Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

1
Double Beta DecayandNeutrino MassesAmand
FaesslerTuebingen

• Accuracy of the Nuclear Matrix Elements.
• It determines the Error of the Majorana Neutrino
  Mass extracted

2
Neutrinoless Double Beta Decay

• The Double Beta Decay

0
1
2-
ß-
ß-
e-
e-
0
Egt2me
0
3
2?ßß-Decay (in SM allowed)

• Thesis Maria Goeppert-Mayer
• 1935 Goettingen

P
P
n
n
4
O?ßß-Decay (forbidden)

• only for Majorana Neutrinos
• ? ?c

P
P
Left
?
Phase Space 106 x 2?ßß
Left
n
n
5
GRAND UNIFICATION

• Left-right Symmetric Models SO(10)
• Majorana Mass

6
P
P
e-
?
?
e-
L/R
l/r
n
n
7
L/R
l/r
P
P
l/r
?
light ? heavy N Neutrinos
l/r
n
n
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Supersymmetry

• Bosons ? Fermions
• --------------------------------------------------
  ---------------------
• 
  Neutralinos
• Neutralinos

P
P
e-
e-
Proton
Proton
u
u
u
u
d
d
Neutron
Neutron
n
n
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Theoretical DescriptionSimkovic, Rodin, Benes,
Vogel, Bilenky, Salesh, Gutsche, Pacearescu,
Haug, Kovalenko, Vergados, Kosmas, Schwieger,
Raduta, Kaminski, Stoica, Suhonen, Civitarese,
Tomoda et al.

P
k
0
e2
P
k
e1
k
?
Ek
1
2-
n
Ei
n
0
0
0?ßß
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Neutrinoless Double Beta- Decay Probability
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Effective Majorana Neutrino-Mass for the
0nbb-Decay
Tranformation from Mass to Flavor Eigenstates
CP
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Neutrino-Masses from the 0?bband Neutrino
Oscillations

• Solar Neutrinos (CL, Ga, Kamiokande, SNO)
• Atmospheric ? (Super-Kamiokande)
• Reactor ? (Chooz KamLand)
• with CP-Invariance

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• ?1, ?2, ?3 Mass States
• ?e, ?µ, ?t Flavor States
• Theta12 32.6 degrees Solar KamLand
• Theta13 lt 13 degrees Chooz
• Theta23 45 degrees S-Kamiokande

D m 212(solar ) 810(-5)
eV2 Dm223(atmospheric ) 2.510(-3)
eV2
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OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies m? OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies m?
Normal m3 m2 m1 m1ltltm2ltltm3 Inverted m2 m1 m3 m3ltltm1ltltm2
Bilenky, Faessler, Simkovic P. R. D
70(2004)33003
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Bilenky, Faessler, Simkovic, Phys.Rev.
D70033003(2004) hep-ph/0402250
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Bilenky, Faessler, Simkovic, Phys.Rev.
D70033003(2004) hep-ph/0402250

• (Bild)

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The best choice

• Quasi-Particle-
• Quasi-Boson-Approx.
• Particle Number non-conserv.
• (important near closed shells)
• Unharmonicities
• Proton-Neutron Pairing

Pairing
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Nucleus 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 134Xe 136Xe 150Nd
T1/2 (exp) years gt9.5 1021 gt1.9 1025 gt1.4 1022 gt1.0 1021 gt5.5 1022 gt7.0 1022 gt8.6 1022 gt1.4 1022 gt5.8 1022 gt7.0 1023 gt1.7 1021
Ref. You Klap- dor Elli-ott Arn. Ejiri Dane-vich Ales. Ales. Ber. Staudt Klimenk.
ltmgteV lt22. lt0.47 lt8.7 lt40. lt2.8 lt3.8 lt17. lt3.2 lt27. lt3.8 lt7.2
?m(p)/M(n) lt200. lt0.79 lt15. lt79. lt6.0 lt7.0 lt27. lt4.9 lt38. lt3.5 lt13.
?(111)10-4 lt8.9 lt1.1 lt5.0 lt9.4 lt2.8 lt3.4 lt5.8 lt2.4 lt6.8 lt2.1 lt3.8
Only for Majorana ? possible.
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Contribution of Different Multipoles to M(0n)
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g(A)4 1.254 2.44 fit to 2nbb
Rodin, Faessler, Simkovic, Vogel, Mar 2005
nucl-th/0503063
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Overlap of Wave Functions of the not involved
core of the initial and final nuclei.
Benesch, Faessler, Simkovic Preliminary (July
2005)
Ge76
Benes, Faessler, Simkovic
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Overlap of the core added to the 0nbb-decay and
new 2nbb-decay data (NEMO).
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R-QRPA-0nbb-Decay Nuclear Matrix Elements with
Lipkin-Nogami ltNgt and ltN²gt and Overlap of the
Core.
Benesch, Faessler, Simkovic (July
2005) Preliminary
No experimental error included
Closed Shells involved
20 50 82
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Renormalized QRPAwith Lipkin-Nogamiincluding
the experimental error of the 2nbb decay
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Relation of M(0n) on M(2n) independent on Size of
Basis ( 21 and 9 or 13 levels)
Ratio M(0n)/M(2n) with g(pp) fixed to M(2n)
independent of basis size
27


