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Ensemble tests and sensitivity calculations

Ensemble tests and sensitivity calculations. Kevin Kr öninger, MPI für Physik GERDA Collaboration Meeting, Tübingen, 11/09 – 11/11/2005. Overview. Monte Carlo simulation of int. background sources ( MaGe ). Creation of ensembles according to activities. Cut-based event selection.

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Ensemble tests and sensitivity calculations

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  1. Ensemble tests and sensitivity calculations Kevin Kröninger, MPI für Physik GERDA Collaboration Meeting, Tübingen, 11/09 – 11/11/2005

  2. Overview Monte Carlo simulation of int. background sources (MaGe) Creation of ensembles according to activities Cut-based event selection Statistical analysis: Definition of discovery ↔ Limit estimation procedure Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  3. Monte Carlo Simulation • Use MaGe for the simulation of background sources (internal) • → see Xiang‘s talk and background note GSTR-05-019 • Setup is ‚ideal‘ Phase II: • 21 segmented detectors (3 z / 6 φ segments) • Total of 44.2 kg germanium • Material according to Phase II design (holder, etc.) • Energy resolution 5 keV FWHM • No primordial or muon induced neutrons included • External background from infrastructure neglected Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  4. Ensembles I • Compile list of materials used in set-up and corresponding activities • Calculate mean number of events for each background source and part • Compile ensemble: a set of events that mimic data after run-time T • Actual number of events in ensemble are Poisson fluctuated • Store time, e.g. halflife of Ge-68 taken into account (exponential decay) A : activity per mass m : mass T : run-time <N> = A · m · T Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  5. Ensembles II Phase II Holder: Copper POOL Co-60 10 μBq/kg POOL Th-232 19 μBq/kg POOL U-238 16 μBq/kg POOL K-40 88 μBq/kg x mass : (31 x 21) g x time : 1 year = 205 events 390 events 328 events 1807 events ENSEMBLE Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  6. Ensembles III 1 year run-time 2.3·10-3 counts/kg/keV/y Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  7. Ensembles IV • Compiling ensembles is CPU time intensive • Use toy ensembles: • Spectra created with flat background + Gaussian peak signal • Tested flat background hypothesis with 2500 kg·years • Vary background and signal contribution Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  8. Event Selection I • Similiar to selection done for background estimate: • Anti-coincidence between segments • Energy window ±80 keV around Qββ • X-ray veto against decay of Ge-68 • No pulse shape analysis used yet • For details on the background contributions see Note GSTR-05-019 Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  9. Statistical Analysis I • Estimate two parameters: signal (A) and background (B) • Question: What is ? • Assume flat background and Gaussian peak at Qββ with width ~ resolution • Divide energy spectrum in 1 keV bins with events ni • Expectation in ith bin Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  10. Statistical Analysis II • Apply Bayes‘ Theorem: • with Poissonian fluctuations in each bin • For details see note GSTR-05-020 Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  11. Statistical Analysis III p(A, B|{ni}) Background B [keV-1] Signal A Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  12. Statistical Analysis IV mode A* mode B* Signal A Background B [keV-1] • Marginalize w.r.t. signal (A) and background (B) Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  13. Statistical Analysis V • Definition of discovery: • Discovery potential: fraction of ensembles with discovery (Freq. prob.) • Limit estimation: integrate p(A|{ni}) to 95% probability • Test different scenarios: • Background index between 0 and 10-2 counts/kg/keV/y • Halflife between (0.8 ·1025 – 5.0 ·1026) years • Run-time between 1 and 10 years A* : most probable value 6·103 corresponds to 5 σ Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  14. Statistical Analysis VI MC simulation (best estimate) 1 year run-time Fraction of discovering ensembles Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  15. Statistical Analysis VII MC simulation (best estimate) 1 year run-time Fraction of discovering ensembles Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  16. Statistical Analysis IX 1 year run-time Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  17. Statistical Analysis X 2 σ environment of recent claim no background 10-4 counts/kg/keV/y 10-3 counts/kg/keV/y 10-2 counts/kg/keV/y Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  18. Conclusion • Ensemble test have been done with fake data sets • Statistical analysis yields following results: • Probability of observing 1.6·1025 years >95% after 1 year • … after 5 years ~5.0·1025 years • Exclusion limit after 1 years ~5.0·1025 years • … after 5 years ~ 2.0·1026 years • Results stable against resolution up to 10 keV FWHM • Results stable against miscalibration up to 2 keV • Need to be better than ~ 10-2 counts/kg/keV/y • Details can be found in note GSTR-05-020 10-3 counts/kg/keV/y Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  19. Event Selection II 1 year run-time before event selection • Signal efficiency ~90% • Resolution added • After event selection ~6% of event left after event selection Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  20. Statistical Analysis VIII Fraction of discovering ensembles Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  21. Resolution Study 1 year run-time, 2.3·10-3 counts/kg/keV/y, T1/2 = 1.6·1025 years Fraction of discovering ensembles Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

  22. Miscalibration Study 1 year run-time, 2.3·10-3 counts/kg/keV/y, T1/2 = 1.6·1025 years Fraction of discovering ensembles Kevin Kröninger, MPI München GERDA Collaboration Meeting Tübingen, 11/09 – 11/11/2005

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