Discoveries and Upper Limits

  • Luca Lista
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 941)

Abstract

The goal of many experiments is to search for new physical phenomena. If an experiment provides a convincing measurement of a new signal, the result should be published and claimed as discovery. If the outcome is not sufficiently convincing, in many cases it is nonetheless interesting to quote, as the result of the search for the new phenomena, an upper limit to the yield of the new signal. From upper limits to the signal yield, it is often possible to indirectly derive limits on the properties of the new signal. Limits could be set to the mass of a new particle or to coupling constants; more in general, it’s possible to exclude regions of the parameter space of a new theory that influences the signal yield.

References

  1. 1.
    Wasserstein, R.L., Lazar, N.A.: The ASA’s statement on p-values: context, process, and purpose. Am. Stat. 70, 129–133 (2016)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Cowan, G., Cranmer, K., Gross, E., Vitells, O.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71, 1554 (2011)ADSCrossRefGoogle Scholar
  3. 3.
    Helene, O.: Upper limit of peak area. Nucl. Instrum. Methods A 212, 319 (1983)CrossRefGoogle Scholar
  4. 4.
    Amsler, C., et al.: The review of particle physics. Phys. Lett. B 667, 1 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    Zech, G.: Upper limits in experiments with background or measurement errors. Nucl. Instrum. Methods A 277, 608 (1989)ADSCrossRefGoogle Scholar
  6. 6.
    Highland, V., Cousins, R.: Comment on “upper limits in experiments with background or measurement errors”. Nucl. Instrum. Methods A 277, 608–610 (1989). Nucl. Instrum. Methods A 398, 429 (1989)Google Scholar
  7. 7.
    Zech, G.: Reply to comment on “upper limits in experiments with background or measurement errors”. Nucl. Instrum. Methods A 277, 608–610 (1989). Nucl. Instrum. Methods A 398, 431 (1989)Google Scholar
  8. 8.
    Abbiendi, G., et al.: Search for the standard model Higgs boson at LEP. Phys. Lett. B 565, 61–75 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    ATLAS Collaboration: Observation of an excess of events in the search for the standard model higgs boson with the ATLAS detector at the LHC. ATLAS-CONF-2012-093 (2012). http://cds.cern.ch/record/1460439
  10. 10.
    Berg, B.: Markov Chain Monte Carlo Simulations and Their Statistical Analysis. World Scientific, Singapore (2004)CrossRefMATHGoogle Scholar
  11. 11.
    Cousins, R., Highland, V.: Incorporating systematic uncertainties into an upper limit. Nucl. Instrum. Methods A 320, 331–335 (1992)ADSCrossRefGoogle Scholar
  12. 12.
    Zhukov, V., Bonsch, M.: Multichannel number counting experiments. In: Proceedings of PHYSTAT2011 (2011)Google Scholar
  13. 13.
    Blocker, C.: Interval estimation in the presence of nuisance parameters: 2. Cousins and highland method. CDF/MEMO/STATISTICS/PUBLIC/7539 (2006). https://www-cdf.fnal.gov/physics/statistics/notes/cdf7539_ch_limits_v2.ps
  14. 14.
    Lista, L.: Including Gaussian uncertainty on the background estimate for upper limit calculations using Poissonian sampling. Nucl. Instrum. Methods A 517, 360 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    Wald, A.: Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Am. Math. Soc. 54, 426–482 (1943)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Asimov, I.: Franchise. In: Asimov, I. (ed.) The Complete Stories, vol. 1. Broadway Books, New York (1990)Google Scholar
  17. 17.
    Grégory Schott for the RooStats Team: RooStats for searches. In: Proceedings of PHYSTAT2011 (2011). https://twiki.cern.ch/twiki/bin/view/RooStats
  18. 18.
    Brun, R., Rademakers, F.: Root—an object oriented data analysis framework. In: Proceedings AIHENP96 Workshop, Lausanne (1996). Nucl. Instrum. Methods A 389 81–86 (1997). http://root.cern.ch/ Google Scholar
  19. 19.
    Ranucci, G.: The profile likelihood ratio and the look elsewhere effect in high energy physics. Nucl. Instrum. Methods A 661, 77–85 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Gross, E., Vitells, O.: Trial factors for the look elsewhere effect in high energy physics. Eur. Phys. J. C 70, 525 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Gross, E., Vitells, O.: Statistical Issues Relevant to Significance of Discovery Claims (10w5068), Banff, Alberta, 11–16 July 2010Google Scholar
  22. 22.
    Davies, R.: Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74, 33 (1987)MATHMathSciNetGoogle Scholar
  23. 23.
    Gross, E.: Proceedings of the European School of High Energy Physics (2015)Google Scholar
  24. 24.
    Vitells, O., Gross, E.: Estimating the significance of a signal in a multi-dimensional search. Astropart. Phys. 35, 230–234 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    ATLAS Collaboration: Search for resonances in diphoton events at \(\sqrt{s} = 13\) TeV with the ATLAS detector. J. High Energy Phys. 09, 001 (2016)Google Scholar
  26. 26.
    Read, A.: Modified frequentist analysis of search results (the CLs method). In: Proceedings of the 1st Workshop on Confidence Limits, CERN (2000)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Luca Lista
    • 1
  1. 1.INFN Sezione di NapoliNapoliItaly

Personalised recommendations