalence principle, Phys. Rev. D 61 (2000) 022001 [INSPIRE].
S. Schlamminger, K. Y. Choi, T. A. Wagner, J. H. Gundlach and E. G. Adelberger, Test of the equivalence principle using a rotating torsion balance, Phys. Rev. Lett. 100 (2008) 041101 [arXiv:0712.0607] [INSPIRE].
J. Bergé, P. Brax, G. Métris, M. Pernot-Borràs, P. Touboul and J.-P. Uzan, MICROSCOPE Mission: First Constraints on the Violation of the Weak Equivalence Principle by a Light Scalar Dilaton, Phys. Rev. Lett. 120 (2018) 141101 [arXiv:1712.00483] [INSPIRE].
R. Spero, J. K. Hoskins, R. Newman, J. Pellam and J. Schultz, Test of the Gravitational Inverse-Square Law at Laboratory Distances, Phys. Rev. Lett. 44 (1980) 1645 [INSPIRE].
J. K. Hoskins, R. D. Newman, R. Spero and J. Schultz, Experimental tests of the gravitational inverse square law for mass separations from 2-cm to 105-cm, Phys. Rev. D 32 (1985) 3084 [INSPIRE].
J. Chiaverini, S. J. Smullin, A. A. Geraci, D. M. Weld and A. Kapitulnik, New experimental constraints on nonNewtonian forces below 100 microns, Phys. Rev. Lett. 90 (2003) 151101 [hep-ph/0209325] [INSPIRE].
C. D. Hoyle et al., Sub-millimeter tests of the gravitational inverse-square law, Phys. Rev. D 70 (2004) 042004 [hep-ph/0405262] [INSPIRE].
S. J. Smullin, A. A. Geraci, D. M. Weld, J. Chiaverini, S. P. Holmes and A. Kapitulnik, New constraints on Yukawa-type deviations from Newtonian gravity at 20 microns, Phys. Rev. D 72 (2005) 122001 [Erratum ibid. 72 (2005) 129901] [hep-ph/0508204] [INSPIRE].
D. J. Kapner et al., Tests of the gravitational inverse-square law below the dark-energy length scale, Phys. Rev. Lett. 98 (2007) 021101 [hep-ph/0611184] [INSPIRE].
M. Bordag, U. Mohideen and V. M. Mostepanenko, New developments in the Casimir effect, Phys. Rept. 353 (2001) 1 [quant-ph/0106045] [INSPIRE].
M. Bordag, G. L. Klimchitskaya, U. Mohideen and V. M. Mostepanenko, Advances in the Casimir effect, Int. Ser. Monogr. Phys. 145 (2009) 1.
S. G. Turyshev and J. G. Williams, Space-based tests of gravity with laser ranging, Int. J. Mod. Phys. D 16 (2007) 2165 [gr-qc/0611095] [INSPIRE].
E. Hardy and R. Lasenby, Stellar cooling bounds on new light particles: plasma mixing effects, JHEP 02 (2017) 033 [arXiv:1611.05852] [INSPIRE].
A. Branca et al., Search for an Ultralight Scalar Dark Matter Candidate with the AURIGA Detector, Phys. Rev. Lett. 118 (2017) 021302 [arXiv:1607.07327] [INSPIRE].
T. Flacke, C. Frugiuele, E. Fuchs, R. S. Gupta and G. Perez, Phenomenology of relaxion-Higgs mixing, JHEP 06 (2017) 050 [arXiv:1610.02025] [INSPIRE].
A. Banerjee, H. Kim, O. Matsedonskyi, G. Perez and M. S. Safronova, Probing the Relaxed Relaxion at the Luminosity and Precision Frontiers, JHEP 07 (2020) 153 [arXiv:2004.02899] [INSPIRE].
P. W. Graham, D. E. Kaplan, J. Mardon, S. Rajendran and W. A. Terrano, Dark Matter Direct Detection with Accelerometers, Phys. Rev. D 93 (2016) 075029 [arXiv:1512.06165] [INSPIRE].
A. Arvanitaki, P. W. Graham, J. M. Hogan, S. Rajendran and K. Van Tilburg, Search for light scalar dark matter with atomic gravitational wave detectors, Phys. Rev. D 97 (2018) 075020 [arXiv:1606.04541] [INSPIRE].
A. Arvanitaki, J. Huang and K. Van Tilburg, Searching for dilaton dark matter with atomic clocks, Phys. Rev. D 91 (2015) 015015 [arXiv:1405.2925] [INSPIRE].
P. Leaci et al., Design of wideband acoustic detectors of gravitational waves equipped with displacement concentrators, Phys. Rev. D 77 (2008) 062001 [INSPIRE].
H. Grote and Y. V. Stadnik, Novel signatures of dark matter in laser-interferometric gravitational-wave detectors, Phys. Rev. Res. 1 (2019) 033187 [arXiv:1906.06193] [INSPIRE].
S. M. Vermeulen et al., Direct limits for scalar field dark matter from a gravitational-wave detector, arXiv:2103.03783 [INSPIRE].
A. Banerjee, H. Kim and G. Perez, Coherent relaxion dark matter, Phys. Rev. D 100 (2019) 115026 [arXiv:1810.01889] [INSPIRE].
A. Strumia and D. Teresi, Cosmological constant: relaxation vs multiverse, Phys. Lett. B 797 (2019) 134901 [arXiv:1904.07876] [INSPIRE].
