Neutrinos, Nuclear Structure and and the Double Beta Decay

1
Neutrinos, Nuclear Structure and and the Double
Beta Decay
Amand Faessler Universität Tübingen
Postdocs Vadim Rodin Guest-Professors Fedor
Simkovic, Valery Kovalenko, Petr Vogel,
Ph.
D.-Student Saleh Jousef
2
Neutrinoless Double Beta Dirac versus Majorana
Neutrinos and absoute Neutrino Masses

• Avignone The nuclear matrix elements for the
  Double Beta Decay are as important as the
  experiment to determine the Neutrino mass
• (Erice 2005)

3
2?ßß-Decay (in SM allowed)

• Thesis Maria Goeppert-Mayer
• 1935 Goettingen

P
P
n
n
4
O?ßß-Decay (forbidden)

• only for massive Majorana Neutrinos
• ? ?c mn gt 0

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
Proton
n
e-
l/r
L/R
W / W
Neutron
P
P
?
light ? heavy N Neutrinos
l/r
n
l/r
n
8
Supersymmetry

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

P
Proton
P
u
u
Proton
e-
e-
Neutron
Neutron
d
u
u
d
n
n
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Theoretical DescriptionTübingen Faessler,
Simkovic, Rodin, Saleh, Kovalenko, Benes, Vogel,
Bilenky, Pacearescu, Haug, Vergados, Kosmas,
Schwieger, Raduta, Kaminski, Stoica, Suhonen,
Civitarese, Tomoda, Moya de Guerra, Sarriguren,
Valle, Hirsch et al.

P
0
k
e2
P
1
k
e1
k
2-
?
Ek
n
Ei
n
0
0
0?ßß
10
Neutrinoless Double Beta- Decay Probability
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The best choice

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

Pairing
Renormalized-QRPA RQRPA
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Effective Majorana Neutrino-Mass for the
0nbb-Decay
Tranformation from Mass to Flavor Eigenstates
CP
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Hierarchies

• (Bild)

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Double Beta Decay Mass as a function of the
lowest mass for normal m1 and inverted m3
hierarchies.
Bilenky, Faessler, Simkovic, Phys.Rev.
D70 033003(2004) hep-ph/0402250
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Accuracy of the 0nbb Matrix Elements

• Fit the gpp in front of the NN interaction for
  each calculations separatly to the experimental
  value of the 2nbb transition probability.
• Do this for three different forces (Bonn,
  Nijwegen, Argonne) and three different basis
  sets small about 3 shells intermediate about 4
  shells large 5 to 6 shells and calculate 9 times
  the 0nbb transition matrix elements.
• Evaluate the standard deviation s and add the
  experimental error of the 2nbb decay.
• Do this for QRPA and R-QRPA (Pauli Principle) and
  for axial coupling gA 1.25 and the quenched
  value gA 1.00 .
• Error of matrix elements 10 to 40. Largest error
  from experimental error of the 2nbb decay
  probability.

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Rodin, Faessler, Simkovic, Vogel,
nucl-th/0503063 Nucl. Phys. A766(2006)107
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Other Mechanisms Heavy Vector Boson Exchange,
Right Handed Currents, Heavy Neutrino Exchange,
Supersymmetry

• SUPER Symmetry
• --------------------------------------------------
  ---------------------
• 
  Neutralinos
• Neutralinos

P
Proton
P
u
u
Proton
e-
e-
Neutron
Neutron
d
u
u
d
n
n
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Ratio of 0nbb Half Lives to the Excited 0 and
the Ground State 0
What is the leading mechanism?
76 As
b
b
0
76 Ge
0
0
76 Se

• EXCHANGE OF
• Light Neutrino ltmngt
• Heavy Neutrino
• SUSY mechanism

Half Live Ratio
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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 (see discussion later)
• 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.
• Short-range Brueckner Correlations not included.
  (Factor 2 smaller)

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Differences

• 1. . Ajustment of gpp for the NN force to the
  total 2nbb-decay probability (Tuebingen) or to
  (Jyväskylä)
• lt0 Single b in second leg 1 gt

1
2-
ß-
1
pn-1
x
np-1
0
x
100Mo
0
This log ft value known in only three double beta
decay nuclei 100Mo, 116Cd, 128Te
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2. leg known only in these three nuclei
2 nbb - Decay
1g
0
For the first leg no agreement
1.75
0
Exp. 0.7
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2. Uncorrelated and Correlated Relative
N-N-Wavefunctionin the N-N-Potential
Short Range Correlations
23
Influence of Short Range Correlations
(Parameters from Miller and Spencer, Ann.
Phys 1976)
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Contributions of different Multipolarities for
0nbbNegative Parity States need at least three
Oscillator Shells
N 3 and 4 oscillator shells
N 0 to 5 oscillator shells
76Ge
76Ge
100Mo
100Mo
Blue Short Range Correlations and Higher Order
Currents. Red Short Range Correlations, no
Higher Order Currents White No Short range
Correlations, no Higher order Currents
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SummaryResults from 0nbb

• ltm(n)gt(0nbb Ge76, Exp. HD-Moscow 2003) lt 0.47
  eV
• Klapdor et al. from 0nbb Ge76 with R-QRPA and gA
  1.25
• Exp. T(1/2 0nbb hep-ph/0512263) (1.19
  0.37 -0.23) x 1025 years
• ltm(n)gt 0.57 to 0.80 eV (theory error
  included)
• 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 7
  eV
• No democratic averaged matrixelements !!!

