Abstract
We propose a framework in which Weinberg’s anthropic explanation of the cosmological constant problem also solves the hierarchy problem. The weak scale is selected by chiral dynamics that controls the stabilization of an extra dimension. When the Higgs vacuum expectation value is close to a fermion mass scale, the radius of an extra dimension becomes large, and develops an enhanced number of vacua available to scan the cosmological constant down to its observed value. At low energies, the radion necessarily appears as an unnaturally light scalar, in a range of masses and couplings accessible to fifth-force searches as well as scalar dark matter searches with atomic clocks and gravitational-wave detectors. The fermion sector that controls the size of the extra dimension consists of a pair of electroweak doublets and several singlets. These leptons satisfy approximate mass relations related to the weak scale and are accessible to the LHC and future colliders.
Article PDF
Similar content being viewed by others
Explore related subjects
Find the latest articles, discoveries, and news in related topics.Avoid common mistakes on your manuscript.
References
V. Agrawal, S.M. Barr, J.F. Donoghue and D. Seckel, The anthropic principle and the mass scale of the standard model, Phys. Rev. D 57 (1998) 5480 [hep-ph/9707380] [INSPIRE].
S. Weinberg, Anthropic Bound on the Cosmological Constant, Phys. Rev. Lett. 59 (1987) 2607 [INSPIRE].
S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys. 61 (1989) 1 [INSPIRE].
C. Csáki, C. Grojean, J. Hubisz, Y. Shirman and J. Terning, Fermions on an interval: Quark and lepton masses without a Higgs, Phys. Rev. D 70 (2004) 015012 [hep-ph/0310355] [INSPIRE].
A. Romeo and A.A. Saharian, Casimir effect for scalar fields under Robin boundary conditions on plates, J. Phys. A 35 (2002) 1297 [hep-th/0007242] [INSPIRE].
N. Birrell and P. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics. Cambridge University Press, (1984).
R. Hofmann, P. Kanti and M. Pospelov, (De)stabilization of an extra dimension due to a Casimir force, Phys. Rev. D 63 (2001) 124020 [hep-ph/0012213] [INSPIRE].
P. Kanti, K.A. Olive and M. Pospelov, On the stabilization of the size of extra dimensions, Phys. Lett. B 538 (2002) 146 [hep-ph/0204202] [INSPIRE].
J. Garriga, O. Pujolàs and T. Tanaka, Radion effective potential in the brane world, Nucl. Phys. B 605 (2001) 192 [hep-th/0004109] [INSPIRE].
L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
T. Appelquist and A. Chodos, The Quantum Dynamics of Kaluza-Klein Theories, Phys. Rev. D 28 (1983) 772 [INSPIRE].
E. Ponton and E. Poppitz, Casimir energy and radius stabilization in five-dimensional orbifolds and six-dimensional orbifolds, JHEP 06 (2001) 019 [hep-ph/0105021] [INSPIRE].
G. von Gersdorff and A. Hebecker, Radius stabilization by two-loop Casimir energy, Nucl. Phys. B 720 (2005) 211 [hep-th/0504002] [INSPIRE].
N. Kaloper, Bent domain walls as brane worlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210] [INSPIRE].
L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557 (1999) 79 [hep-th/9810155] [INSPIRE].
P. Meszaros, The behaviour of point masses in an expanding cosmological substratum, Astron. Astrophys. 37 (1974) 225 [INSPIRE].
S. Weinberg, Cosmological fluctuations of short wavelength, Astrophys. J. 581 (2002) 810 [astro-ph/0207375] [INSPIRE].
N. Craig, A. Katz, M. Strassler and R. Sundrum, Naturalness in the Dark at the LHC, JHEP 07 (2015) 105 [arXiv:1501.05310] [INSPIRE].
