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 B s 0 oscillations(CDF)  Search for the Higgs(CDF/D0)  Conclusions PHYSTAT 2011 Harrison B. Prosper2

3. Introduction 3

4. The Tevatron (1991 – 2011) Goals: 1.To test the Standard Model (SM) 2.To find hints of new physics A few key SM predictions: 1.jet spectra ✓ 2.existence of top quark ✓ 3.creation of top quarks singly ✓ 4.creation of di-bosons (WW/ZZ/WZ/Wγ/Zγ) ✓ 5.properties of B mesons ✓ 6.existence of Higgs PHYSTAT 2011 Harrison B. Prosper4

5. 5 “There are known knowns… There are known unknowns… But there are also unknown unknowns.” Donald Rumsfeld

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. Prosper6

7. CDF & D0 PHYSTAT 2011 Harrison B. Prosper7

8. Particle Physics Data Each collision event yields ~ 1MB of data. However, these data are compressed by a factor of ~10 3 – 10 4 during event reconstruction: PHYSTAT 2011 Harrison B. Prosper8 Courtesy CDF

9. Particle Physics Data PHYSTAT 2011 Harrison B. Prosper9 CDF (24 September 1992) proton + anti-proton 3positron (e + ) 2neutrino (ν) 3Jet1 3Jet2 3Jet3 3Jet4 A total of 17 measurements, after event reconstruction

10. Case Studies PHYSTAT 2011 Harrison B. Prosper10

11. Search for a Rare Decay (D0) PHYSTAT 2011 Harrison B. Prosper11

12. Search for a Rare Decay (D0) PHYSTAT 2011 Harrison B. Prosper12 The goal: test the Standard Model prediction

13. Search for a Rare Decay (D0) PHYSTAT 2011 Harrison B. Prosper13 Compress data to the unit interval using a Bayesian neural network β = BNN(Data) Cuts 1. β > 0.9 2. 5.0 ≤ m μμ ≤ 5.8 GeV define the signal region Phys.Lett. B693 (2010) 539-544 e-Print: arXiv:1006.3469 [hep-ex]

14. Search for a Rare Decay (D0) PHYSTAT 2011 Harrison B. Prosper14 D0 results (6.1 fb -1 )observedbackground RunIIan a = 256B a = 264 ± 13 event RunIIbn b = 823B b = 827 ± 23 events The likelihood for these data is the 2-count model p(n|s, μ) = Poisson(n a |s a + μ a ) Poisson(n b |s b + μ b ) 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.

15. A Search for a Rare Decay PHYSTAT 2011 Harrison B. Prosper15 For D0, the branching fraction (BF) is related to be the signals as follows BF = (4.90 ± 1.00) × 10 -9 × s a (RunIIa) BF = (1.84 ± 0.36) × 10 -9 × s b (RunIIb) The limit BF < 5.1 x 10 -8 @ 95% C.L. is derived using CL s, based on the statistic x = log[p(n|BF) / p(n|0)], where p(n|BF) is the likelihood marginalized over all nuisance parameters. [Recap CL s (Luc’s talk): define p 1 (BF) = P[x < x 0 | H 1 (BF)], reject all BF for which p 1 (BF) < γ p 1 (0), and define a (1 – γ) C.L. upper limit as the smallest rejected value of BF.]

16. Search for Single Top (D0) PHYSTAT 2011 Harrison B. Prosper16

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 m top =170 GeV). This corresponds to a production rate of ~ 1 in 10 10 collisions. PHYSTAT 2011 Harrison B. Prosper17

18. Search for Single Top PHYSTAT 2011 Harrison B. Prosper18 S/B ~ 1/260

19. Search for Single Top PHYSTAT 2011 Harrison B. Prosper19 The data are reduced to M counts described by the likelihood where σ (the cross section) is the parameter of interest and the ε i and μ i are nuisance parameters.

20. Search for Single Top D0 (and CDF) compute the posterior p(σ | n) assuming: 1.a flat prior for π(σ) 2.an evidence-based prior for π(ε, μ) PHYSTAT 2011 Harrison B. Prosper20

21. Search for Single Top Estimate of “signal significance” using a p-value: p 0 = P[t > t 0 | H 0 ] The statistic t is the mode of the the posterior density. PHYSTAT 2011 Harrison B. Prosper21

22. Search for B s 0 Oscillations (CDF) PHYSTAT 2011 Harrison B. Prosper22

23. Search for B s 0 Oscillations PHYSTAT 2011 Harrison B. Prosper23 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)

24. There are (at least) two complications: 1.the time of decay t of a B particle is measured with some uncertainty 2.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 σ 2 that depends on t. Search for B s 0 Oscillations PHYSTAT 2011 Harrison B. Prosper24 Nino T. Leonardo (PhD Dissertation, MIT, 2006)

25. 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. Search for B s 0 Oscillations PHYSTAT 2011 Harrison B. Prosper25

26. 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: p 0 = P[Λ < Λ 0 | H 0 ] = 8 x 10 -8 Search for B s 0 Oscillations PHYSTAT 2011 Harrison B. Prosper26 CDF, PRL 97, 242003 (2006)

27. Search for the Higgs PHYSTAT 2011 Harrison B. Prosper27

28. Search for the Higgs PHYSTAT 2011 Harrison B. Prosper28 Here is all available evidence about the Higgs:

29. 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! Higgs @ CERN PHYSTAT 2011 Harrison B. Prosper29

30. Conclusions PHYSTAT 2011 Harrison B. Prosper30  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.  CL s still lives…alas!  Physicists can be taught!