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Finetuned Cancellations and Improbable Theories

  • James D. WellsEmail author
Article
  • 29 Downloads

Abstract

It is argued that the \(x-y\) cancellation model (XYCM) is a good proxy for discussions of finetuned cancellations in physical theories. XYCM is then analyzed from a statistical perspective, where it is argued that a finetuned point in the parameter space is not abnormal, with any such point being just as probable as any other point. However, landing inside a standardly defined finetuned region (i.e., the full parameter space of finetuned points) has a much lower probability than landing outside the region, and that probability is invariant under assumed ranges of parameters. This proposition requires asserting also that the finetuned target region is a priori established. Therefore, it is surmised that a highly finetuned theory (i.e., remaining parameter space is finetuned) is generally expected to be highly improbable. An actionable implication of this moderate naturalness position is that the search for a non-finetuned explanation to supplant an apparently finetuned theory is likely to be a valid pursuit, but not guaranteed to be. A statistical characterization of this moderate position is presented, as well as those of the extreme pro-naturalness and anti-naturalness positions.

Keywords

Finetuning Naturalness Probability Hierarchy problem 

Notes

Acknowledgements

This work was JDW supported in part by the DOE under Grant No. DE-SC0007859. I wish to thank G. Giudice, S. Martin, A. Pierce, N. Steinberg and Y. Zhao for helpful conversations on these issues.