CMS collaboration, Search for direct pair production of supersymmetric partners to the τ lepton in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J. C 80 (2020) 189 [arXiv:1907.13179] [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].
nEDM collaboration, Measurement of the permanent electric dipole moment of the neutron, Phys. Rev. Lett. 124 (2020) 081803 [arXiv:2001.11966] [INSPIRE].
C. Abel et al., The n2EDM experiment at the Paul Scherrer Institute, EPJ Web Conf. 219 (2019) 02002 [arXiv:1811.02340] [INSPIRE].
nEDM experiment at Spallation Neutron Source. http://www.nedm.caltech.edu/, (last accessed on 05-28-2021).
B. W. Filippone, Worldwide Search for the Neutron EDM, in 13th Conference on the Intersections of Particle and Nuclear Physics, (2018) [arXiv:1810.03718] [INSPIRE].
N. R. Hutzler et al., Searches for new sources of CP-violation using molecules as quantum sensors, arXiv:2010.08709 [INSPIRE].
D. E. Maison, L. V. Skripnikov and V. V. Flambaum, Theoretical study of 173 YbOH to search for the nuclear magnetic quadrupole moment, Phys. Rev. A 100 (2019) 032514 [arXiv:1906.11487] [INSPIRE].
Y. Hao et al., High accuracy theoretical investigations of caf, srf, and baf and implications for laser-cooling, J. Chem. Phys. 151 (2019) 034302.
M. Bishof et al., Improved limit on the 225 Ra electric dipole moment, Phys. Rev. C 94 (2016) 025501 [arXiv:1606.04931] [INSPIRE].
P. Yu and N. R. Hutzler, Probing Fundamental Symmetries of Deformed Nuclei in Symmetric Top Molecules, Phys. Rev. Lett. 126 (2021) 023003 [arXiv:2008.08803] [INSPIRE].
K.-H. Leong, H.-Y. Schive, U.-H. Zhang and T. Chiueh, Testing extreme-axion wave-like dark matter using the BOSS Lyman-alpha forest data, Mon. Not. Roy. Astron. Soc. 484 (2019) 4273 [arXiv:1810.05930] [INSPIRE].
V. Iršič, M. Viel, M. G. Haehnelt, J. S. Bolton and G. D. Becker, First constraints on fuzzy dark matter from Lyman-α forest data and hydrodynamical simulations, Phys. Rev. Lett. 119 (2017) 031302 [arXiv:1703.04683] [INSPIRE].
T. Kobayashi, R. Murgia, A. De Simone, V. Iršič and M. Viel, Lyman-α constraints on ultralight scalar dark matter: Implications for the early and late universe, Phys. Rev. D 96 (2017) 123514 [arXiv:1708.00015] [INSPIRE].
E. Armengaud, N. Palanque-Delabrouille, C. Yèche, D. J. E. Marsh and J. Baur, Constraining the mass of light bosonic dark matter using SDSS Lyman-α forest, Mon. Not. Roy. Astron. Soc. 471 (2017) 4606 [arXiv:1703.09126] [INSPIRE].
B. Bozek, D. J. E. Marsh, J. Silk and R. F. G. Wyse, Galaxy UV-luminosity function and reionization constraints on axion dark matter, Mon. Not. Roy. Astron. Soc. 450 (2015) 209 [arXiv:1409.3544] [INSPIRE].
J. Zhang, J.-L. Kuo, H. Liu, Y.-L.S. Tsai, K. Cheung and M.-C. Chu, The Importance of Quantum Pressure of Fuzzy Dark Matter on Lyman-Alpha Forest, Astrophys. J. 863 (2018) 73 [arXiv:1708.04389] [INSPIRE].
K. Schutz, Subhalo mass function and ultralight bosonic dark matter, Phys. Rev. D 101 (2020) 123026 [arXiv:2001.05503] [INSPIRE].
D. J. E. Marsh and J. C. Niemeyer, Strong Constraints on Fuzzy Dark Matter from Ultrafaint Dwarf Galaxy Eridanus II, Phys. Rev. Lett. 123 (2019) 051103 [arXiv:1810.08543] [INSPIRE].
M. Safarzadeh and D. N. Spergel, Ultra-light Dark Matter is Incompatible with the Milky Way’s Dwarf Satellites, arXiv:1906.11848 [INSPIRE].
N. Bar, D. Blas, K. Blum and S. Sibiryakov, Galactic rotation curves versus ultralight dark matter: Implications of the soliton-host halo relation, Phys. Rev. D 98 (2018) 083027 [arXiv:1805.00122] [INSPIRE].
J. B. Muñoz, C. Dvorkin and F.-Y. Cyr-Racine, Probing the Small-Scale Matter Power Spectrum with Large-Scale 21-cm Data, Phys. Rev. D 101 (2020) 063526 [arXiv:1911.11144] [INSPIRE].
LSST Dark Matter Group collaboration, Probing the Fundamental Nature of Dark Matter with the Large Synoptic Survey Telescope, arXiv:1902.01055 [INSPIRE].
M. Baryakhtar, M. Galanis, R. Lasenby and O. Simon, Black hole superradiance of self-interacting scalar fields, Phys. Rev. D 103 (2021) 095019 [arXiv:2011.11646] [INSPIRE].
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D’Agnolo, R.T., Teresi, D. Sliding naturalness: cosmological selection of the weak scale. J. High Energ. Phys. 2022, 23 (2022). https://doi.org/10.1007/JHEP02(2022)023
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DOI: https://doi.org/10.1007/JHEP02(2022)023