Abstract
The small and negative value of the Standard Model Higgs quartic coupling at high scales can be understood in terms of anthropic selection on a landscape where large and negative values are favored: most universes have a very short-lived electroweak vacuum and typical observers are in universes close to the corresponding metastability boundary. We provide a simple example of such a landscape with a Peccei-Quinn symmetry breaking scale generated through dimensional transmutation and supersymmetry softly broken at an intermediate scale. Large and negative contributions to the Higgs quartic are typically generated on integrating out the saxion field. Cancellations among these contributions are forced by the anthropic requirement of a sufficiently long-lived electroweak vacuum, determining the multiverse distribution for the Higgs quartic in a similar way to that of the cosmological constant. This leads to a statistical prediction of the Higgs boson mass that, for a wide range of parameters, yields the observed value within the 1σ statistical uncertainty of ∼ 5 GeV originating from the multiverse distribution. The strong CP problem is solved and single-component axion dark matter is predicted, with an abundance that can be understood from environmental selection. A more general setting for the Higgs mass prediction is discussed.
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References
S. Weinberg, Anthropic Bound on the Cosmological Constant, Phys. Rev. Lett. 59 (1987) 2607 [INSPIRE].
H. Martel, P.R. Shapiro and S. Weinberg, Likely values of the cosmological constant, Astrophys. J. 492 (1998) 29 [astro-ph/9701099] [INSPIRE].
R. Bousso, R. Harnik, G.D. Kribs and G. Perez, Predicting the Cosmological Constant from the Causal Entropic Principle, Phys. Rev. D 76 (2007) 043513 [hep-th/0702115] [INSPIRE].
R. Bousso, B. Freivogel, S. Leichenauer and V. Rosenhaus, A geometric solution to the coincidence problem and the size of the landscape as the origin of hierarchy, Phys. Rev. Lett. 106 (2011) 101301 [arXiv:1011.0714] [INSPIRE].
R. Bousso, B. Freivogel, S. Leichenauer and V. Rosenhaus, Geometric origin of coincidences and hierarchies in the landscape, Phys. Rev. D 84 (2011) 083517 [arXiv:1012.2869] [INSPIRE].
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].
L.J. Hall, D. Pinner and J.T. Ruderman, The Weak Scale from BBN, JHEP 12 (2014) 134 [arXiv:1409.0551] [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [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].
B. Feldstein, L.J. Hall and T. Watari, Simultaneous solutions of the strong CP and mu problems, Phys. Lett. B 607 (2005) 155 [hep-ph/0411013] [INSPIRE].
J.A. Frieman, S. Dimopoulos and M.S. Turner, Axions and Stars, Phys. Rev. D 36 (1987) 2201 [INSPIRE].
L.J. Hall and Y. Nomura, Grand Unification and Intermediate Scale Supersymmetry, JHEP 02 (2014) 129 [arXiv:1312.6695] [INSPIRE].
L.J. Hall, Y. Nomura and S. Shirai, Grand Unification, Axion and Inflation in Intermediate Scale Supersymmetry, JHEP 06 (2014) 137 [arXiv:1403.8138] [INSPIRE].
A.D. Linde, Vacuum Instability, Cosmology and Constraints on Particle Masses in the Weinberg-Salam Model, Phys. Lett. B 92 (1980) 119 [INSPIRE].
M. Lindner, Implications of Triviality for the Standard Model, Z. Phys. C 31 (1986) 295 [INSPIRE].
M. Sher, Precise vacuum stability bound in the standard model, Phys. Lett. B 317 (1993) 159 [hep-ph/9307342] [INSPIRE].
M. Holthausen, K.S. Lim and M. Lindner, Planck scale Boundary Conditions and the Higgs Mass, JHEP 02 (2012) 037 [arXiv:1112.2415] [INSPIRE].
J. Elias-Miro et al., Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
B. Feldstein, L.J. Hall and T. Watari, Landscape Prediction for the Higgs Boson and Top Quark Masses, Phys. Rev. D 74 (2006) 095011 [hep-ph/0608121] [INSPIRE].
F. D’Eramo, L.J. Hall and D. Pappadopulo, Multiverse Dark Matter: SUSY or Axions, JHEP 11 (2014) 108 [arXiv:1409.5123] [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
G.F. Giudice, M.A. Luty, H. Murayama and R. Rattazzi, Gaugino mass without singlets, JHEP 12 (1998) 027 [hep-ph/9810442] [INSPIRE].
T. Gherghetta, G.F. Giudice and J.D. Wells, Phenomenological consequences of supersymmetry with anomaly induced masses, Nucl. Phys. B 559 (1999) 27 [hep-ph/9904378] [INSPIRE].
C. Cheung, G. Elor and L.J. Hall, The Cosmological Axino Problem, Phys. Rev. D 85 (2012) 015008 [arXiv:1104.0692] [INSPIRE].
M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, Dimensionless constants, cosmology and other dark matters, Phys. Rev. D 73 (2006) 023505 [astro-ph/0511774] [INSPIRE].
K.J. Bae, J.-H. Huh and J.E. Kim, Update of axion CDM energy, JCAP 09 (2008) 005 [arXiv:0806.0497] [INSPIRE].
B. Freivogel, Anthropic Explanation of the Dark Matter Abundance, JCAP 03 (2010) 021 [arXiv:0810.0703] [INSPIRE].
R. Bousso and L. Hall, Why Comparable? A Multiverse Explanation of the Dark Matter-Baryon Coincidence, Phys. Rev. D 88 (2013) 063503 [arXiv:1304.6407] [INSPIRE].
R. Mahbubani and L. Senatore, The Minimal model for dark matter and unification, Phys. Rev. D 73 (2006) 043510 [hep-ph/0510064] [INSPIRE].
F. D’Eramo, Dark matter and Higgs boson physics, Phys. Rev. D 76 (2007) 083522 [arXiv:0705.4493] [INSPIRE].
R. Enberg, P.J. Fox, L.J. Hall, A.Y. Papaioannou and M. Papucci, LHC and dark matter signals of improved naturalness, JHEP 11 (2007) 014 [arXiv:0706.0918] [INSPIRE].
T. Cohen, J. Kearney, A. Pierce and D. Tucker-Smith, Singlet-Doublet Dark Matter, Phys. Rev. D 85 (2012) 075003 [arXiv:1109.2604] [INSPIRE].
A. Salam and J.A. Strathdee, On Superfields and Fermi-Bose Symmetry, Phys. Rev. D 11 (1975) 1521 [INSPIRE].
M.T. Grisaru, W. Siegel and M. Roček, Improved Methods for Supergraphs, Nucl. Phys. B 159 (1979) 429 [INSPIRE].
N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 2. Yukawa Couplings, Nucl. Phys. B 236 (1984) 221 [INSPIRE].
U. Ellwanger, C. Hugonie and A.M. Teixeira, The Next-to-Minimal Supersymmetric Standard Model, Phys. Rept. 496 (2010) 1 [arXiv:0910.1785] [INSPIRE].
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ArXiv ePrint: 1502.06963
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D’Eramo, F., Hall, L.J. & Pappadopulo, D. Radiative PQ breaking and the Higgs boson mass. J. High Energ. Phys. 2015, 117 (2015). https://doi.org/10.1007/JHEP06(2015)117
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DOI: https://doi.org/10.1007/JHEP06(2015)117