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Systematic Analysis of HEP Collider Data

Systematic Analysis of HEP Collider Data. Sleuth Quaero Optimal binning. Bruce Knuteson MIT. “Objects” seen in the detector. e. . . b. j. . . (the colors are meaningless). A cartoon collision (An “event”).  4 objects per event  3 numbers per object energy E

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Systematic Analysis of HEP Collider Data

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  1. Systematic Analysis of HEP Collider Data Sleuth Quaero Optimal binning Bruce Knuteson MIT

  2. “Objects” seen in the detector e   b j   (the colors are meaningless)

  3. A cartoon collision (An “event”) •  4 objects per event • 3 numbers per object • energy E • directions ,  • Each event is described by  4object types and  12 numbers 10-16 m

  4. Standard Model the null hypothesis

  5. The theoretical landscape Murayama, Lepton Photon 2003 summary talk

  6. The theoretical landfill www.southampton.gov.uk/government/ environment/waste.htm

  7. Sleuth A detective. (From sleuthhound – a dog, such as a bloodhound, used for tracking or pursuing.)

  8. e Partition the data   e+ p b e-   p j  e+jjbb e+e- e+bb e+3j e+e-2jj e+jj e+μ+ e+ e+  e+e+e- +3jj e+μ-jj ee4j +bb Sleuth

  9. Define variables e+ e- proton anti-proton  If new TeV-scale physics enters here outgoing particles will be energetic relative to Standard Model and instrumental backgrounds Use object pT's Sleuth

  10. Search for regions of excess (more data events than expected from background) within that variable space For each final state . . . Input:1 data file, estimated backgrounds • transform variables into the unit box • define regions about sets of data points • Voronoi diagrams • define the “interestingness” of an arbitrary region • the probability that the background within that region fluctuates up to or beyond the observed number of events • search the data to find the most interesting region,R • determineP, the fraction ofhypothetical similar experimentsin which you would see something more interesting thanR • Take account of the fact that we have looked in many different places Output:R,P Sleuth

  11. Run I data Sleuth Results agree with SM expectation Phys.Rev.D62:092004,2000; hep-ex/0006011 Phys.Rev.D64:012004,2001; hep-ex/0011067 Phys.Rev.Lett.86:3712,2001; hep-ex/0011071

  12. # events model-independent general search in same spirit presented by H1 at EPS 2003 watch this space in HERA II

  13. 7) Does Sleuth find anything interesting in Run I data? Question: Is it possible to perform a data-driven search for new phenomena? No.A systematic search of many final states reveals no evidence of new high pT physics. 8) Apply to Run II 1) Define final states 6) Can Sleuth find something interesting? Sleuth (yes!) top bkg 2) Define variables p p 3) Define regions 4) Define "interestingness" 5) Run hypothetical similar experiments

  14. Quaero Automating tests of specific hypotheses against HEP collider data NASA astronomy picture of the day Oct 1, 2002 Surface of Mars

  15. Wish list • Reduce analysis time by factor of 10000 • Reduce human bias • Publish data in full dimensionality • Expunge exclusion contours from conference talks • Automate optimization of analyses • Rigorously propagate systematic errors • Increase robustness of results • Easily combine results among different experiments • All of this on the web

  16. Search for New Physics Using Quaero: A General Interface to DØ Event Data Run I data since June 2001 http://quaero.fnal.gov/ hep-ex/0106039 PRL 87 231801

  17. Quaero algorithm overview (you wish to test a hypothesisH) • H events are run through the detector simulation • H, SM, data are partitioned into final states • Variables are chosen automatically • Binning is chosen automatically • A binned likelihood is calculated • Results from different final states are combined • Results from different experiments are combined • Systematic errors are integrated numerically • Result returned

  18. Typical problem true distributions our knowledge wish to determine

  19. Want to provide the strongest evidence possible in favor ofhifhis correct . . . . . . and the strongest evidence possible in favor ofbifbis correct

  20. Figure of MeritM (Choice of binning for likelihood ratio calculation) sum over all possible outcomes of the experiment. # of data eventsdkin each binkis [0,) the evidence obtained in favor ofhin this outcome . . . plus the same thing, but switchhandb minus a penalty term weight outcome by the probability of its occurrence, assuming the validity ofh + ditto forb expected evidence in favor ofhifhis correct

  21. Example #1 Expected # of events / unit of x Expected evidence

  22. Example #2 Expected # of events / unit of x Expected evidence

  23. Multivariate generalization Using the same procedure, create a d-dimensional grid: x e.g., y - or - Use Kernel Density Estimation to reduce the problem to 1-d

  24. FewKDE Typical kernel solution 1) place “bumps of probability” around each Monte Carlo point 2) sum these bumps into a continuous distribution Time cost is O(N2) FewKDE • fit for parameters of five Gaussians • appropriately handle hard physical boundaries

  25. Example #3 h b true distributions (contours) Monte Carlo events f e d c b a e f d c b KDE discriminant

  26. Summary Sleuth model-independent search for new high pT physics Quaero automates tests of specific models Optimal Binningchoosing the bins for binned likelihood ratios Special thanks to: and many others

  27. Backup

  28. How “sensitive” is Sleuth to WW  eET ? Observed at 2.3 CDF, “Observation of W+W- production . . . .” PRL 78 4536 (1997) 5 events observed on a bkg of 1.20.3 Sleuth

  29. How “sensitive” is Sleuth to tt  eETjj ? Observed at 2.1 DØ, “Measurement of the Top Quark Pair Production Cross Section in ppbar Collisions” PRL 79 1203 (1997) 5 events observed on a bkg of 1.40.4 Sleuth

  30. Run I data: eμETX Backgrounds include 1) 2) 3) • fakes • Z • WW • tt • fakes • Z • WW • tt • fakes • Z • WW • tt DØ data DØ data DØ data Excesses corresponding (presumably) to WW and tt Excesses corresponding (presumably) to tt No evidence for new physics Sleuth

  31. An hour’s worth of a typical conference (HCP 2002, Th Oct 10 4-5pm) basically useless

  32. How to choose a set of cuts without bias? signal region data background region

  33. D

  34. Variables Dimensional Rule of Thumb: > 10d events are needed to adequately populate a d-dimensional space Corollary: analysis should be performed in a space of dimensionality d = log10NMC Prescription: 1.Generate a long (but finite) list of relevant variables TeV:pT, , , ij, Rij, mij, mijk, mijkl LEP:E, , , ij, Rij, mij, mijk, mijkl 2.Order according to decreasing discrepancy (HvsSM) 3.Use the firstdvariables in the list, removing highly correlated variables

  35. Simplification and sample special cases Simplification and special cases Large statistics (NMC, hk) Signal + background s x b bins 1 2 Recover the familiar

  36. Penalty term Origin: wantM =0whenh = b factorizes: MC event weights # MC events # bins can be derived analytically in the case of equal weights is determined empirically (expression holds over five orders of magnitude from 101 < nMC < 106) is simply proportional to the number of bins

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