1. Rare Charm Decays from FOCUS Angel M. López University of Puerto Rico (Mayaguez) Outline  Theory – Why Study These Decays?  Basic Blind Analysis Methodology  Event Selection  Problem – Background Fluctuations  Affect Limit Calculations  Affect Cut Optimization  Improved Analysis Methodology - Solutions  Include background statistics  Dual Bootstrap  Results EPS2003 July 19, 2003 – Aachen, Germany

3. Results Based on the Analysis Work of: Daniel Engh Vanderbilt University Hugo Hernandez University of Puerto Rico

4. Successor to E687. Designed to study charm particles produced by ~200 GeV photons using a fixed target spectrometer with upgraded Vertexing, Cerenkov, E+M Calorimetry, and Muon id capabilities. 1 million charm particles reconstructed into D  K , K2 , K3  Over 1 million reconstructed!!

5. Excellent Particle ID and Vertexing “kaonicity” kaonspions 405511 signal events Decays/200  m BeO tarsil primary vtx secondary vtx Super efficient- low noise muon id Flexible Cerenkov identification: - Study mis-id backgrounds Segmented target: - 62% of charm decay in air. Excellent lifetime resolve (8% D0) physics running Requiring out-of-target secondary vertices massively reduces non- charm backgrounds.

6. Search for New Physics in Two Categories of Decays FCNC D +  K + l + l – D +   + l + l – D s +  K + l + l – D s +   + l + l – D 0  l + l – LNV D +  K - l + l + D +   - l + l + D s +  K - l + l + D s +   - l + l +

7. FCNC Charm Decays In SM Short Distance Diagrams are Small 10 -19 10 -16 10 -8 Short Distance

8. FCNC Charm Decays 10 -13 10 -8 10 -6 Long Distance Enhancement from SM Long Distance Effects Lepton Number Violating Decays are Forbidden

10. In some cases, we have predictions from new physics MSSM R-Parity Violating Terms Boost FCNC Rates [hep-ph/0112235 v2] -Look for new Physics!- (Burdman, Golowich, Hewett, Pakvasa) (Away from poles!)

11. Decay Fraction Previous (E791) MSSM R-Parity SM-1SM-2 D+ ++-D+ ++- 4.4x10 -5 7.1x10 -9 D+ -++D+ -++ 12x10 -5 D+ ++-D+ ++- 1.5x10 -5 1.9x10 -6 1.0x10 -6 D+ -++D+ -++ 1.7x10 -5 Ds+ ++-Ds+ ++- 1.4x10 -4 4.3x10 -8 Ds+ -++Ds+ -++ 1.8x10 -4 Ds+ ++-Ds+ ++- 1.4x10 -4 6.1x10 -6 Ds+ -++Ds+ -++ 0.8x10 -4 D0 +-D0 +- 4.1x10 -6 3.5x10 -6 3.0x10 -13 Previous Limits and Recent Theoretical Predictions S. Fajfer, S. Prelovsek and P. Singer Phys. Rev. D Volume 64, 114009 (2001) [hep-ph/0112235 v2] (Burdman, Golowich, Hewett, Pakvasa) Share SM formalism (E687)

12. Basic Blind Analysis Skim data with loose cuts. Consider all tight cut combinations in a cut grid. Data sidebands are used to optimize cuts. Data sidebands are also used to estimate background. Open box. Look at signal region. Calculate confidence limits from Feldman-Cousins table. Problems: Feldman-Cousins does not consider statistical uncertainty in background estimate. Use of the same data to both select cuts and to estimate background biases the latter.

13. Event Selection Criteria Vertexing (Candidate driven) –Secondary vertex Confidence Level (CLS) Isolation - No other tracks come from that vertex. (ISOS) –Primary vertex Require consistent with D track from secondary Confidence Level (CLP) Require a minimum multiplicity Isolation - No tracks from secondary are consistent with coming from the primary.(ISOP) In target (z position) –Detachment (L/  )

14. More Event Selection Criteria Muon Identification –Number of Muon Planes with Hits (Mupl) –Confidence Level (MuCL) –Minimum momentum –Not consistent with being a kaon. Hadron identification – Triple Cerenkov System –Log likelihood for consistency between Cerenkov hits and a particular particle id hypothesis –Compare log likelihoods for different species (Kaonicity)

15. Fixed (loose) Cuts for Two Body Mode Vertexing –CLP and CLS > 1% –Primary Multiplicity > 2 –L/  > 3 Muon Identification –Mupl  4 –MuCL > 1%

16. An Example Dimuon Mass Distributions with Loose Cuts Fairly clean even with loose cuts but can be improved. Signal area (±2  ) has been masked in data (blind analysis).