2.76 (QRPA) 2.34 (RQRPA)
Muto corrected
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M0? (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
1
x x x
2-
ß-
ß-
e-
e-
0
Egt2me
0
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
2nbb decay by adjusting g(pp).
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Fit of g(pp) to the single beta (2. leg) and the
2n double beta decay (small and large basis).
Fit to 1 to 0
Fit to 2nbb
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Uncorrelated and Correlated Relative
N-N-Wavefunctionin the N-N-Potential
Short Range Correlations
33
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 QRPA
s.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 2nbbHalf Lives with Shell model
Results from Strassburg
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0nbb-Decay Matrix Elements in R-QRPA and the
Strassburg Shell Model
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Contribution of GT 1 States and the Sum of all
other States to M(0n)
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Multipole Decomposition of M(0n) in QRPA
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M0? (R-QRPA 1.25) S. Stoica,
H.V. Klapdor-Kleingrothaus, NPA 694 (2001) 269

• A similar procedure of fixing g(pp) to the two
  neutrino decay in one basis (?).
• Higher order terms of nucleon
• current not considered
• Nucleus l.m.s s.m.s
  our
• 76Ge 1.87 (l12) 3.74 (s9)
  2.40(.12)
• 100Mo 3.40 4.36
  1.20(.15)
• 130Te 3.00 4.55
  1.46(.46)
• 136Xe 1.02 1.57
  0.85(.23)
• Model space dependence ?
• Disagreement also between his tables and figures
  for R-QRPA and S-QRPA!

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Neutrinoless Double Beta Decay Matrix
ElementsEVZ-88 Engel, Vogel, Zirnbauer MBK-89
Muto. Bender, Klapdor T-91 Tomoda SKF-91
Suhonen, Khadkikar, Faessler PSVF-96 Pantis,
Simkovic, Vergados, Faessler AS-98 Aunola,
Suhonen SPVF-99 Simkovic, Pantis, Vergados,
Faessler SK-01 Stoica, Klapdor CS-03
Civitarese, Suhonen.
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Neutrinoless Double Beta Decay Matrix
ElementsEVZ-88 Engel, Vogel, Zirnbauer MBK-89
Muto. Bender, Klapdor T-91 Tomoda SKF-91
Suhonen, Khadkikar, Faessler PSVF-96 Pantis,
Simkovic, Vergados, Faessler AS-98 Aunola,
Suhonen SPVF-99 Simkovic, Pantis, Vergados,
Faessler SK-01 Stoica, Klapdor CS-03
Civitarese, Suhonen.
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Neutrinoless Double Beta Decay Matrix
ElementsEVZ-88 Engel, Vogel, Zirnbauer MBK-89
Muto. Bender, Klapdor T-91 Tomoda SKF-91
Suhonen, Khadkikar, Faessler PSVF-96 Pantis,
Simkovic, Vergados, Faessler AS-98 Aunola,
Suhonen SPVF-99 Simkovic, Pantis, Vergados,
Faessler SK-01 Stoica, Klapdor CS-03
Civitarese, Suhonen.
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Neutrinoless Double Beta Decay and the
Sensitivity to the Neutrino Massof planed
Experiments
expt. T1/2 y ltmvgt 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 Massof planed
Experiments
expt. T1/2 y ltmvgt 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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Neutrino-Masses from the 0?bband Neutrino
Oscillations

• Solar Neutrinos (CL, Ga, Kamiokande, SNO)
• Atmospheric ? (Super-Kamiokande)
• Reactor ? (Chooz KamLand)
• with CP-Invariance

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Solar Neutrinos (KamLand)

• (KamLand)
  
• Atmospheric Neutrinos
• 
  (Super-Kamiok.)

