The Higgs boson Faster-than-light neutrino’s 09:00-12:3014:00-17:00 Aart Heijboer and Ivo van Vulpen Nikhef Topical lectures on Statistics (3 rd day) December 2011 All information (slides, code, exercises) can be found at 

If you want to reproduce this plot, but cannot please let us know, now or step by later Simple likelihood plot Can everybody do this ? TMath::Poisson( Nevt_bin, alpha )

Di-photon mass 4-lepton mass Excluded cross-sections Significance s

Counting events in a mass window SM10 Higgs 5 Data12 Standard Model Ok, now what ? SM SM+Higgs data Distribution of expected number of events from a large number of LHC’s discovery exclusion

SM10 Higgs 5 Data12 1) What is the expected significance ? Expected significance Discovery-aimed: p-value and significance incompatibiliy with the SM-only hypothesis Observed significance p-value = 8.35% 1.38 sigma p-value = 30.3% 0.5 sigma 2) What is the observed significance ?

SM10 Higgs 5 3) At what Lumi do you expect to be able to claim a discovery ? Expected significance Discovery-aimed: p-value and significance p-value = 8.35% 1.38 sigma SM30 Higgs 15 p-value = 0.19% 2.9 sigma Expected significance 3 times more LUMINOSITY Discovery if p-value < 2.87x10 -7

exected p-value observed p-value 3.6 sigma

Exclusion: when/how do you exclude a signal SM10 Higgs 5 Data12 SM SM+Higgs CL s+b = 18.5% incompatibiliy with the SM+Higgs hypothesis. CL s+b = 7.0% Observed CL s+b Expected CL s+b Excluded if CL < 5% 1)Observed confidence level ? >5%  NO Can we exclude the SM+Higgs hypothesis ? 2) Expected confidence level ? >5%  NO Did we expect to be able to exclude the SM+Higgs hypothesis ?

SM10 Higgs7.5 Data12 Exclusion: What about 1.5 x the Higgs cross-sec ? Expected CL s+b Observed CL s+b CL s+b = 2.0% CL s+b = 6.8% 3) What σ h /σ h SM can we exclude ? Observed excluded cross-section σ h /σ h SM, = 1.64

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

Test statistic An (event) variable that tries to separate the 2 hypotheses: 1)The number of events 2)Likelihood ratio: Π Probability to observe n i events When you expect λ SM + μλ Higgs Loop over all bins L(μ) =A) Event counting B) NN output, or complex multi-dimensional fit, … used today Used in ATLAS/CMS

Exercises

Mock h  γγ analysis and try to reproduce 4 characteristic ATLAS numbers for a single mass (126 GeV), indicated by ATLAS-CONF

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

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

Some crucial functions: generate_dataset

Some crucial functions: compute_test_statistic

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

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)