17. Cut Grid for Three Body Modes L/  – vary from >5-21 L pp ss ISOP – CL DK’s in prim (vary <0.1 –0.001) Vary Cerenkov cuts for  ’s and K’s (likelihood differences) CLS – CL of DK vertex (>1 -- 4%) MuCL – CL for Muon ID (>1 – 10%) Cut on  P, (bigger MCS, more h-  at low P)

18. Normalize to Golden/Silver modes Ds+  +-+Ds+  +-+ D+  -+-D+  -+- (loosest cuts) D0  -+D0  -+

19. Cut Optimization Used the “experimental sensitivity” as the figure of merit. (Branching Ratio) (Sensitivity) N L is the average of the 90% upper limit for an ensemble of experiments with zero signal and the background rate estimated from the sidebands. Does not depend on signal. Qualifies as a blind analysis.

20. Mass Distributions for Typical Tight Cuts There are two events in the sidebands.

21. Solution to First Problem W. Rolke and A. Lopez, NIM-A458:745(2001) Probability of observing x events in a signal region and y events in background sidebands given a signal rate , a background rate in the signal region b, and a ratio of the background in the sidebands to the signal region  :

22. Example of a 90% Confidence Intervals Table Including Uncertainty in Background Estimate The number of events in the signal region is x. The background is estimated as y /  from an observation of y sideband events. This table is for the case  = 2.

23. Solution to Second Problem Dual Bootstrap (sample with replacement) W. Rolke and A. Lopez – NIM-A503:617(2003) It’s still a blind analysis!

24. After 1 st Bootstrap After 2 nd Bootstrap Raw Cut Grid Sensitivities D +   +  +  - Typical Dual Bootstrap Results Preliminary Raw BR Upper Limits (All Cuts)

25. Typical Mass Plots - Average Best Cuts Signal Excluded

26. Decay Mode Dual Bootstrap Sensitivity Sys. Error Result W/sys Previous (E791) D+ ++-D+ ++- 9.17.57.5%9.244 D+ -++D+ -++ 134.87.5%13120 D+ ++-D+ ++- 8.77.67.5%8.815 D+ -++D+ -++ 4.85.67.5%4.817 Ds+ ++-Ds+ ++- 33 27.5%36140 Ds+ -++Ds+ -++ 132127.5%13180 Ds+ ++-Ds+ ++- 243127.5%26140 Ds+ -++Ds+ -++ 262327.5%2980 (E687) Dominated by PDG rate to normalizing mode Final Results from FOCUS – Submitted to PLB BR 90% Upper Limits x 10 6

27. Closing in on Long range SM predictions Sets MSSM constraint Close to Long Distance Predictions Lots of Room At the bottom!   Preliminary FOCUS D 0   +  - Sensitivity – 2.3x10 -6.

28. SUMMARY (1) An improved methodology for the analysis of small signals has been developed. (2) FOCUS obtains upper limits for several rare and forbidden decays which are approximately an order of magnitude lower than existing. (3) FOCUS FCNC limits are below R-parity violating MSSM model predictions.

30. Cut Grid for Two Body Mode Vertexing L/  > 5, 7, 9 CLS > 1%, 5%, 10% ISOS < 10 -4, 10 -3, 10 -2 ISOP < 10 -4, 10 -3, 10 -2 Distance of primary outside target edge < 0, 2 Muon Identification Mupl  4, 5, 6 MuCL > 1%, 3%, 5% Kaonicity < 2, 5, 8

31. A reminder during “Journeys of an Accidental Statistician” [Gary Feldman, Fermilab conference on CL, March 2000] from the 1998 PDG [Euro. Phys. J. C3(1998)]: “…we suggest that… a measure of sensitivity should be reported whenever expected background is larger or comparable to the number of observed counts.”

32. Data from 96-97 run of FOCUS Over 1,000,000 Reco’d. Charm Excellent: -Vertex Resolution -Particle ID -Momentum Res. -Lots of Pubs… FOCUS Detector References: [NIM A320(1992) 519] [NIM A329(1993) 62] [hep-ex/0108011] [hep-ex/0109028] [hep-ex/0204023]

33. Improvements to Small Signal Search Methodology Handling of Background Fluctuations 1. In predicting background in the signal region. Good cuts minimize background and often lead to background samples with limited statistics. Previously existing method (Feldman-Cousins) does not take into account background uncertainty. Our method (NIM-A458:745-758) provides the correct statistical treatment and always gives physical limits with the correct coverage. 2. In the selection of optimum cuts. In a blind analysis, cuts are optimized on background but fluctuations bias the background prediction. The basic problem is that the same sample is used for optimization and for prediction. A solution based on the “bootstrap” procedure has been submitted to NIM. Bootstrap means sampling with replacement. In our “dual bootstrap” one sample is used for optimization and another for prediction.