A. Hook, Anomalous solutions to the strong CP problem, Phys. Rev. Lett. 114 (2015) 141801 [arXiv:1411.3325] [INSPIRE].
W. Beenakker, M. Klasen, M. Krämer, T. Plehn, M. Spira and P.M. Zerwas, The production of charginos/neutralinos and sleptons at hadron colliders, Phys. Rev. Lett. 83 (1999) 3780 [Erratum ibid. 100 (2008) 029901] [hep-ph/9906298] [INSPIRE].
M. Krämer et al., Supersymmetry production cross sections in pp collisions at \( \sqrt{s}=7 \) TeV, arXiv:1206.2892 [INSPIRE].
ATLAS collaboration, Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in \( \sqrt{s}=8 \) TeV pp collisions with the ATLAS detector, JHEP 04 (2014) 169 [arXiv:1402.7029] [INSPIRE].
CMS collaboration, Searches for electroweak production of charginos, neutralinos and sleptons decaying to leptons and W, Z and Higgs bosons in pp collisions at 8 TeV, Eur. Phys. J. C 74 (2014) 3036 [arXiv:1405.7570] [INSPIRE].
CMS collaboration, Search for gluino mediated bottom- and top-squark production in multijet final states in pp collisions at 8 TeV, Phys. Lett. B 725 (2013) 243 [arXiv:1305.2390] [INSPIRE].
CMS collaboration, Search for supersymmetry in hadronic final states with missing transverse energy using the variables α T and b-quark multiplicity in pp collisions at \( \sqrt{s}=8 \) TeV, Eur. Phys. J. C 73 (2013) 2568 [arXiv:1303.2985] [INSPIRE].
ATLAS collaboration, Search for direct production of charginos, neutralinos and sleptons in final states with two leptons and missing transverse momentum in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, JHEP 05 (2014) 071 [arXiv:1403.5294] [INSPIRE].
CMS collaboration, Searches for electroweak neutralino and chargino production in channels with Higgs, Z and W bosons in pp collisions at 8 TeV, Phys. Rev. D 90 (2014) 092007 [arXiv:1409.3168] [INSPIRE].
CMS collaboration, Search for electroweak SUSY production in multilepton final states in pp collisions at \( \sqrt{s}=13 \) TeV with 12.9/fb, CMS-PAS-SUS-16-024 (2016).
T. Han, S. Padhi and S. Su, Electroweakinos in the Light of the Higgs Boson, Phys. Rev. D 88 (2013) 115010 [arXiv:1309.5966] [INSPIRE].
M. Berggren, T. Han, J. List, S. Padhi, S. Su and T. Tanabe, Electroweakino Searches: A Comparative Study for LHC and ILC (A Snowmass White Paper), in proceedings of Community Summer Study 2013: Snowmass on the Mississippi (CSS2013) Minneapolis, MN, U.S.A., July 29 - August 6, 2013, 2013. arXiv:1309.7342 [INSPIRE].
S. Gori, S. Jung, L.-T. Wang and J.D. Wells, Prospects for Electroweakino Discovery at a 100 TeV Hadron Collider, JHEP 12 (2014) 108 [arXiv:1410.6287] [INSPIRE].
CMS collaboration, Projected Performance of an Upgraded CMS Detector at the LHC and HL-LHC: Contribution to the Snowmass Process, in the proceedings of Community Summer Study 2013: Snowmass on the Mississippi (CSS2013) Minneapolis, MN, U.S.A., July 29 - August 6, 2013, arXiv:1307.7135 [INSPIRE].
ATLAS collaboration, Physics at a High-Luminosity LHC with ATLAS, in the proceedings of Community Summer Study 2013: Snowmass on the Mississippi (CSS2013) Minneapolis, MN, U.S.A., July 29 - August 6, 2013, arXiv:1307.7292 [INSPIRE].
A. Arvanitaki, N. Craig, S. Dimopoulos and G. Villadoro, Mini-Split, JHEP 02 (2013) 126 [arXiv:1210.0555] [INSPIRE].
CEPC-SPPC Study Group collaboration, CEPC-SPPC Preliminary Conceptual Design Report. 1. Physics and Detector, http://cepc.ihep.ac.cn/preCDR/main preCDR.pdf.
