1 / 53

The maximum likelihood method used to analyse NEMO-3 results

The maximum likelihood method used to analyse NEMO-3 results. interest of the method technical explanation of the method very preliminary results obtained. Laurent SIMARD, LAL-ORSAY ILIAS Prague meeting, 20-21/04/06. Interest of the method.

archer
Download Presentation

The maximum likelihood method used to analyse NEMO-3 results

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The maximum likelihood method used to analyse NEMO-3 results interest of the method technical explanation of the method very preliminary results obtained Laurent SIMARD, LAL-ORSAY ILIAS Prague meeting, 20-21/04/06

  2. Interest of the method not a simple counting method, use the information of all 2e- events in the spectrum above 2 MeV Use all information from the events, not only Etot = E1 + E2, but also E1, E2, cos q

  3. Maximize L as a function of x0n L = P(event i)= x0nPon + xradonPradon + x int 208Tl P int 208Tl + … + (1-x0n- xradon - x int 208Tl - …) P2n Fixed with channels with higher statistics For each signal/background P is obtained from simulation P = P(Etot)P(Emin/Etot)P(cos q/Emin) Method of fit of the 0n fraction

  4. Signal • either bb0n from <mn> • or bb0n from V+A process • or bbc (Majoron) List of processes taken into account • radon (in fact 214Bi) emitted from the tracking volume or deposited on the foil surface • 208Tl in the sources • 214Bi in the sources • 208Tl in the glass of the PMTs • 214Bi in the glass of the PMTs Backgrounds

  5. Parametrisation of Etot

  6. Fit of bb2n SSD Monte Carlo used • 500 000 000 events • 10 000 000 events between 1.8 and 2.1 MeV • 10 000 000 events between 2.1 and 2.4 MeV • 10 000 000 events between 2.4 and 2.7 MeV • 10 000 000 events between 2.7 and 2.9 MeV • 10 000 000 events between 2.9 and 3 MeV • 10 000 000 events between 3 and 3.1 MeV weights to add these MC calculated from the theoretical formula (taken from the simulation)

  7. Fit between 2 and 2.7 MeV Etot/me Etot/me

  8. Fit between 2.7 and 3.1 MeV Etot/me Etot/me

  9. Fit between 3.1 and 3.27 MeV Etot/me Etot/me

  10. Fit of bb0n Monte Carlo used : 10 000 000 events Etot/me

  11. Fit between 2 and 2.76 MeV Etot/me

  12. Fit between 2.76 and 2.81 MeV Etot/me

  13. Fit between 2.81 and 4.1MeV Etot/me

  14. Fit of 208Tl internal Monte Carlo used : 675 000 000 events

  15. Fit between 2 and 2.04 MeV Etot/me

  16. Fit between 2.04 and 2.15 MeV Etot/me

  17. Fit between 2.15 and 3.07 MeV Etot/me

  18. Fit between 3.07 and 4.34 MeV Etot/me

  19. Parametrisation of Emin/Etot The Monte Carlo statistics above 2 MeV in Etot is divided in bins of 50 keV width • For each signal or background 2 steps : • fit Emin for each bin of Etot with some parameters • then fit the parameters as a function of Etot

  20. for 0.26 MeV < Emin < 0.36 MeV : threshold effect (cut at 200 keV) for 0.36 MeV<Emin<Etot/2 analogy with Doi : P(E1,E2) = E1p1E2p2 2 parameters to fit as a function of Etot Fit of Emin in bins of Etot for bb2n

  21. 2 MeV<Etot<2.05 MeV 2.05 MeV<Etot<2.1 MeV 2.1 MeV<Etot<2.15 MeV 2.15 MeV<Etot<2.2 MeV

  22. 2.4 MeV<Etot<2.45 MeV 2.45 MeV<Etot<2.5 MeV 2.5 MeV<Etot<2.55 MeV 2.55 MeV<Etot<2.6 MeV

  23. 2.8 MeV<Etot<2.85 MeV 2.85 MeV<Etot<2.9 MeV 2.9 MeV<Etot<2.95 MeV 2.95 MeV<Etot<3MeV

  24. Fit of the parameters as a function of Etot for bb2n

  25. Parameterization of Emin for V+A 2 MeV<Etot<2.05 MeV 2.05 MeV<Etot<2.1 MeV 2.1 MeV<Etot<2.15 MeV 2.15 MeV<Etot<2.2 MeV

  26. 2.2 MeV<Etot<2.25 MeV 2.25 MeV<Etot<2.3 MeV 2.3 MeV<Etot<2.35 MeV 2.35 MeV<Etot<2.4 MeV

  27. 2.4 MeV<Etot<2.45 MeV 2.45 MeV<Etot<2.5 MeV 2.5 MeV<Etot<2.55 MeV 2.55 MeV<Etot<2.6 MeV

