DBD matrix elements

• Welcome and aim of the workshop

• Experimental situation• Outcome

• (A,Z) (A,Z+2) + 2 e- + 2e 2 • (A,Z) (A,Z+2) + 2 e- 0

-

0+0+

1+

(A,Z)(A,Z+1)

(A,Z+2)

0: Only possible if neutrinos are Majorana particles

In nature there are 35 isotopes

Double beta decay

2: Seen in 9 isotopes, important for nuclear physics input

3 Flavour oscillations (PMNS)

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⇒⇒⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

τ

μ

τττ

μμμ

τ

μ

e2i

3

2

1

321

321

3e2e1ee

E2

m

UUU

UUU

UUU

Analogous to CKM matrix

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U =

cosθ12 sinθ12 0

−sinθ12 cosθ12 0

0 0 1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

cosθ13 0 sinθ13e−iδ

0 1 0

−sinθ13eiδ 0 cosθ13

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

1 0 0

0 cosθ23 sinθ23

0 −sinθ23 cosθ23

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

1 0 0

0 eiα 21 0

0 0 e iα 31

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Double beta decay: Effective Majorana neutrino mass

ki

kekk

kekee meUmUmm ekα

∑∑ ==≡22

relative CP phases = 1

Neutrino mass hierarchiesNORMAL INVERTED

„inverted“ mass hierarchy m3 < m1 < m2

hierarchical

quasi-degenerate

Neutrino mass schemes and DBD „normal“ mass hierarchy m1<m2<m3

almost degenerate neutrinos m1≈ m2≈ m3

Spectral shapes

Sum energy spectrum of both electrons

0: Peak at Q-value of nuclear transition

T1/2 a • (M•t/E•B)1/2

1 / T1/2 = PS * ME2 * (m / me)2

Measured quantity: Half-life

Dependencies (BG limited)

link to neutrino mass

Heidelberg -Moscow• Five Ge diodes (overall mass 10.9 kg) Five Ge diodes (overall mass 10.9 kg) isotopically enriched ( 86%) in isotopically enriched ( 86%) in 7676GeGe • Lead box and nitrogen flushing ofLead box and nitrogen flushing of the detectors the detectors • Digital Pulse ShapeDigital Pulse Shape Analysis (factor 5 reductionAnalysis (factor 5 reduction)) Peak at 2039 keVPeak at 2039 keV

Evidence ?

H.V. Klapdor-Kleingrothaus et al, PLB 586,198 (2004)

Running experiments

DBD Q-value

CUORICINO: cryogenic bolometers40.7 kg TeO2

Future: CUORE760 kg TeO2

approved

NEMO-3: TPC

10 kg enriched foils,6 kg 100Mo

Idea: Super-NEMO (100 kg)

T1/2 > 1.8 x 1024 yr (90% CL) Arnaboldi et al, hep-ex/050134

T1/2 > 3.1 x 1023 yr (90% CL) Arnold et al, Pis‘ma v ZhETF, 80, 429 (2004)

The 64 detector arrayAim for next 2 years: The next step towards a large scale experiment,Scalable modular design, explore coincidences

Include:CoolingNitrogen flushing

Mass factor 16 higher,about 0.4 kg CdZnTe

Physics: - Can access2ECEC in theoreticallypredicted region-Precision measurement of 113Cd- New limitsPart of the detectors at Dortmund

0 Experimental Situation

Experiment Isotope T1/20 (y) <m> (eV)

You Ke et al. 1998 48Ca > 9.5 1021 (76%) < 8.3Klapdor-Kleingrothaus 2001 76Ge > 1.9 1025 < 0.35Aalseth et al 2002 > 1.57 1025 < 0.33 - 1.35Arnold et al. 2004 82Se > 1.3 x 1023 < 1.5-3.1Arnold et al. 2004 100Mo >3.1 1023 < 0.33-0.84Danevich et al. 2000 116Cd > 1 1023 < 2.2Bernatowicz et al. 1993 130/128Te* (3.52 0.11) 10-4 < 1.1 – 1.5Bernatowicz et al. 1993 128Te* > 7.7 1024 < 1.1 – 1.5Arnaboldi et al. 2005 130Te > 1.8 1024 < 0.5 – 1.1Luescher et al. 1998 136Xe > 4.4 1023 < 1.8 – 5.2Belli et al. 2001 136Xe > 7 1023 < 1.4 – 4.1De Silva et al. 1997 150Nd > 1.2 1021 < 3Danevich et al. 2001 160Gd > 1.3 1021 < 26

2 main experimental approaches2 main experimental approaches::

• Active SourceActive Source• Passive SourcePassive Source

Best 0Best 022 results involve active source experiments results involve active source experiments

2 Experimental situation

Isotope T1/22(y)

MGT2 (MeV-

1)48Ca (4.25 1.6) 1019 0.0576Ge (1.38 0.14) 1021 0.1582Se (8.9 1.0) 1019 0.1096Zr (1.43+3.4