H. Baer et al., The International Linear Collider Technical Design Report - Volume 2: Physics, arXiv:1306.6352 [INSPIRE].
ATLAS collaboration, Constraints on new phenomena via Higgs boson couplings and invisible decays with the ATLAS detector, JHEP 11 (2015) 206 [arXiv:1509.00672] [INSPIRE].
CMS collaboration, A combination of searches for the invisible decays of the Higgs boson using the CMS detector, CMS-PAS-HIG-15-012 (2015).
CMS collaboration, Searches for invisible Higgs boson decays with the CMS detector., CMS-PAS-HIG-16-016 (2016).
CMS collaboration, Search for dark matter in final states with an energetic jet, or a hadronically decaying W or Z boson using 12.9 fb −1 of data at \( \sqrt{s}=13 \) TeV, CMS-PAS-EXO-16-037 (2016).
CMS collaboration, Search for dark matter in Z + E missT events using 12.9 fb−1 of 2016 data, CMS-PAS-EXO-16-038 (2016).
ATLAS collaboration, Search for new phenomena in the Z(→ ℓℓ) + E missT final state at \( \sqrt{s}=13 \) TeV with the ATLAS detector, ATLAS-CONF-2016-056 (2016).
ATLAS collaboration, ATLAS Higgs physics prospects at the high luminosity LHC, PoS(EPS-HEP2015)160.
S.P. Martin, Extra vector-like matter and the lightest Higgs scalar boson mass in low-energy supersymmetry, Phys. Rev. D 81 (2010) 035004 [arXiv:0910.2732] [INSPIRE].
M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992) 381 [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
CMS collaboration, Search for new physics in the compressed mass spectra scenario using events with two soft opposite-sign leptons and missing transverse momentum at \( \sqrt{s}=13 \) TeV, CMS-PAS-SUS-16-025 (2016).
N. Arkani-Hamed, K. Blum, R.T. D’Agnolo and J. Fan, 2:1 for Naturalness at the LHC?, JHEP 01 (2013) 149 [arXiv:1207.4482] [INSPIRE].
J. Kearney, A. Pierce and N. Weiner, Vectorlike Fermions and Higgs Couplings, Phys. Rev. D 86 (2012) 113005 [arXiv:1207.7062] [INSPIRE].
M. Carena, I. Low and C.E.M. Wagner, Implications of a Modified Higgs to Diphoton Decay Width, JHEP 08 (2012) 060 [arXiv:1206.1082] [INSPIRE].
ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s}=7 \) and 8 TeV, JHEP 08 (2016) 045 [arXiv:1606.02266] [INSPIRE].
J. Fan, M. Reece and L.-T. Wang, Possible Futures of Electroweak Precision: ILC, FCC-ee and CEPC, JHEP 09 (2015) 196 [arXiv:1411.1054] [INSPIRE].
J. Garriga and T. Tanaka, Gravity in the brane world, Phys. Rev. Lett. 84 (2000) 2778 [hep-th/9911055] [INSPIRE].
C. Csáki, M. Graesser, L. Randall and J. Terning, Cosmology of brane models with radion stabilization, Phys. Rev. D 62 (2000) 045015 [hep-ph/9911406] [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].
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].
A.A. Geraci, S.J. Smullin, D.M. Weld, J. Chiaverini and A. Kapitulnik, Improved constraints on non-Newtonian forces at 10 microns, Phys. Rev. D 78 (2008) 022002 [arXiv:0802.2350] [INSPIRE].
E. Fischbach and C. Talmadge, Ten years of the fifth force, in Dark matter in cosmology, quantum measurements, experimental gravitation. Proceedings, 31st Rencontres de Moriond, 16th Moriond Workshop, Les Arcs, France, January 2-27, 1996, pp. 443-451, (1996) hep-ph/9606249 [INSPIRE].
