# A finely-predicted Higgs boson mass from a finely-tuned weak scale

- 238 Downloads
- 68 Citations

## Abstract

If supersymmetry is broken directly to the Standard Model at energies not very far from the unified scale, the Higgs boson mass lies in the range (128–141) GeV. The end points of this range are tightly determined. Theories with the Higgs boson dominantly in a single supermultiplet predict a mass at the upper edge, (141 ± 2) GeV, with the uncertainty dominated by the experimental errors on the top quark mass and the QCD coupling. This edge prediction is remarkably insensitive to the supersymmetry breaking scale and to supersymmetric threshold corrections so that, in a wide class of theories, the theoretical uncertainties are at the level of ±0.4 GeV. A reduction in the uncertainties from the top quark mass and QCD coupling to the level of ±0.3 GeV may be possible at future colliders, increasing the accuracy of the confrontation with theory from 1.4% to 0.4%. Verification of this prediction would provide strong evidence for supersymmetry, broken at a very high scale of ≈10^{14±2} GeV, and also for a Higgs boson that is elementary up to this high scale, implying fine-tuning of the Higgs mass parameter by ≈20–28 orders of magnitude. Currently, the only known explanation for such fine-tuning is the multiverse.

## Keywords

Supersymmetry Breaking Beyond Standard Model Superstring Vacua## References

- [1]H. Georgi, H.R. Quinn and S. Weinberg,
*Hierarchy of interactions in unified gauge theories*,*Phys. Rev. Lett.***33**(1974) 451 [SPIRES].CrossRefADSGoogle Scholar - [2]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] [SPIRES].ADSGoogle Scholar - [3]T. Damour and J.F. Donoghue,
*Constraints on the variability of quark masses from nuclear binding*,*Phys. Rev.***D 78**(2008) 014014 [arXiv:0712.2968] [SPIRES].ADSGoogle Scholar - [4]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] [SPIRES].CrossRefADSGoogle Scholar - [5]S. Weinberg,
*Anthropic bound on the cosmological constant*,*Phys. Rev. Lett.***59**(1987) 2607 [SPIRES].CrossRefADSGoogle Scholar - [6]WMAP collaboration, E. Komatsu et al.,
*Five-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation*,*Astrophys. J. Suppl.***180**(2009) 330 [arXiv:0803.0547] [SPIRES].CrossRefADSGoogle Scholar - [7]Supernova Cosmology Project collaboration, M. Kowalski et al.,
*Improved cosmological constraints from new, old and combined supernova datasets*,*Astrophys. J.***686**(2008) 749 [arXiv:0804.4142] [SPIRES].CrossRefADSGoogle Scholar - [8]R. Bousso and J. Polchinski,
*Quantization of four-form fluxes and dynamical neutralization of the cosmological constant*,*JHEP***06**(2000) 006 [hep-th/0004134] [SPIRES].CrossRefMathSciNetADSGoogle Scholar - [9]S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi,
*de Sitter vacua in string theory*,*Phys. Rev.***D 68**(2003) 046005 [hep-th/0301240] [SPIRES].MathSciNetADSGoogle Scholar - [10]
- [11]M.R. Douglas,
*The statistics of string/M theory vacua*,*JHEP***05**(2003) 046 [hep-th/0303194] [SPIRES].CrossRefADSGoogle Scholar - [12]R.D. Peccei and H.R. Quinn,
*CP conservation in the presence of instantons*,*Phys. Rev. Lett.***38**(1977) 1440 [SPIRES].CrossRefADSGoogle Scholar - [13]
- [14]F. Wilczek,
