Amand Faessler, München, 24. November 2005

1

Double Beta Decayand

Physics beyond the Standard ModelAmand Faessler

Tuebingen

Accuracy of the Nuclear Matrix Elements.

It determines the Error of the Majorana Neutrino Mass extracted

Amand Faessler, München, 24. November 2005

4

Oνββ-Decay (forbidden)

only for Majorana Neutrinos ν = νc

P

P

n n

Left

Leftν

Phase Space

106 x 2νββ

Amand Faessler, München, 24. November 2005

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GRAND UNIFICATION

Left-right Symmetric Models SO(10)

Majorana Mass:

Amand Faessler, München, 24. November 2005

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P P

νν

n n

e-

e-

L/R l/r

Amand Faessler, München, 24. November 2005

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l/r

P

ν

P

l/r

n n

light ν

heavy N

Neutrinos

l/r

L/R

Amand Faessler, München, 24. November 2005

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Supersymmetry

Bosons ↔ Fermions--------------------------------------------------------------------

---

Neutralinos

Neutralinos

P P

e- e-

n n

u

u u

ud d

Proton Proton

Neutron Neutron

Amand Faessler, München, 24. November 2005

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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, Valle, Moya de Guerra,

Sarriguren et al.

0+

0+

0+

1+

2-

k

k

ke1

e2PP

ν Ek

Ein n

0νββ

Never in Tuebingen: Muto/Tokyo, Hirsch/Valencia

Amand Faessler, München, 24. November 2005

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Neutrinoless Double Beta-

Decay Probability

Amand Faessler, München, 24. November 2005

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Effective Majorana Neutrino-Mass

for the 0Decay

CP

Tranformation from Mass to Flavor Eigenstates

Amand Faessler, München, 24. November 2005

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Bilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250

Amand Faessler, München, 24. November 2005

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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

Amand Faessler, München, 24. November 2005

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g(A)**4 = 1.25**4 = 2.44 fit to 2

Rodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063

Amand Faessler, München, 24. November 2005

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2.76 (QRPA) 2.34 (RQRPA) Muto corrected

Amand Faessler, München, 24. November 2005

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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, …)!

Amand Faessler, München, 24. November 2005

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Uncorrelated and Correlated Relative N-N-

Wavefunctionin the N-N-Potential

Short Range Correlations

Amand Faessler, München, 24. November 2005

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Influence of Short Range Correlations

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

Amand Faessler, München, 24. November 2005

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Comparison of 2Half Lives with Shell model Results from Strassburg

Amand Faessler, München, 24. November 2005

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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)

2 X 1026 0.11

CANDLES (48Ca)

1 X 1026 0.2

MOON (100Mo)

1 X 1027 0.058

Amand Faessler, München, 24. November 2005

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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

Amand Faessler, München, 24. November 2005

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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 ~0.90 (preliminary)

Amand Faessler, München, 24. November 2005

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Summary:Results from

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

<m()>(GeExp. Klapdor) 0.47 [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 !!!

Amand Faessler, München, 24. November 2005

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Open Problems:1. Overlapping but slightly different

Hilbert spaces 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? (e.g.: 150Nd ) THE END

β-

0+

0+

2-

1+

0+

pn-1

np-1