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The Higgs boson

Nikhef Topical lectures on Statistics (3 rd day). 14-16 December 2011. All information (slides, code, exercises) can be found at  http://www.nikhef.nl/~ivov/TopicalLectures. The Higgs boson. Faster-than-light neutrino’s. 09:00-12:30. 14:00-17:00. Aart Heijboer and Ivo van Vulpen.

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The Higgs boson

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  1. Nikhef Topical lectures on Statistics (3rd day) 14-16 December 2011 All information (slides, code, exercises) can be found at http://www.nikhef.nl/~ivov/TopicalLectures The Higgs boson Faster-than-light neutrino’s 09:00-12:30 14:00-17:00 Aart Heijboer and Ivo van Vulpen

  2. Simple likelihood plot Can everybody do this ? If you want to reproduce this plot, but cannot please let us know, now or step by later TMath::Poisson( Nevt_bin, alpha ) http://www.nikhef.nl/~ivov/TopicalLectures/SimpleFit/

  3. 4-lepton mass Di-photon mass Excluded cross-sections Significances

  4. Counting events in a mass window Standard Model Ok, now what ? Distribution of expected number of events from a large number of LHC’s SM SM+Higgs discovery exclusion data

  5. Discovery-aimed: p-value and significance incompatibiliy with the SM-only hypothesis Expected significance p-value = 8.35% 1.38 sigma 1) What is the expected significance ? Observed significance p-value = 30.3% 0.5 sigma 2) What is the observed significance ?

  6. Discovery-aimed: p-value and significance Expected significance p-value = 8.35% 1.38 sigma 3) At what Lumi do you expect to be able to claim a discovery ? 3 times more LUMINOSITY Expected significance p-value = 0.19% 2.9 sigma Discovery if p-value < 2.87x10-7

  7. exected p-value 3.6 sigma observed p-value

  8. Exclusion: when/how do you exclude a signal incompatibiliy with the SM+Higgs hypothesis. Observed CLs+b Excluded if CL < 5% SM SM+Higgs CLs+b = 18.5% • Observed confidence level ? Can we exclude the SM+Higgs hypothesis ? >5%  NO Expected CLs+b 2) Expected confidence level ? Did we expect to be able to exclude the SM+Higgs hypothesis ? CLs+b = 7.0% >5%  NO

  9. Exclusion: What about 1.5 x the Higgs cross-sec ? Expected CLs+b CLs+b = 2.0% Observed CLs+b CLs+b = 6.8% 3) What σh/σhSM can we exclude ? Observed excluded cross-section σh/σhSM , = 1.64

  10. Excluded cross-sections We will try to reproduce a few of these numbers

  11. Test statistic • An (event) variable that tries to separate the 2 hypotheses: • The number of events • Likelihood ratio: used today Used in ATLAS/CMS Π A) Event counting L(μ) = Probability to observe ni events When you expect λSM+ μλHiggs Loop over all bins B) NN output, or complex multi-dimensional fit, …

  12. Exercises

  13. ATLAS-CONF-2011-161 http://cdsweb.cern.ch/record/1406356/files/ATLASCONF2011161.pdf Mock hγγ analysis and try to reproduce 4 characteristic ATLAS numbers for a single mass (126 GeV), indicated by

  14. Quick intro into some of the usefull functions in the code  higgs.C In root: .L higgs.C++ higgs()

  15. Some crucial functions:init_pdfs ATLAS our imitation Global histograms (TH1F*): pdf_bgr and pdf_sig

  16. Some crucial functions:generate_dataset

  17. Some crucial functions:compute_test_statistic

  18. Some crucial functions:get_test_statistic_distribution See also: plot_with bands (TH1F* h) from utils.h

  19. Some additional helper functions that you need (in utils.h) double median (TH1F*) double get_fraction_below(TH1F* h, double x_value) double get_fraction_above(TH1F* h, double x_value) TH1F* read_dataset(Tstring filename)

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