-0.8) 1019 0.12100Mo (8.2 0.6) 1018 0.22

100Mo(0+*) (6.8 1.2) 1020 0.1116Cd (3.2 0.3) 1019 0.12128Te (7.2 0.3) 1024 0.025130Te (2.7 0.1) 1021 0.017136Xe > 8.1 1020 <0.03150Nd (7.0+12.0

-1.0) 1018 0.07238U (2.0 0.6) 1021 0.05

22ndnd order weak process order weak processSevere test for nuclear matrix elements calculationsSevere test for nuclear matrix elements calculations

Weighted average of the most recent experimentsWeighted average of the most recent experimentsi)i) average asymmetryc barsaverage asymmetryc barsii)ii) add systematic errors in quadratureadd systematic errors in quadrature

Elliott and Vogel 2002Elliott and Vogel 2002

[ ] 2221221 00 í

GTíí

/ M(Q,Z)G)(T =→−++

Nuclear structure effectsNuclear structure effectscause variations by a cause variations by a

factor ~10factor ~10 on the matrix elementson the matrix elements

i.e. a i.e. a factor ~100factor ~100on the lifetimeon the lifetime

Phase Space IntegralPhase Space IntegralExactly CalculableExactly Calculable

Calculated values span a range of Calculated values span a range of 3-4 orders of magnitude3-4 orders of magnitude

around the experimental valuearound the experimental value

Tretyak and Zdesenko 2002Tretyak and Zdesenko 2002

The interesting ones decay rate scales with Q5

2 decay rate scales with Q11

 

Q-value (keV)

Isotope Nat. abund. (%)

Ca 48 4271 0.187Ge 76 2039 7.8Se 82 2995 9.2Zr 96 3350 2.8Mo 100 3034 9.6Pd 110 2013 11.8Cd 116 2809 7.5Sn 124 2288 5.64Te 130 2529 34.5Xe 136 2479 8.9Nd 150 3367 5.6

Experiments

ELEGANT, CANDLESGERDA, MAJORANANEMO-3

NEMO-3, MOON

COBRA, CAMEO

CUORICINO, COBRAEXO, XMASS

ZORRO

DCBA

Nuclear matrix elements

To be sure:

A factor 3 uncertainty in the NME means about factor of 10 in half-life

P. Vogel,PDG 02

++ - modes

• (A,Z) (A,Z-2) + 2 e+ (+2e) ++ • e- + (A,Z) (A,Z-2) + e+ (+2e ) +/EC

• 2 e- + (A,Z) (A,Z-2) (+2e) EC/EC

Important to reveal mechanism if 0 is discoveredEnhanced sensitivity to right handed weak currents

(V+A)

n

n

p

pe

eIn general:

Q-4mec2

Q-2mec2

Q

Double charged higgs bosons,R-parity violating SUSY couplings,leptoquarks...

Neutrino mass vs. right handed currents++++ +++∝ RRLRRLLL JjJjJjJjH ληκint

€

λ,η <<1

<m> (eV)

<λ>

Possible evidence

M. Hirsch et al., Z. Phys. A 347,151 (1994)

EC/ß+

106Cd: COBRA, TGV

Why are we here?1 / T1/2 = PS * ME2 * (m / me)2

0+

1+

(A,Z)

(A,Z+1)

(A,Z+2)0+

charge exchange muon capture

beta decaysantineutrino-capture

nu N scattering

Theory: Shopping list what to measure to improve calculationsExperiment: Where can it be measured, who?

„Ultimate dream“: coherent effort, strategy paper to get things done

Q - values

Agenda

Monday, May 23

9:00 J. Stirling (Durham): Welcome

9:05 K. Zuber (Sussex): Introduction

9:25 K.Blaum (Mainz): Q-value determinations with ISOLTRAP and SMILETRAP

10:10 Coffee Break

11:00 F. Simkovic (Bratislava): Neutrinoless Double Beta Decay: Is there a converge ofQRPA results?

11:45 J. Suhonen (Jyvaskyla): Ways to probe double beta matrix elements by independent data

12:30 Lunch break

14:00 H. Ejiri (Osaka): Charge exchange reactions for spin isospin multipole responsesrelevant to neutrino-less double beta decays

14:45 D. Frekers (Münster): Measurement of double beta decay matrix elements using chargeexchange reactions

15:15 Coffee break

16:00 Start discussion: Towards a coherent effort of measurements and calculations,preparing of a strategy paper

20:00 Conference Dinner

Tuesday, May 24

9:00 S. Barabash (ITEP): SSD mechanism: experimental look on the problem

9:30 K. Jungmann (KVI): Muon capture experiments

10:00 C. Vo lpe (Orsay) Matrix elements from neutrino-nucleus scattering

10:20 Coffee break

11:00: S. Wychech (Warsaw): Double Electron capture calculations and the inducedpseudoscalar coupling in double beta decay