*Problem of strong p and t invariance in the presence of instantons*,*Phys. Rev. Lett.***40**(1978) 279 [SPIRES].CrossRefADSGoogle Scholar - [15]
- [16]F. Wilczek,
*A model of anthropic reasoning, addressing the dark to ordinary matter coincidence*, hep-ph/0408167 [SPIRES]. - [17]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] [SPIRES].ADSGoogle Scholar - [18]Tevatron Electroweak Working Group collaboration,
*Combination of CDF and D*0*results on the mass of the top quark*, arXiv:0903.2503 [SPIRES]. - [19]Particle Data Group collaboration, C. Amsler et al.,
*Review of particle physics*,*Phys. Lett.***B 667**(2008) 1 [SPIRES].ADSGoogle Scholar - [20]S. Bethke,
*The 2009 Wolrd Average of α*_{s}(*M*_{Z}),*Eur. Phys. J.***C 64**(2009) 689 [arXiv:0908.1135] [SPIRES].CrossRefADSGoogle Scholar - [21]American Linear Collider Working Group collaboration, T. Abe et al.,
*Linear collider physics resource book for Snowmass*2001*.*1*: introduction*, hep-ex/0106055 [SPIRES]. - [22]American Linear Collider Working Group collaboration, T. Abe et al.,
*Linear collider physics resource book for Snowmass*2001*.*2*: Higgs and supersymmetry studies*, hep-ex/0106056 [SPIRES]. - [23]American Linear Collider Working Group collaboration, T. Abe et al.,
*Linear collider physics resource book for Snowmass*2001*.*3*: studies of exotic and standard model physics*, hep-ex/0106057 [SPIRES]. - [24]American Linear Collider Working Group collaboration, T. Abe et al.,
*Linear collider physics resource book for Snowmass*2001*.*4*: theoretical, accelerator and experimental options*, hep-ex/0106058 [SPIRES]. - [25]N. Arkani-Hamed, S. Dimopoulos and S. Kachru,
*Predictive landscapes and new physics at a TeV*, hep-th/0501082 [SPIRES]. - [26]R. Mahbubani and L. Senatore,
*The minimal model for dark matter and unification*,*Phys. Rev.***D 73**(2006) 043510 [hep-ph/0510064] [SPIRES].ADSGoogle Scholar - [27]G. Elor, H.-S. Goh, L. J. Hall, P. Kumar and Y. Nomura,
*Environmentally selected WIMP dark matter with high-scale supersymmetry breaking*, to appear.Google Scholar - [28]M. Binger,
*Higgs boson mass in split supersymmetry at two-loops*,*Phys. Rev.***D 73**(2006) 095001 [hep-ph/0408240] [SPIRES].ADSGoogle Scholar - [29]V. Barger, C.-W. Chiang, J. Jiang and T. Li,
*Axion models with high-scale supersymmetry breaking*,*Nucl. Phys.***B 705**(2005) 71 [hep-ph/0410252] [SPIRES].CrossRefADSGoogle Scholar - [30]V. Barger, J. Jiang, P. Langacker and T. Li,
*Gauge coupling unification in the standard model*,*Phys. Lett.***B 624**(2005) 233 [hep-ph/0503226] [SPIRES].ADSGoogle Scholar - [31]V. Barger, J. Jiang, P. Langacker and T. Li,
*Non-canonical gauge coupling unification in high-scale supersymmetry breaking*,*Nucl. Phys.***B 726**(2005) 149 [hep-ph/0504093] [SPIRES].CrossRefADSGoogle Scholar - [32]D. Emmanuel-Costa and R. Gonzalez Felipe,
*Minimal string-scale unification of gauge couplings*,*Phys. Lett.***B 623**(2005) 111 [hep-ph/0505257] [SPIRES].ADSGoogle Scholar - [33]I. Gogoladze, T. Li and Q. Shafi,
*Higgs boson mass from orbifold GUTs*,*Phys. Rev.***D 73**(2006) 066008 [hep-ph/0602040] [SPIRES].MathSciNetADSGoogle Scholar - [34]L.J. Hall and Y. Nomura,