References

  1. 1.
    Wells, J.D.: Lexicon of Theory Qualities. Resource Manuscripts (19 June 2018). http://www-personal.umich.edu/~jwells/manuscripts/prm2018b.pdf
  2. 2.
    Giudice, G.F.: Naturally Speaking: The Naturalness Criterion and Physics at the LHC, [arXiv:0801.2562 [hep-ph]]
  3. 3.
    Fichet, S.: Quantified naturalness from Bayesian statistics. Phys. Rev. D 86, 125029 (2012).  https://doi.org/10.1103/PhysRevD.86.125029. [arXiv:1204.4940 [hep-ph]]
  4. 4.
    Farina, M., Pappadopulo, D., Strumia, A.: A modified naturalness principle and its experimental tests. JHEP 1308, 022 (2013).  https://doi.org/10.1007/JHEP08(2013)022. [arXiv:1303.7244 [hep-ph]]
  5. 5.
    Tavares, G Marques, Schmaltz, M., Skiba, W.: Higgs mass naturalness and scale invariance in the UV. Phys. Rev. D 89(1), 015009 (2014).  https://doi.org/10.1103/PhysRevD.89.015009. [arXiv:1308.0025 [hep-ph]]
  6. 6.
    Kawamura, Y.: Naturalness, Conformal Symmetry and Duality. PTEP 2013(11), 113B04 (2013).  https://doi.org/10.1093/ptep/ptt098. [arXiv:1308.5069 [hep-ph]]
  7. 7.
    de Gouvea, A., Hernandez, D., Tait, T.M.P.: Criteria for Natural Hierarchies. Phys. Rev. D 89(11), 115005 (2014).  https://doi.org/10.1103/PhysRevD.89.115005. [arXiv:1402.2658 [hep-ph]]
  8. 8.
    Williams, P.: Naturalness, the autonomy of scales, and the 125 GeV Higgs. Stud. Hist. Phil. Sci. B 51, 82 (2015).  https://doi.org/10.1016/j.shpsb.2015.05.003 CrossRefzbMATHGoogle Scholar
  9. 9.
    Dine, M.: Naturalness under stress. Ann. Rev. Nucl. Part. Sci. 65, 43 (2015).  https://doi.org/10.1146/annurev-nucl-102014-022053. [arXiv:1501.01035 [hep-ph]]
  10. 10.
    Athron, P., Balazs, C., Farmer, B., Fowlie, A., Harries, D., Kim, D.: JHEP 1710, 160 (2017).  https://doi.org/10.1007/JHEP10(2017)160. [arXiv:1709.07895 [hep-ph]]
  11. 11.
    Wells, J.D.: Higgs naturalness and the scalar boson proliferation instability problem. Synthese 194(2), 477 (2017).  https://doi.org/10.1007/s11229-014-0618-8. [arXiv:1603.06131 [hep-ph]]
  12. 12.
    Giudice, G.F.: The Dawn of the Post-Naturalness Era, arXiv:1710.07663 [physics.hist-ph]
  13. 13.
    Hossenfelder, S.: Screams for Explanation: Finetuning and Naturalness in the Foundations of Physics. arXiv:1801.02176 [physics.hist-ph]
  14. 14.
    Wells, J.D.: Naturalness, Extra-Empirical Theory Assessments, and the Implications of Skepticism. arXiv:1806.07289 [physics.hist-ph]
  15. 15.
    Ellis, J.R., Enqvist, K., Nanopoulos, D.V., Zwirner, F.: Observables in low-energy superstring models. Mod. Phys. Lett. A 1, 57 (1986).  https://doi.org/10.1142/S0217732386000105 ADSCrossRefGoogle Scholar
  16. 16.
    Barbieri, R., Giudice, G.F.: Upper bounds on supersymmetric particle masses. Nucl. Phys. B 306, 63 (1988).  https://doi.org/10.1016/0550-3213(88)90171-X ADSCrossRefGoogle Scholar
  17. 17.
    Anderson, G.W., Castaño, D.J.: Measures of fine tuning. Phys. Lett. B 347, 300 (1995).  https://doi.org/10.1016/0370-2693(95)00051-L. [arXiv:hep-ph/9409419]
  18. 18.
    Anderson, G.W., Castaño, D.J.: Naturalness and superpartner masses or when to give up on weak scale supersymmetry. Phys. Rev. D 52, 1693 (1995).  https://doi.org/10.1103/PhysRevD.52.1693. [arXiv:hep-ph/9412322]
  19. 19.
    Conway, J., Haber, H., Hobbs, J., Prosper, H.: Statistical conventions and method for combing channels for the Tevatron Run 2 SUSY/Higgs Workshop, Higgs Working Group, Version 5, 24 (February 1999). https://pdfs.semanticscholar.org/2f9f/67348cbf53bd0162ae62fea0dd0dc9848796.pdf. Accessed 27 August 2018
  20. 20.
    Cranmer, K.: Practical Statistics for the LHC.  https://doi.org/10.5170/CERN-2015-001.247,  https://doi.org/10.5170/CERN-2014-003.267. arXiv:1503.07622 [physics.data-an]
  21. 21.
    Gross, E., Vitells, O.: Trial factors for the look elsewhere effect in high energy physics. Eur. Phys. J. C 70, 525 (2010).  https://doi.org/10.1140/epjc/s10052-010-1470-8. [arXiv:1005.1891 [physics.data-an]]
  22. 22.
    Mastrandrea, M.D., et al.: (IPCC), Guidance Note for Lead Authors of the IPCC Fifth Assessment Report on Consistent Treatment of Uncertainties. IPCC, (July 2010). https://www.ipcc.ch/pdf/supporting-material/uncertainty-guidance-note.pdf. Accessed 27 August 2018
  23. 23.
    Hebecker, A., Hisano, J.: Grand unified theories. In: Patrignani, C. et al. (Particle Data Group). Chin. Phys. C 40, 100001 (2016). 2017 updateCrossRefGoogle Scholar
  24. 24.
    Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989).  https://doi.org/10.1103/RevModPhys.61.1 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Douglas, M.R.: The statistics of string/M theory vacua. JHEP 0305, 046 (2003).  https://doi.org/10.1088/1126-6708/2003/05/046. [arXiv:hep-th/0303194]
  26. 26.
    Martin, S.P.: A supersymmetry primer. Adv. Ser. Direct. High Energy Phys. 21, 1 (2010)CrossRefzbMATHGoogle Scholar
  27. 27.
    Martin, S.P.: A supersymmetry primer. Adv. Ser. Direct. High Energy Phys. 18, 1 (1998)  https://doi.org/10.1142/9789814307505_0001 [arXiv:hep-ph/9709356]. Version 7 from January 27, (2016)
  28. 28.
    Randall, L., Sundrum, R.: A Large mass hierarchy from a small extra dimension. Phys. Rev. Lett. 83, 3370 (1999).  https://doi.org/10.1103/PhysRevLett.83.3370. [arXiv:hep-ph/9905221]

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Leinweber Center for Theoretical Physics, Physics DepartmentUniversity of MichiganAnn ArborUSA

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