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 

3. P( event i)= x  P o  + x radon P radon + x int 208Tl P int 208Tl + … + (1- x  - x radon - x int 208Tl - …) P 2 Method of fit of the  fraction For each signal/background P is obtained from simulation P = P(Etot)P(Emin/Etot)P(cos  /Emin) L = Maximize L as a function of x  Fixed with channels with higher statistics

4. List of processes taken into account radon (in fact 214 Bi) emitted from the tracking volume or deposited on the foil surface 208 Tl in the sources 214 Bi in the sources 208 Tl in the glass of the PMTs 214 Bi in the glass of the PMTs Signal either  from or  from V+A process or  Majoron  Backgrounds

5. Parametrisation of Etot

6. Fit of  2 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

8. Fit between 2.7 and 3.1 MeV Etot/me

9. Fit between 3.1 and 3.27 MeV Etot/me

10. Fit of  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 208 Tl 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) Fit of Emin in bins of Etot for  for 0.36 MeV<Emin<Etot/2 analogy with Doi : P(E1,E2) = E 1 p 1 E 2 p 2 2 parameters to fit as a function of Etot

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 

26. 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 Parameterization of Emin for V+A

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

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

34. 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

35. 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

36. 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

37. Fit of the parameters as a function of Emin for 

42. radon activity is measured in the tracking detector using the e -  channel A(radon in the tracking volume) ~0.95 Bq (high- radon period), 0.14 Bq(low- radon period) Fraction of the backgrounds (except  ) 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

43. 208 Tl fraction from 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 208 Tl in the sources is derived 208 Tl activity in the sources is measured using the e - 2  and e - 3  channel A( 208 Tl) from the 100 Mo sources ~ 100  Bq/kg

44. Limits obtained for 25 MC samples after 5 years for 100Mo, with : T(1/2)(  ) = 7.7 10 18 y A(208Tl internal) = 100  Bq/kg A(214Bi internal) = 300  Bq/kg no radon

45. T ½  limits with window,1D,2D,3D likelihood Window 2900-3300 keV In corrected energy (gas…) 1.3 10 24 y 1D likelihood Etot 1.1 10 24 y 2D likelihood Etot, Emin 1.3 10 24 y 3D likelihood Etot, Emin cos  1.3 10 24 y

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

47. T ½ V+A limits with window,1D,2D,3D likelihood Window 2900-3300 keV In corrected energy (gas…) 0.5 10 24 y 1D likelihood Etot 0.5 10 24 y 2D likelihood Etot, Emin 0.7 10 24 y 3D likelihood Etot, Emin cos  0.8 10 24 y

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

49. Very preliminary results for likelihood for 100 Mo : low radon period 3D Likelihood (90% CL) T ½ (  3 10 23 y T ½ (V+A) > 2.2 10 23 y Window (90% CL) 2.9 MeV-3.3 MeV in corrected energy Nexpected = 2.6 Nobserved = 2 Nexcluded = 3.7 T ½ (  3.6 10 23 y T ½ (V+A) > 1.5 10 23 y 2D Likelihood (90% CL) T ½ (  3 10 23 y T ½ (V+A) > 2.3 10 23 y 1D Likelihood (90% CL) T ½ (  3.5 10 23 y T ½ (V+A) > 1.6 10 23 y 6452 events above 2 MeV(dec 04 -> mar 06 : 257.1 days)

50. Etot Emin cos  3

51. Very preliminary results for likelihood for 82 Se : low radon period 3D Likelihood (90% CL) T ½ (  2.2 10 23 y T ½ (V+A) > 1.2 10 23 y Window (90% CL) 2.8 MeV-3.3 MeV in corrected energy Nexpected = 1 Nobserved = 0 Nexcluded = 2.3 T ½ (  1.6 10 23 y T ½ (V+A) > 0.7 10 23 y 2D Likelihood (90% CL) T ½ (  2.1 10 23 y T ½ (V+A) > 1.2 10 23 y 1D Likelihood (90% CL) T ½ (  2.1 10 23 y T ½ (V+A) > 1 10 23 y 115 events above 2 MeV (dec 04 -> mar 06 : 257.1 days)

52. Etot Emin cos 

53. Conclusion method to take into account all information from a tracko-calo detector (not only total energy deposited, but also individual energies, angle) Gain in sensitivity obtained for the V+A process, mainly by using Emin information