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Experience from Searches at the Tevatron

Experience from Searches at the Tevatron. Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN. Outline. Introduction Case Studies Search for a rare decay ( D0 ) Search for single top ( D0 ) Search for B s 0 oscillations ( CDF )

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Experience from Searches at the Tevatron

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  1. Experience from Searches at the Tevatron Harrison B. Prosper Florida State University 18 January, 2011 PHYSTAT 2011 CERN

  2. Outline • Introduction • Case Studies • Search for a rare decay (D0) • Search for single top (D0) • Search for Bs0 oscillations (CDF) • Search for the Higgs (CDF/D0) • Conclusions PHYSTAT 2011 Harrison B. Prosper

  3. Introduction PHYSTAT 2011 Harrison B. Prosper

  4. The Tevatron (1991 – 2011) Goals: • To test the Standard Model (SM) • To find hints of new physics A few key SM predictions: • jet spectra ✓ • existence of top quark ✓ • creation of top quarks singly ✓ • creation of di-bosons (WW/ZZ/WZ/Wγ/Zγ) ✓ • properties of B mesons ✓ • existence of Higgs PHYSTAT 2011 Harrison B. Prosper

  5. “There are known knowns… There are known unknowns… But there are also unknown unknowns.” Donald Rumsfeld PHYSTAT 2011 Harrison B. Prosper

  6. The Standard Model in Action The observed transverse momentum spectrum of jets agrees with SM predictions over 10 orders of magnitude This illustrates why we take our null hypothesis, the Standard Model, seriously. PHYSTAT 2011 Harrison B. Prosper

  7. CDF & D0 PHYSTAT 2011 Harrison B. Prosper

  8. Particle Physics Data Each collision event yields ~ 1MB of data. However, these data are compressed by a factor of ~103 – 104 during event reconstruction: Courtesy CDF PHYSTAT 2011 Harrison B. Prosper

  9. Particle Physics Data CDF (24 September 1992) proton + anti-proton 3 positron (e+) 2 neutrino (ν) 3Jet1 3Jet2 3 Jet3 3Jet4 A total of 17 measurements, after event reconstruction PHYSTAT 2011 Harrison B. Prosper

  10. Case Studies PHYSTAT 2011 Harrison B. Prosper

  11. Search for a Rare Decay (D0) PHYSTAT 2011 Harrison B. Prosper

  12. Search for a Rare Decay (D0) The goal: test the Standard Model prediction PHYSTAT 2011 Harrison B. Prosper

  13. Search for a Rare Decay (D0) • Compress data to the unit • interval using a Bayesian • neural network • β = BNN(Data) • Cuts • β > 0.9 • 5.0 ≤ mμμ ≤ 5.8 GeV • define the signal region Phys.Lett. B693 (2010) 539-544 e-Print: arXiv:1006.3469 [hep-ex] PHYSTAT 2011 Harrison B. Prosper

  14. Search for a Rare Decay (D0) D0 results (6.1 fb-1) observed background RunIIana = 256 Ba = 264 ± 13 event RunIIbnb = 823 Bb = 827 ± 23 events The likelihood for these data is the 2-count model p(n|s, μ) = Poisson(na|sa+ μa) Poisson(nb|sb+ μb) where the s and μ are the expected signal and background counts, respectively. The evidence-based prior for the backgrounds is taken to be the product of two normal distributions. PHYSTAT 2011 Harrison B. Prosper

  15. A Search for a Rare Decay For D0, the branching fraction (BF) is related to be the signals as follows BF = (4.90 ± 1.00) × 10-9 × sa (RunIIa) BF = (1.84 ± 0.36) × 10-9 × sb (RunIIb) The limit BF < 5.1 x 10-8 @ 95% C.L. is derived using CLs, based on the statistic x = log[p(n|BF) / p(n|0)], where p(n|BF) is the likelihood marginalized over all nuisance parameters. [RecapCLs (Luc’s talk): define p1(BF) = P[x < x0| H1(BF)], reject all BF for which p1(BF) < γ p1(0), and define a (1 – γ) C.L. upper limit as the smallest rejected value of BF.] PHYSTAT 2011 Harrison B. Prosper