N. Arkani-Hamed, Y. Grossman and M. Schmaltz, Split fermions in extra dimensions and exponentially small cross-sections at future colliders, Phys. Rev. D 61 (2000) 115004 [hep-ph/9909411] [INSPIRE].
T.A. Wagner, S. Schlamminger, J.H. Gundlach and E.G. Adelberger, Torsion-balance tests of the weak equivalence principle, Class. Quant. Grav. 29 (2012) 184002 [arXiv:1207.2442] [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. Dimopoulos, P.W. Graham, J.M. Hogan and M.A. Kasevich, Testing general relativity with atom interferometry, Phys. Rev. Lett. 98 (2007) 111102 [gr-qc/0610047] [INSPIRE].
B. Bertotti, L. Iess and P. Tortora, A test of general relativity using radio links with the Cassini spacecraft, Nature 425 (2003) 374 [INSPIRE].
D. Blas, D.L. Nacir and S. Sibiryakov, Ultra-Light Dark Matter Resonates with Binary Pulsars, arXiv:1612.06789 [INSPIRE].
A. Arvanitaki and S. Dubovsky, Exploring the String Axiverse with Precision Black Hole Physics, Phys. Rev. D 83 (2011) 044026 [arXiv:1004.3558] [INSPIRE].
A. Arvanitaki, M. Baryakhtar and X. Huang, Discovering the QCD Axion with Black Holes and Gravitational Waves, Phys. Rev. D 91 (2015) 084011 [arXiv:1411.2263] [INSPIRE].
A. Gruzinov, Black Hole Spindown by Light Bosons, arXiv:1604.06422 [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.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, S. Dimopoulos and K. Van Tilburg, Sound of Dark Matter: Searching for Light Scalars with Resonant-Mass Detectors, Phys. Rev. Lett. 116 (2016) 031102 [arXiv:1508.01798] [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, arXiv:1606.04541 [INSPIRE].
K. Van Tilburg, N. Leefer, L. Bougas and D. Budker, Search for ultralight scalar dark matter with atomic spectroscopy, Phys. Rev. Lett. 115 (2015) 011802 [arXiv:1503.06886] [INSPIRE].
A. Hees, J. Guéna, M. Abgrall, S. Bize and P. Wolf, Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons, Phys. Rev. Lett. 117 (2016) 061301 [arXiv:1604.08514] [INSPIRE].
N. Hinkley et al., An Atomic Clock with 10−18 Instability, Science 341 (2013) 1215 [arXiv:1305.5869].
T.L. Nicholson et al., Systematic evaluation of an atomic clock at 2×10−18 total uncertainty, Nature Commun. 6 (2015) 6896 [arXiv:1412.8261].
N. Nemitz et al., Frequency ratio of Yb and Sr clocks with 5 × 10−17 uncertainty at 150 seconds averaging time, Nature Photon. 10 (2016) 258 [arXiv:1601.04582].
N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm and E. Peik, Single-ion atomic clock with 3 × 10−18 systematic uncertainty, Phys. Rev. Lett. 116 (2016) 063001 [arXiv:1602.03908].
M. Schioppo et al., Ultra-stable optical clock with two cold-atom ensembles, Nature Photon. 11 (2017) 48 [arXiv:1607.06867].
E. Peik and C. Tamm, Nuclear laser spectroscopy of the 3.5 eV transition in Th-229, Europhys. Lett. 61 (2003) 181.
C.J. Campbell, A.G. Radnaev, A. Kuzmich, V.A. Dzuba, V.V. Flambaum and A. Derevianko, A Single-Ion Nuclear Clock for Metrology at the 19th Decimal Place, Phys. Rev. Lett. 108 (2012) 120802 [arXiv:1110.2490] [INSPIRE].
E.V. Tkalya, C. Schneider, J. Jeet and E.R. Hudson, Radiative lifetime and energy of the low-energy isomeric level in 229 Th, Phys. Rev. C 92 (2015) 054324 [arXiv:1509.09101] [INSPIRE].
