0 decay to the excited state 0+ of 130Xe

Comparison of the GE and SC analyses

S. Di Domizio, December 2010

2

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

3Efficiency – scenario1 – SC – 536

= (0.82 +/- 0.03)%

4Efficiency – scenario1 – SC – 734

= (0.82 +/- 0.02)%

5Efficiency – scenario1 – SC – 1257

= (0.80 +/- 0.03)%

6Efficiency – scenario2 – SC - 1257

= (2.58 +/- 0.04)%

7Efficiency – scenario2 – SC – 1270

= (2.56 +/- 0.03)%

8Efficiency – scenario3 – SC – 536

= (1.72 +/- 0.03)%

9Efficiency – scenario3 – SC – 1991

= (1.76 +/- 0.03)%

10GE – scenario1 - 1257

Using GE algorithms and SC cuts

11GE – scenario2 - 1270

Using GE algorithms and SC cuts

12GE – scenario3 - 1257

Using GE algorithms and SC cuts

13

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

14Comparison

scenario1

scenario2

scenario3

GE SC

N·t = 9.11 x 1025 y N·t = 8.74 x 1025 y

N·t = 8.96 x 1025 y

0.60%

2.29%

1.41%

0.80%

2.58%

1.75%

scenario1

scenario2

scenario3

GE SC

0.48%

1.93%

1.19%

0.64%

2.18%

1.48%

Geometric only total (with psa, noise, etc.)

statistics

N·t = 9.50 x 1025 y

values reported in the note

Forgot to include the three “dead” channels 2, 3 and 50

“My” evaluation with “SC” method

efficiency

GE SC

15Result (GE)

Posterior pdf for

< 6.74 x 10-25 y-1 90%CL

> 1.03 x 1024 y 90%CL

16Result (SC)

Posterior pdf for

< 5.98 x 10-25 y-1 90%CL

> 1.16 x 1024 y 90%CL

17

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

18Treating the differences as syst errors

± =SC

2±

∣ S−C∣2

N · t±N ·t =N · t GEN · t SC

2±

∣N · t GE−N · t SC∣2

2= 2= 2⋅ 2

2 N · t 2

N · t 2 X syst2 =

− 2

2

P = · N · t⋅e− · N · t · X stat2 = −logP − −logP = · N · t ·

1

2= 1

stat2

1

syst2

Use the approach discussed in Adam's internal note

1

2

3

efficiency

(0.56+/-0.08)%

(2.06+/-0.13)%

(1.34+/-0.15)%

scenario

Statistics: N·t = (9.23 +/- 0.27) x 1025 y

19Result (combined)

Posterior pdf for

< 6.39 x 10-25 y-1 90%CL

> 1.09 x 1024 y 90%CL

20Summary

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

21Method 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.

22Treating the differences as syst errors

TOT= SC

2±

∣ S−C∣2

STAT TOT=STAT SSTAT C

2±

∣STAT S−STAT C∣2

= counts⋅STAT

2= 2= 2⋅ 2

2 STAT

2

STAT 2 X syst2 =

− 2

2 = 1

2

2 STAT

2

STAT 2

P counts = e−counts P = ⋅STAT⋅e−⋅STAT⋅

X stat2 = −log P − −logP = ⋅STAT⋅

1

2 = 1

stat2 1

syst2 = 1

⋅STAT⋅ 2

2 STAT

2

STAT 2

P syst =e

− ⋅STAT⋅

1⋅STAT⋅⋅1

syst2