  16. Search for Single Top (D0) PHYSTAT 2011 Harrison B. Prosper

  17. Search for Single Top The goal: test the Standard Model prediction that the process exists and has a total cross section of 3.46 ± 0.18 pb (assuming a top quark mass of mtop=170 GeV). This corresponds to a production rate of ~ 1 in 1010 collisions. PHYSTAT 2011 Harrison B. Prosper

  18. Search for Single Top S/B ~ 1/260 PHYSTAT 2011 Harrison B. Prosper

  19. Search for Single Top The data are reduced to M counts described by the likelihood where σ (the cross section) is the parameter of interest and the εi and μiare nuisance parameters. PHYSTAT 2011 Harrison B. Prosper

  20. Search for Single Top D0 (and CDF) compute the posterior p(σ | n) assuming: • a flat prior for π(σ) • an evidence-based prior for π(ε, μ) PHYSTAT 2011 Harrison B. Prosper

  21. Search for Single Top Estimate of “signal significance” using a p-value: p0 = P[t > t0| H0] The statistic t is the mode of the the posterior density. PHYSTAT 2011 Harrison B. Prosper

  22. Search for Bs0 Oscillations (CDF) PHYSTAT 2011 Harrison B. Prosper

  23. Search for Bs0 Oscillations The goal: test the Standard Model prediction that the oscillation process exists and is governed by the time-dependent probabilities with A = 1 Nino T. Leonardo (PhD Dissertation, MIT, 2006) PHYSTAT 2011 Harrison B. Prosper

  24. Search for Bs0 Oscillations There are (at least) two complications: • the time of decay t of a B particle is measured with some uncertainty • there is background • The probability model is therefore a convolution of a signal plus • background mixture and a resolution function. • The latter is modeled as • a normal with a • variance σ2 that • depends on t. Nino T. Leonardo (PhD Dissertation, MIT, 2006) PHYSTAT 2011 Harrison B. Prosper

  25. Search for Bs0 Oscillations The likelihood is a product of these functions, one for each measured decay time: Finding the amplitude A. For a given oscillation frequency, Δm, a maximum likelihood fit is performed for the amplitude. It is found that at Δm = 17.8/ps, A = 1.21 ± 0.20, which is consistent with A = 1 and inconsistent with A = 0. PHYSTAT 2011 Harrison B. Prosper

  26. Search for Bs0 Oscillations Estimating the “signal significance”. This is done using the likelihood ratio test statistic Λ = log[p(t | A=0) / p(t | A=1, Δm)], The significance is defined to be the p-value: p0 = P[Λ < Λ0| H0] = 8 x 10-8 CDF, PRL 97, 242003 (2006) PHYSTAT 2011 Harrison B. Prosper

  27. Search for the Higgs PHYSTAT 2011 Harrison B. Prosper

  28. Search for the Higgs Here is all available evidence about the Higgs: PHYSTAT 2011 Harrison B. Prosper

  29. Higgs @ CERN Given the evidence-based prior, π(s), that encodes what we know about the Higgs from the Tevatron and LEP, we could test the Higgs hypothesis with current LHC data by computing a Bayes factor (see Jim Berger’s talk): or by computing the expected loss (d(N)) (see José Bernardo’s talk) …just a thought! PHYSTAT 2011 Harrison B. Prosper

  30. Conclusions • Discoveries can be had, in spite of our eclectic, and sometimes muddled, approach to statistics. • “We” remain ferociously fond of exact frequentist coverage. • p-values remain king! But Bayes is tolerated. • CLs still lives…alas! • Physicists can be taught! PHYSTAT 2011 Harrison B. Prosper

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