*Gauge unification in higher dimensions*,*Phys. Rev.***D 64**(2001) 055003 [hep-ph/0103125] [SPIRES].ADSGoogle Scholar - [35]R. Barbieri, L.J. Hall and Y. Nomura,
*A constrained standard model from a compact extra dimension*,*Phys. Rev.***D 63**(2001) 105007 [hep-ph/0011311] [SPIRES].ADSGoogle Scholar - [36]Y. Kawamura,
*Triplet-doublet splitting, proton stability and extra dimension*,*Prog. Theor. Phys.***105**(2001) 999 [hep-ph/0012125] [SPIRES].CrossRefADSGoogle Scholar - [37]J. Scherk and J.H. Schwarz,
*Spontaneous breaking of supersymmetry through dimensional reduction*,*Phys. Lett.***B 82**(1979) 60 [SPIRES].ADSGoogle Scholar - [38]J. Scherk and J.H. Schwarz,
*How to get masses from extra dimensions*,*Nucl. Phys.***B 153**(1979) 61 [SPIRES].CrossRefMathSciNetADSGoogle Scholar - [39]D.E. Kaplan and N. Weiner,
*Radion mediated supersymmetry breaking as a Scherk-Schwarz theory*, hep-ph/0108001 [SPIRES]. - [40]R. Barbieri, L.J. Hall and Y. Nomura,
*Models of Scherk-Schwarz symmetry breaking in*5D*: classification and calculability*,*Nucl. Phys.***B 624**(2002) 63 [hep-th/0107004] [SPIRES].CrossRefMathSciNetADSGoogle Scholar - [41]R. Barbieri et al.,
*Radiative electroweak symmetry breaking from a quasi-localized top quark*,*Nucl. Phys.***B 663**(2003) 141 [hep-ph/0208153] [SPIRES].CrossRefADSGoogle Scholar - [42]Supernova Cosmology Project collaboration, S. Perlmutter et al.,
*Measurements of and*Ω*from*42*high-redshift supernovae*,*Astrophys. J.***517**(1999) 565 [astro-ph/9812133] [SPIRES].CrossRefADSGoogle Scholar - [43]Supernova Search Team collaboration, A.G. Riess et al.,
*Observational evidence from supernovae for an accelerating universe and a cosmological constant*,*Astron. J.***116**(1998) 1009 [astro-ph/9805201] [SPIRES].CrossRefADSGoogle Scholar - [44]A.H. Guth and E.J. Weinberg,
*Could the universe have recovered from a slow first order phase transition?*,*Nucl. Phys.***B 212**(1983) 321 [SPIRES].CrossRefADSGoogle Scholar - [45]A. Vilenkin,
*The birth of inflationary universes*,*Phys. Rev.***D 27**(1983) 2848 [SPIRES].MathSciNetADSGoogle Scholar - [46]A.D. Linde,
*Eternally existing selfreproducing chaotic inflationary universe*,*Phys. Lett.***B 175**(1986) 395 [SPIRES].ADSGoogle Scholar - [47]
- [48]M. Fukugita and T. Yanagida,
*Baryogenesis without grand unification*,*Phys. Lett.***B 174**(1986) 45 [SPIRES].ADSGoogle Scholar - [49]B. Feldstein, L.J. Hall and T. Watari,
*Landscape predictions for the Higgs boson and top quark masses*,*Phys. Rev.***D 74**(2006) 095011 [hep-ph/0608121] [SPIRES].ADSGoogle Scholar - [50]I. Gogoladze, N. Okada and Q. Shafi,
*Higgs boson mass from gauge-Higgs unification*,*Phys. Lett.***B 655**(2007) 257 [arXiv:0705.3035] [SPIRES].ADSGoogle Scholar - [51]L.J. Hall and Y. Nomura,
*Evidence for the multiverse in the standard model and beyond*,*Phys. Rev.***D 78**(2008) 035001 [arXiv:0712.2454] [SPIRES].ADSGoogle Scholar - [52]C.J. Hogan,
*Why the universe is just so*,*Rev. Mod. Phys.***72**(2000) 1149 [astro-ph/9909295] [SPIRES].CrossRefADSGoogle Scholar - [53]R. Bousso, L.J. Hall and Y. Nomura,
*Multiverse understanding of cosmological coincidences*,*Phys. Rev.***D 80**(2009) 063510 [arXiv:0902.2263] [SPIRES].ADSGoogle Scholar

## Copyright information

**Open Access** This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.