Combining and comparing neutrinoless double beta decay experiments using. using different nuclei

Transcription

1 Combining and comparing neutrinoless double beta decay experiments using different nuclei Department of Theoretical Physics, KTH Royal Institute of Technology January 2013

2 Based on: different nuclei arxiv: (18 Dec 2012)

3 Outline 1 Introduction

4 Introduction Neutrino oscillations require at least two out of the three SM neutrinos to be massive. If Majorana, neutrinoless double beta decay of heavy nuclei can occur with half-life T 1 N = G N M N 2 mee, 2 (1) m ee (M ν) ee = U 2 eim i = m 1c12c m 2s12c 2 13e 2 2iα +m 3s13e 2 2iβ (2) i Nuclear matrix elements (NMEs) M N are very difficult to calcuate large theoretical uncertainties.

5 Introduction No generally excepted detection, but subset of Heidelberg-Moscow collaboration has made a claim, using 76 Ge and their own optimized event selection algorithms. (m ee = O(0.3) ev ) Untested by independent experiments for long time.

6 Introduction No generally excepted detection, but subset of Heidelberg-Moscow collaboration has made a claim, using 76 Ge and their own optimized event selection algorithms. (m ee = O(0.3) ev ) Untested by independent experiments for long time. Recently competitive experiments using 136 Xe have released data. Comparison only possible within a particle physics model, and Xe and Ge have different NMEs, both with large uncertainties. In a comparison of Ge and Xe data, the statistical uncertainty of both data sets as well as the NMEs should be considered. Not done by experimental collaborations.

7 Introduction No generally excepted detection, but subset of Heidelberg-Moscow collaboration has made a claim, using 76 Ge and their own optimized event selection algorithms. (m ee = O(0.3) ev ) Untested by independent experiments for long time. Recently competitive experiments using 136 Xe have released data. Comparison only possible within a particle physics model, and Xe and Ge have different NMEs, both with large uncertainties. In a comparison of Ge and Xe data, the statistical uncertainty of both data sets as well as the NMEs should be considered. Not done by experimental collaborations. Frequentist analysis could fix NMEs and calculate a p-value assuming consistency. Bayesian analysis can furthermore consider NME uncertainties, and also give actual probability of consistency.

8 Introduction Allows probability of hypotheses and makes powerful inference tools available. General aim (of science): select between hypotheses (H i) r i=1, using observed data D.

9 Introduction Allows probability of hypotheses and makes powerful inference tools available. General aim (of science): select between hypotheses (H i) r i=1, using observed data D. Bayesian solution: use Bayes theorem Implies that the odds Pr(H i D) = Pr(D Hi)Pr(Hi). (3) Pr(D) Pr(H i D) Pr(H = Pr(D Hi) Pr(H i) j D) Pr(D H j) Pr(H = Zi Pr(H i) j) Z j Pr(H. (4) j)

10 Introduction Allows probability of hypotheses and makes powerful inference tools available. General aim (of science): select between hypotheses (H i) r i=1, using observed data D. Bayesian solution: use Bayes theorem Implies that the odds Pr(H i D) = Pr(D Hi)Pr(Hi). (3) Pr(D) Pr(H i D) Pr(H = Pr(D Hi) Pr(H i) j D) Pr(D H j) Pr(H = Zi Pr(H i) j) Z j Pr(H. (4) j) For complex hypotheses with free parameters Θ, the evidence Z Pr(D H) = Pr(D Θ,H)Pr(Θ H)d N Θ = L(Θ)π(Θ)d N Θ (5) L = likelihood, π = prior.

11 log(odds) odds Pr(H 1 D) Interpretation < : Inconclusive : Weak evidence : Moderate evidence : Strong evidence Within a model, the posterior distribution of the parameters are Pr(Θ D,H) = Pr(D Θ,H)Pr(Θ H) Pr(D H) = L(Θ)π(Θ), (6) Z NOTE: Evaluation of posterior only relevant if the evidence is not very small! The evidence comes first, and then possibly the posterior.

12 Bayesian consistency test Test the consistency of D test = (D 1,D 2,...,D k ), within H and given D bkg (a set of possible background data) Perform model selection between C (consistent) and C (inconsistent), with Bayes factor (k = 2) R = Our case: Pr(D 1,D 2 D bkg,h) Pr(D 1 D bkg,h)pr(d 2 D bkg,h) = Pr(D1,D2,D bkg H)Pr(D bkg H) Pr(D 1,D bkg H)Pr(D 2,D bkg H) H= Majorana neutrinos D 1 = claim using 76 Ge D 2 = recent measurements using 136 Xe D bkg = neutrino oscillations + beta decay

13 First, reanalyze the spectrum of the final claim. 6 5 Data Orginal fit Maximum likelihood Posterior mean, s ~ U(0,30) Posterior mean, s ~ Log(0.1,30) 4 Counts/keV E 0 /kev

14 Interesting exercise in statistiscs. Let H 0 : Only constant background. H 1 : Background + line somewhere in the spectrum. H 2 : Background + line close to Q-value ( kev).

15 Interesting exercise in statistiscs. Let H 0 : Only constant background. H 1 : Background + line somewhere in the spectrum. H 2 : Background + line close to Q-value ( kev). Strong evidence for H 1 vs. H 0, but only moderate for H 2 vs. H 1 Much larger statistical error on signal strength than original analysis. Must be taken into account when comparing with other data but not done by EXO nor KamLAND-Zen.

16 Parameter constraints 2040 E 0 /kev b lg(σ/kev) s E 0 /kev b lg(σ/kev)

17 Global fit: parameters and priors 14 parameters: mixing angles + phases + mij s 2 + m 0 + NMEs + experimental nuisance. Sensitive to priors on m 0 and the two NMEs. Two priors on m 0: log prior (A) and prior 1/ m 0 (B) Correlated 2D prior on the NMEs specified by the relative uncertainty and the relative uncertainty on the ratios of NMEs (believed to be more accurately known)

18 Parameter constraints using background data normal, m 0 A normal, m 0 B inverted, m 0 A inverted, m 0 B Posterior lg(m ee /ev)

19 Parameter constraints using Ge and Xe data Ge, fixed Ge, conservative Xe, fixed Xe, conservative all, fixed all, conservative Posterior Posterior lg(m /ev) lg(m /ev) ee ee

20 2D parameter constraints: samples from posterior Using Ge Using Xe M Ge 6 M Ge lg(m /ev) ee lg(m /ev) ee

21 Consistency test (σ M,σ r) = (1,1) (1.15,1.1) (1.3,1.1) (1.3,1.25) m 0 A m 0 B Moderate to strong evidence against consistency: logr [ 4.35, 3.68], R 1 [40,80] (7) D Ge and D Xe are about 40 to 80 times more probable under the hypothesis that they are incompatible. Equal prior probabilities yields posterior probability of consistency Pr(C D Ge,D Xe,D bkg ) = 1.3% 2.5%. (8)

22 Global fit of neutrinoless double beta decay data within SM with Majorana neutrinos. Taken into account all the relevant statistical and NME uncertainties. Strong evidence for a signal in the claimed data. Moderate to strong evidence against consistency with recent Xe data. Check out:,combining and comparing neutrinoless double beta decay experiments using different nuclei, arxiv:

23 Thanks for listening! Thanks for listening! Questions?