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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.

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The maximum likelihood method used to analyse NEMO-3 results

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  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

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