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Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

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It determines the Error of the Majorana Neutrino Mass extracted. Amand Faessler, 22. Oct. 2004 ... Accuracy of Neutrino Masses from 0nbb ... – PowerPoint PPT presentation

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Title: 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
P
P
l/r
?
light ? heavy N Neutrinos
l/r
n
n
8
Supersymmetry
  • Bosons ? Fermions
  • --------------------------------------------------
    ---------------------
  • Neutralinos

P
P
e-
e-
Proton
Proton
u
u
u
u
d
d
Neutron
Neutron
n
n
9
Theoretical DescriptionSimkovic, Rodin,
Pacearescu, Haug, Kovalenko, Vergados, Kosmas,
Schwieger, Raduta, Kaminski, Gutsche, Bilenky,
Vogel, Stoica, Suhonen, Civitarese, Tomoda et
al.

P
k
0
e2
P
k
e1
k
?
Ek
1
2-
n
Ei
n
0
0
0?ßß
10
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11
The best choice
  • Quasi-Particle-
  • Quasi-Boson-Approx.
  • Particle Number non-conserv.
  • (important near closed shells)
  • Unharmonicities
  • Proton-Neutron Pairing

Pairing
12
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13
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.
14
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15
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16
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)
  • A different procedure of fixing gpp to single
    beta decays. What is their g(pp) with error? How
    well is the 2-neutrino decay reproduced?
  • 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?
  • We hope to understand the differences. But for
    that we need to know their input parameters (
    g(pp), g(ph),basis, )!

17
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18
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19
M0? (R-QRPA 1.25) S. Stoica,
H.V. Klapdor-Kleingrothaus, NPA 694 (2001) 269
  • The same procedure of fixing g(pp)
  • 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!

20
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
GENIUS (76Ge) 1 X 1028 0.023
CANDLES (48Ca) 1 X 1026 0.2
MOON (100Mo) 1 X 1027 0.058
21
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
22
Neutrino-Masses from the 0?bband Neutrino
Oscillations
  • Solar Neutrinos (CL, Ga, Kamiokande, SNO)
  • Atmospheric ? (Super-Kamiokande)
  • Reactor ? (Chooz KamLand)
  • with CP-Invariance

23
Solar Neutrinos (KamLand)
  • (KamLand)
  • Atmospheric Neutrinos

  • (Super-Kamiok.)

24
Reactor Neutrinos (Chooz)
CP
25
  • ?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

26
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
27
  • (Bild)

28
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)).

29
SummaryResults from 0nbb
  • ltm(n)gt(0nbb Ge76, Exp. Klapdor) lt 0.47 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 m(n) lt 2.2 eV
  • Astro Physics (SDSS) Sum m(n) lt 1 to 2 eV
  • Klapdor et al. from 0nbb Ge76 with R-QRPA (no
    error of theory included)
  • 0.15 to 0.72 eV, if confirmed.
  • The Theory Groups must check their
  • Results against each other.

30
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
n
n
n
n
31
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

32
  • ?-Mass-Matrix by Mixing with
  • Diagrams on the Tree level
  • Majorana Neutrinos

33
Loop Diagrams
  • Figure 0.1 quark-squark 1-loop contribution to mv

X
X
Majorana Neutrino
34
  • Figure 0.2 lepton-slepton 1-loop contribution to
    mv
  • (7x7) Mass-Matrix

X
Block Diagonalis.
X
35
7 x 7 Neutrino-Massmatrix
  • Basis
  • Eliminate Neutralinos in 2. Order

separabel
Mass Eigenstate
Vector in flavor space
for 2 independent and possible
36
  • Super-K

37
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

38
How to calculate ?i33 (and ?i33) from ?333?
  • U(1) charge conserved!
  • 1,2,3 families

39
  • gPP fixed to 2?ßß M(0nbb) MeV(-1)
  • Each point (3 basis sets) x (3 forces) 9
    values

40
  • 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
41
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