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Page 1: Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

Amand Faessler, GERDA, 11. November 2005

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Double Beta Decayand

Neutrino MassesAmand Faessler

Tuebingen

Accuracy of the Nuclear Matrix Elements.

It determines the Error of the Majorana Neutrino Mass extracted

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Amand Faessler, GERDA, 11. November 2005

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Oνββ-Decay (forbidden)

only for Majorana Neutrinos ν = νc

PP

n nLeft

Leftν

Phase Space106 x 2νββ

Page 3: Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

Amand Faessler, GERDA, 11. November 2005

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GRAND UNIFICATION

Left-right Symmetric Models SO(10)

Majorana Mass:

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P Pνν

n n

e-e-

L/R l/r

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l/r

P

ν

P

l/r

n n

light νheavy NNeutrinos

l/r L/R

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SupersymmetryBosons ↔ Fermions---------------------------------------------------------------------

--

Neutralinos

Neutralinos

P P

e- e-

n n

u

u u

ud d

Proton Proton

Neutron Neutron

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Theoretical Description:Simkovic, Rodin, Benes, Vogel, Bilenky,

Salesh, Gutsche, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger,

Raduta, Kaminski, Stoica, Suhonen, Civitarese, Tomoda et al.

0+

0+

0+

1+

2-

kkk

e1

e2PP

ν Ek

Ein n

0νββ

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Amand Faessler, GERDA, 11. November 2005

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Neutrinoless Double Beta-

Decay Probability

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Effective Majorana Neutrino-Mass

for the 0Decay

CP

Tranformation from Mass to Flavor Eigenstates

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Neutrino-Masses from the 0ν

and Neutrino Oscillations

Solar Neutrinos (CL, Ga, Kamiokande, SNO)Atmospheric ν (Super-Kamiokande)Reactor ν (Chooz; KamLand)

with CP-Invariance:

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ν1, ν2, ν3 Mass Statesνe, νμ, ντ Flavor States

Theta12 = 32.6 degrees Solar + KamLandTheta13 < 13 degrees ChoozTheta23 = 45 degrees S-Kamiokande

m 212(solar

8eV

m223atmosphericeV

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OSCILLATIONS AND DOUBLE BETA DECAY

Hierarchies: mν

Normal m3

m2

m1

m1<<m2<<m3

Inverted m2

m1

m3

m3<<m1<<m2

Bilenky, Faessler, Simkovic P. R. D 70(2004)33003

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The best choice:Quasi-Particle-

(a) Quasi-Boson-Approx.:

(b) Particle Number non-conserv.(important near closed shells)

(c) Unharmonicities(d) Proton-Neutron Pairing

Pairing

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Page 16: Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

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Contribution of Different Multipoles to M(0)

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2.76 (QRPA) 2.34 (RQRPA) Muto corrected

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M0ν (QRPA)

O. Civitarese, J. Suhonen, NPA 729 (2003) 867

Nucleus their(QRPA, 1.254) our(QRPA, 1.25)

76Ge 3.33 2.68(0.12) 100Mo 2.97 1.30(0.10) 130Te 3.49 1.56(0.47) 136Xe 4.64 0.90(0.20)

g(pp) fitted differently

Higher order terms of nucleon Current included differently with Gaussian form

factors based on a special quark model ( Kadkhikar, Suhonen, Faessler, Nucl. Phys. A29(1991)727). Does neglect pseudoscalar coupling (see eq. (19a)), which is an effect of 30%.

We: Higher order currents from Towner and Hardy.

What is the basis and the dependence on the size of the basis?

Short-range Brueckner Correlations not included. But finite size effects included.

We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)!

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Neutrinoless Double Beta Decay

The Double Beta Decay:

0+

0+

0+

β-

1+

2-

β-

e- e-

E>2me

x x x

xxx Gamov-Teller single beta decay in the second leg fitted with g(pp) by Suhonen et al.. Underestimates the first leg.

We fit the full 2decay by adjusting g(pp).

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Fit of g(pp) to the single beta (2. leg) and the 2 double beta decay (small and large basis).

Fit to 2

Fit to 1+ to 0+

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Uncorrelated and Correlated Relative N-N-

Wavefunctionin the N-N-Potential

Short Range Correlations

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Jastrow-Function multiplying the relative

N-N wavefunction

(Parameters from Miller and Spencer, Ann. Phys 1976)

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Influence of Short Range Correlations

(Parameters from Miller and Spencer, Ann. Phys 1976)

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Contribution of Different Multipoles to the zero Neutrino

Matrixelements in QRPAs.r.c. = short range correlations

h.o.t. = higher order currents

Different Multipoles

a) 76Ge small model space ( 9 levels) b) 76Ge large model space (21 levels)

C) 100Mo small model space ( 13 levels) d) 100Mo large model space ( 21 levels)

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Comparison of 2Half Lives with Shell model Results from Strassburg

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Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass

of planed Experiments

expt. T1/2

[y]<mv>[eV]

DAMA (136Xe)

1.2 X 1024 2.3

MAJORANA (76Ge)

3 X 1027 0.044

EXO 10t (136Xe)

4 X 1028 0.012

GEM (76Ge)

7 X 1027 0.028

GERDA II(76Ge)

1 X 1026 0.16

CANDLES (48Ca)

1 X 1026 0.2

MOON (100Mo)

1 X 1027 0.058

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Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass

of planed Experiments

expt. T1/2

[y]<mv>[eV]

XMASS (136Xe)

3 X 1026 0.10

CUORE (130Te)

2 X 1026 0.10

COBRA (116Cd)

1 X 1024 1

DCBA (100Mo)

2 X 1026 0.07

DCBA (82Se)

3 X 1026 0.04

CAMEO (116Cd)

1 X 1027 0.02

DCBA (150Nd)

1 X 1026 0.02

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Summary:Accuracy of Neutrino

Masses from 0

Fit the g(pp) by in front of the particle-particle NN matrixelement include exp. Error of .

Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets (small about 2 shells, intermediate 3 shells and large 5 shells) the

Use QRPA and R-QRPA (Pauli principle)

Use: g(A) = 1.25 and 1.00

Error of matrixelement 20 to 40 % (96Zr larger; largest errors from experim. values of T(1/2, 2))

Core overlap reduction by ~0.85 (preliminary)

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Summary:Results from

<m()>(GeExp. Klapdor) 0.47 [eV]

Klapdor et al. from Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV].

<M(heavy >[GeV]

<M(heavy Vector B)> > 5600 [GeV]

SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4)

Mainz-Troisk, Triton Decay: m(2.2 [eV]

Astro Physics (SDSS): Sum{ m() } < ~0.5 to 2 [eV]

Do not take democratic averaged matrix elements !!!

THE END

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Open Problems:1. Overlapping but slightly different

Hilbert space in intermediate Nucleus for QRPA from intial and from final nucleus.

2. Pairing does not conserve Nucleon

number. Problem at closed shells. Particle projection. Lipkin-Nogami <N>, <N2>

3. Deformed nuclei?