  28. 2.6 MeV<Etot<2.65 MeV 2.65 MeV<Etot<2.7 MeV 2.7 MeV<Etot<2.75 MeV 2.75 MeV<Etot<2.8 MeV

  29. 2.8 MeV<Etot<2.85 MeV 2.85 MeV<Etot<2.9 MeV 2.9 MeV<Etot<2.95 MeV 2.95 MeV<Etot<3 MeV

  30. 3 MeV<Etot<3.05 MeV 3.05 MeV<Etot<3.1 MeV 3.1 MeV<Etot<3.15 MeV 3.15 MeV<Etot<3.2 MeV

  31. 3.2 MeV<Etot<3.25 MeV 3.25 MeV<Etot<3.3 MeV 3.3 MeV<Etot<3.35 MeV 3.35 MeV<Etot<3.4 MeV

  32. Fits of cos q/Emin The Monte Carlo statistics above 0.25 MeV in Emin is divided in bins of 50 keV width Same formula for all processes For -1<cos q<0.9 P(cos q/Emin) = const ( 1 – coef1(cos q) + coef2 (cos q)2 + coef3 (cos q)3 + coef4 (cos q)4) For –0.9<cos q parameters to fit as a function of Emin P(cos q/Emin) =pente (racine - cos q) try to use derive formulae from Doi for bb0n and bb2n

  33. 0.25 MeV<Emin<0.3 MeV 0.3 MeV<Emin<0.35 MeV 0.35 MeV<Emin<0.4 MeV 0.4 MeV<Emin<0.45 MeV

  34. 0.85 MeV<Emin<0.9 MeV 0.9 MeV<Emin<0.95 MeV 0.95 MeV<Emin<1 MeV 1 MeV<Emin<1.05 MeV

  35. 1.05 MeV<Emin<1.1 MeV 1.1 MeV<Emin<1.15 MeV 1.15 MeV<Emin<1.2 MeV 1.2 MeV<Emin<1.25 MeV

  36. Fit of the parameters as a function of Emin for bb2n

  37. Fit of the parameters as a function of Emin for bb2n

  38. radon activity is measured in the tracking detector using the e-a channel A(radon in the tracking volume) ~0.95 Bq (high-radon period), 0.14 Bq(low-radon period) Fraction of the backgrounds (except bb2n) is fixed using dedicated higher-statistics channels Example : radon fraction which contribute to the 2e- channel above 2 MeV Then using simulation, the expected number of 2e - events above 2 MeV due to radon is derived

  39. 208Tl activity in the sources is measured using the e-2g and e-3g channel A(208Tl) from the 100Mo sources ~ 100 mBq/kg 208Tl fractionfrom the sources which contribute to the 2e- channel above 2 MeV Then using simulation, the expected number of 2e - events above 2 MeV due to 208Tl in the sources is derived

  40. Limits obtained for 25 MC samples after 5 years for 100Mo, with: T(1/2)(bb2n) = 7.7 1018 y A(208Tl internal) = 100 mBq/kg A(214Bi internal) = 300 mBq/kg no radon

  41. T ½bb0n limits with window,1D,2D,3D likelihood 1D likelihood Etot 1.1 1024 y Window 2900-3300 keV In corrected energy (gas…) 1.3 1024 y 2D likelihood Etot, Emin 1.3 1024 y 3D likelihood Etot, Emin cos q 1.3 1024 y

  42. Correlations between T ½bb0n limits gain when adding Emin ~ same limit with window or 3D-lik

  43. T ½V+A limits with window,1D,2D,3D likelihood 1D likelihood Etot 0.5 1024 y Window 2900-3300 keV In corrected energy (gas…) 0.5 1024 y 2D likelihood Etot, Emin 0.7 1024 y 3D likelihood Etot, Emin cos q 0.8 1024 y

  44. Correlations between T ½V+A limits gain when adding Emin Better limit with 3D-lik than for window

  45. Window (90% CL) 2.9 MeV-3.3 MeV in corrected energy Nexpected = 2.6 Nobserved = 2 Nexcluded = 3.7 T½ (bb0n <mn>) > 3.6 1023 y T½ (V+A) > 1.5 1023 y 3D Likelihood (90% CL) T½ (bb0n <mn>) > 3 1023 y T½ (V+A) > 2.2 1023 y 2D Likelihood (90% CL) T½ (bb0n <mn>) > 3 1023 y T½ (V+A) > 2.3 1023 y 1D Likelihood (90% CL) T½ (bb0n <mn>) > 3.5 1023 y T½ (V+A) > 1.6 1023 y Very preliminary results for likelihood for 100Mo: low radon period 6452 events above 2 MeV(dec 04 -> mar 06 : 257.1 days)

  46. Etot Etot 3 Emin cos q

More Related