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Reactor Neutrinos (Chooz)
CP
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• ?1, ?2, ?3 Mass States
• ?e, ?µ, ?t Flavor States
• Theta(1,2) 32.6 degrees Solar KamLand
• Theta(1,3) lt 13 degrees Chooz
• Theta(2,3) 45 degrees S-Kamiokande

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OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies m? OSCILLATIONS AND DOUBLE BETA DECAY Hierarchies m?
Normal m3 m2 m1 m1ltltm2ltltm3 Inverted m2 m1 m3 m3ltltm1ltltm2
Bilenky, Faessler, Simkovic P. R. D
70(2004)33003
53

• (Bild)

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SummaryAccuracy of Neutrino Masses from 0nbb

• Fit the g(pp) by 2nbb in front of the
  particle-particle NN matrixelement include exp.
  Error of 2nbb.
• 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
  0nbb.
• 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,
  2nbb)).
• Core overlap reduction by 0.85 (preliminary)

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SummaryResults from 0nbb

• ltm(n)gt(0nbb Ge76, Exp. Klapdor) lt 0.47 eV
• Klapdor et al. from 0nbb Ge76 with R-QRPA (no
  error of theory included) 0.15 to 0.72 eV.
• ltM(heavy n)gt gt 1.2 GeV
• ltM(heavy Vector B)gt gt 5600 GeV
• SUSYR-Parity l(1,1,1) lt 1.110(-4)
• Mainz-Troisk, Triton Decay m(n) lt 2.2 eV
• Astro Physics (SDSS) Sum m(n) lt 0.5 to 2
  eV
• Do not take democratic
• averaged matrix elements !!!

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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 ltNgt, ltN2gt
• 3. Deformed nuclei?

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SummaryAccuracy of Neutrino Masses by the
Double Beta Decay

• Dirac versus Majorana Neutrinos
• Grand Unified Theories (GUTs), R-Parity
  violatingSupersymmetry ?Majorana-Neutrino
  Antineutrinos

P
P
u
u
u
u
P
P
d
d
d
d
u
u
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n
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3. Neutrino Masses and Supersymmetry

• R-Parity violating Supersymmetry mixes Neutrinos
  with Neutrinalinos (Photinos, Zinos, Higgsinos)
  and Tau-Susytau-Loops, Bottom-Susybottom-Loops ?
  Majorana-Neutrinos (Faessler, Haug, Vergados
  Phys. Rev. D )
• m(neutrino1) 0 0.02 eV
• m(neutrino2) 0.002 0.04 eV
• m(neutrino3) 0.03 1.03 eV
• 0-Neutrino Double Beta decay
• ltmßßgt 0.009 - 0.045 eV
• ßß Experiment ltmßßgt lt 0.47 eV
• Klapdor et al. ltmßßgt 0.1 0.9 eV
• Tritium (Otten, Weinheimer, Lobashow)
• ltmgt lt 2.2 eV
• THE END

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• ?-Mass-Matrix by Mixing with
• Diagrams on the Tree level
• Majorana Neutrinos

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Loop Diagrams

• Figure 0.1 quark-squark 1-loop contribution to mv

X
X
Majorana Neutrino
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• Figure 0.2 lepton-slepton 1-loop contribution to
  mv
• (7x7) Mass-Matrix

X
Block Diagonalis.
X
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7 x 7 Neutrino-Massmatrix

• Basis
• Eliminate Neutralinos in 2. Order

separabel
Mass Eigenstate
Vector in flavor space
for 2 independent and possible
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• Super-K

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Horizontal U(1) Symmetry

• U(1) Field
• U(1) charge
• R-Parity breaking terms must be without
• U(1) charge change (U(1) charge conservat.)
• Symmetry Breaking

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How to calculate ?i33 (and ?i33) from ?333?

• U(1) charge conserved!
• 1,2,3 families

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• gPP fixed to 2?ßß M(0nbb) MeV(-1)
• Each point (3 basis sets) x (3 forces) 9
  values

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• Assuming only Electron Neutrinos
• (ES) 2.35106 F
• (CC) 1.76106 F
• (NC) 5.09106 F
• Including Muon and Tauon ?

F(?e) 1.76106 (CC)
F(?µ?t) 3.41106 (CCES)
F(?e?µ?t) 5.09106 (NC)
F(?-Bahcall) 5.14106
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