1. Statistical issues in Particle Physics analyses Louis Lyons Imperial College and Oxford CMS and CDF experiments l.lyons@physics.ox.ac.uk Ovronnaz, Sept 2009

2. Lecture topics • Introduction to Particle Physics Learning to love the Covariance Matrix 2) Do’s and Dont’s with Likelihoods 3) Statistical issues concerning searches for New Physics: exclusions and discoveries

3. Particle Physics • What it is • Typical experiments • Typical data • Typical analysis

4. What is it? Search for ultimate constituents of matter Ancient tradition What constitutes acceptable theory? “Number of fundamental entities at most A F E W ” Early ideas due to Greeks

5. What is it? Search for ultimate constituents of matter Ancient tradition What constitutes acceptable theory? “Number of fundamental entities at most A ir F ire E arth W ater ”

6. How many? Greeks’ AFEW 4 Dalton’s atoms ~20  120 e and p 2 and n, π, μ, Ω… >1000 “Elementary” particles Quark model 3  35 Future substructure? 1?

7. How big? Human ~ 1 metre Dust ~10-5 metres Atom ~ 10-10 metres Nucleus ~ 10-15 metres Quarks < 10-18 metres Mass of proton = 1 GeV neutrino < 2 eV top = 175 GeV

8. Forces of nature • Gravity (mediated by Gravitons, ) • Electromagnetism (Photons, γ ) • Nuclear strong force (Gluons, g) • Nuclear weak force (Int Vect Bosons, W Z)

10. Elementary particles: Force carriers: photon, W and Z, graviton, gluons Higgs for the masses LEPTONS: e μτ and neutrinos Composite particles: HADRONS: Made from qqq or q q e.g. proton = uud, π+ = u d

11. Typical Experiments • Experiment Energy Beams # events Result • LEP 200 GeV e+ e- 107 Z N = 2.987± 0.008 • BaBar/Belle 10 GeV e+ e- 108 B anti-B CP-violation • Tevatron 2000 GeV p anti-p “1014” SUSY? • LHC 14000 GeV p p (2010…) Higgs? • KK ~3 GeV μ 100 ν oscillations

13. In the LHC tunnel

14. ATLAS Detector at LHC 45 metres long, 25 m high. 3000 physicists from 40 countries

16. CDF at Fermilab

17. Simulated SUSY event in ATLAS Jet Muons Jet Missing ET

18. Interesting Physics is rare

19. TypicalAnalysis • Parameter determination: dn/dt = 1/τ * exp(-t / τ) Worry about backgrounds, t resolution, t-dependent efficiency • 1) Reconstruct tracks • 2) Select real events • 3) Select wanted events • 4) Extract t from L and v • 5) Model signal and background • 6) Likelihood fit for lifetime and statistical error • 7) Estimate systematic error τ± στ(stat)± στ(syst) Goodness of fit

20. Separate signal from background Typical x: masses energies missing E b-tag event shape isolated γ ……. p(data|H0) x2 p(data|H1) x1 Use cuts, decision trees, Fisher discriminants, NN, SVM, boosting, bagging,….. All aim to approximate optimal likelihood ratio ordering

21. Width of Z0 3 light neutrinos

22. TypicalAnalysis Hypothesis testing: Peak or statistical fluctuation? • Why 5σ ? • Past experience • Look elsewhere • Bayes priors

23. Read more LL, “Open statistical issues in Particle Physics”, Annals of Applied Statistics 2 (2008) 887 PHYSTAT-LHC and earlier workshops CDF Statistics Committee web-page