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## 0 nbb decay to the excited state 0 + of 130 Xe

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**0nbb decay to the excited state 0+ of 130Xe**Comparison of the GE and SC analyses S. Di Domizio, December 2010**Part 1: comparison of the methods**In the following slides I will evaluate the efficiencies using the SC cuts with the GE and SC algorithms**Efficiency – scenario1 – SC – 536**e = (0.82 +/- 0.03)%**Efficiency – scenario1 – SC – 734**e = (0.82 +/- 0.02)%**Efficiency – scenario1 – SC – 1257**e = (0.80 +/- 0.03)%**Efficiency – scenario2 – SC - 1257**e = (2.58 +/- 0.04)%**Efficiency – scenario2 – SC – 1270**e = (2.56 +/- 0.03)%**Efficiency – scenario3 – SC – 536**e = (1.72 +/- 0.03)%**Efficiency – scenario3 – SC – 1991**e = (1.76 +/- 0.03)%**GE – scenario1 - 1257**Using GE algorithms and SC cuts**GE – scenario2 - 1270**Using GE algorithms and SC cuts**GE – scenario3 - 1257**Using GE algorithms and SC cuts**Part 2: comparison of the results**In the following slides I will summarize the differences in the two approaches and will extract the half life limits**Comparison**statistics GE SC N·t = 9.11 x 1025 y N·t = 8.74 x 1025 y values reported in the note N·t = 9.50 x 1025 y N·t = 8.96 x 1025 y Forgot to include the three “dead” channels 2, 3 and 50 “My” evaluation with “SC” method efficiency Geometric only total (with psa, noise, etc.) GE SC GE SC scenario1 0.60% 0.80% scenario1 0.48% 0.64% scenario2 2.29% 2.58% scenario2 1.93% 2.18% scenario3 1.41% 1.75% scenario3 1.19% 1.48%**Result (GE)**G < 6.74 x 10-25 y-1 90%CL T1/2 > 1.03 x 1024 y 90%CL Posterior pdf for G**Result (SC)**G < 5.98 x 10-25 y-1 90%CL T1/2 > 1.16 x 1024 y 90%CL Posterior pdf for G**Part 3: the approach proposed by Frank**In the following slides I will show the method and the results I obtained by treating the difference between GE and SC analysis as a systematic error**Treating the differences as syst errors**Use the approach discussed in Adam's internal note scenario efficiency 1 (0.56+/-0.08)% Statistics: N·t = (9.23 +/- 0.27) x 1025 y 2 (2.06+/-0.13)% 3 (1.34+/-0.15)%**Result (combined)**G < 6.39 x 10-25 y-1 90%CL T1/2 > 1.09 x 1024 y 90%CL Posterior pdf for G**Summary**GE: T1/2 > 1.0 x 1024 y @90%CL SC: T1/2 > 1.2 x 1024 y @90%CL GE+SC: T1/2 > 1.1 x 1024 y @90%CL**Method comparison**Consider the limit case of an experiment with two crystals where one has 100% dead time and the other has 0 dead time. Since no coincidences can be recorded in these conditions, the number of signal and background counts will be zero. The SC approach would give a finite value for both the efficiency and the accumulated statistics, thus resulting in a non trivial limit for the half life of the process. The GE approach would give a finite value for the statistics and a null value for the efficiency, therefore nothing can be said about the half life of the process.