L. von der Wense et al., Direct detection of the 229 Th nuclear clock transition, Nature 533 (2016) 47.
V.V. Flambaum, Enhanced effect of temporal variation of the fine structure constant and the strong interaction in Th-229, Phys. Rev. Lett. 97 (2006) 092502 [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].
P. Leaci et al., Design of wideband acoustic detectors of gravitational waves equipped with displacement concentrators, Phys. Rev. D 77 (2008) 062001 [INSPIRE].
M. Goryachev and M.E. Tobar, Gravitational Wave Detection with High Frequency Phonon Trapping Acoustic Cavities, Phys. Rev. D 90 (2014) 102005 [arXiv:1410.2334] [INSPIRE].
L.J. Hall, K. Jedamzik, J. March-Russell and S.M. West, Freeze-In Production of FIMP Dark Matter, JHEP 03 (2010) 080 [arXiv:0911.1120] [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].
L.F. Abbott, A Mechanism for Reducing the Value of the Cosmological Constant, Phys. Lett. B 150 (1985) 427 [INSPIRE].
P.W. Graham, D.E. Kaplan and S. Rajendran, to appear.
L. Alberte, P. Creminelli, A. Khmelnitsky, D. Pirtskhalava and E. Trincherini, Relaxing the Cosmological Constant: a Proof of Concept, JHEP 12 (2016) 022 [arXiv:1608.05715] [INSPIRE].
L. Susskind, Is Eternal Inflation Past-Eternal? And What if It Is?, arXiv:1205.0589 [INSPIRE].
A.D. Linde, Sinks in the Landscape, Boltzmann Brains and the Cosmological Constant Problem, JCAP 01 (2007) 022 [hep-th/0611043] [INSPIRE].
J. Polchinski, The Cosmological Constant and the String Landscape, in The Quantum Structure of Space and Time: Proceedings of the 23rd Solvay Conference on Physics, Brussels, Belgium, 1-3 December 2005, pp. 216-236, (2006), hep-th/0603249 [INSPIRE].
R. Bousso, TASI Lectures on the Cosmological Constant, Gen. Rel. Grav. 40 (2008) 607 [arXiv:0708.4231] [INSPIRE].
G. Dvali and A. Vilenkin, Cosmic attractors and gauge hierarchy, Phys. Rev. D 70 (2004) 063501 [hep-th/0304043] [INSPIRE].
A.M. Polyakov, A few projects in string theory, in Gravitation and quantizations. Proceedings, 57th Session of the Les Houches Summer School in Theoretical Physics, NATO Advanced Study Institute, Les Houches, France, July 5 - August 1, 1992, pp. 0783-804, (1993) hep-th/9304146 [INSPIRE].
T. Damour and A.M. Polyakov, The string dilaton and a least coupling principle, Nucl. Phys. B 423 (1994) 532 [hep-th/9401069] [INSPIRE].
A. Arvanitaki, S. Dimopoulos, V. Gorbenko, J. Huang and K. Van Tilburg, to appear.
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].
C. Csáki, TASI lectures on extra dimensions and branes, in From fields to strings: Circumnavigating theoretical physics. Ian Kogan memorial collection (3 volume set), World Scientific (2004), pp. 605-698, hep-ph/0404096 [INSPIRE].
C. Csáki, M.L. Graesser and G.D. Kribs, Radion dynamics and electroweak physics, Phys. Rev. D 63 (2001) 065002 [hep-th/0008151] [INSPIRE].
C. Charmousis, R. Gregory and V.A. Rubakov, Wave function of the radion in a brane world, Phys. Rev. D 62 (2000) 067505 [hep-th/9912160] [INSPIRE].
W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1609.06320
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Arvanitaki, A., Dimopoulos, S., Gorbenko, V. et al. A small weak scale from a small cosmological constant. J. High Energ. Phys. 2017, 71 (2017). https://doi.org/10.1007/JHEP05(2017)071
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2017)071