The END
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How to solve the discrepancy between Matrix
Elements ?

• Global Analysis for Majorana Neutrino Mass with
  Statitical
• Evaluation of all relevant Data like for the
  Neutrino Oscillations
• Establish a data basis in spherical nuclei
• 1. 2nbb-Data
• 2. Log ft values in first and second Legs of bb
  decay nuclei.
• 3. Muon Capture from the final Nucleus.
• 4. Charge Transfer Reactions in the first leg
  (p,n) (3He,3H) and the second leg (d,2p) (3H,
  3He).
• Different basis sets different realistic
  forces and different many body methods QRPA
  Renormalized QRPA Shell Model ?.

The END
Statistical versus Systematic Errors
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C5a) Double Beta Decay and Physics beyond the
Standard Model

• 0nbb and R Parity violating Supersymmetry
  R-SUSY
• 0nbb Decay in Deformed Nuclei with Realistic
  Forces
• Continuum Quasi-Particle Random Phase Approx.
• C-QRPA and 0nbb Decay
• Renormalized R-QRPA, Selfconsitent SR-RPA,
• Fully Renormalized FR-QRPA (Ikeda S
  rule)
• Multi-Phonon QRPA ( 4particle- 4hole, 6p-6h)
• Double Electron Capture 0nbb Decay
• p p eb eb -gt n n

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Short Range Correlations beweeen Nucleons favor
Pion Exchange Term
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Supersymmetry and 0nbb Decay

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More R-Parity Violating SUSY Diagrams
32
More R-Parity Violating SUSY 0nbb Decay Diagrams
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Light Neutrino Exchange with Loop Diagram
producing a Majorana Neutrino Mass
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Double electron Capture with Majorana Neutrino
Exchange and with a SUSY Diagram
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Overlap Factor of the Initial and Final Nuclear
Wave function for Different Deformations
Phenomenological N-N Force
37
Deformation Effects on the Double Beta Decay with
Realistic Forces
Initial Nucleus
Final Nucleus
Initial, intermediate and final states can have
different deformations e.g. 150 Nd .
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C5b) Lepton-Flavor and Lepton-Number Violation in
Rare Processes

• µ- - e- conversion two-nucleon currents with
  pion-exchange and R-Parity violation
• µ- - e conversion two pion exchange

39
Muon-Electron Conversions Diagrams Calculated in
our Earlier Work
Interaction at Vertex Neutrino
Flavor Propagation by Mass Eigenstate,
Oscillations
40
Two nucleon currents for µ-e conversion (LFV)
41
Transitional magnetic moment of Majorana
neutrinos (LNV)
42
LFV and LNV decays of t
43
LFV and LNV decays of t

• effective Lagrangian
• for example in general

Hadronization (long distance effects, enhancement)
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LFV decays of heavy mesons
45
C5c) Dark Matter Cross Section

• Evaluate Cross Section of the Lightest SUSY
  Particles with Even Mass and Odd Mass Nuclei
  (Vector and Axial Vector Interaction).
• One, Three and Five Quasi-Particles for Odd Mass
  nuclei
• For Odd-Odd Mass Nuclei.
• Influence of Two Nucleon Currents with Pion
  Exchange
• Influence of Excited States

46
Dark Matter - Evidence
rotation curves (orbital speed vs radius) of
galaxies
orbitalvelocity
distance to center
gt Dark Matter halo in galaxy
there must be more matter in the universe than we
see
47
C5c) Dark Matter Cross Section WIMP Measurement

• direct detection
• WIMP Scattering and nuclear recoil detection
• WIMP-WIMP annihilation and detection of secondary
  particles
• ( g Wim de Boer et al.
• MWIMP 50 100 GeV)

Accumulate in Sun, Earth or Galactic Centre cc -gt
quark- antiquark
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Wave Function of the Groundstate of one and two
Phonen QRPA
Two Phonon QRPA
One Phonon Quasi-Particle Random Phase Approx.
QRPA
50
Odd Mass Nuclei 71Ga, 73Ga, 127I Test the Axial
Vector Interaction
One and three quasi-particles
More important ? Ground State correlations, 5
quasi-particles
51
Ground State Correlations(Fluctuations 2p-2h 4
quasi particles)
52
Two nucleon Currents with Pion Exchange and an
Intermediate Susy-Quark in the Pion Neutralino
Interaction

• c Neutralino
• LSP

q
gt
c
squark
gt
c
q
53
Open Questions for the 0nbb to be solved

• 1. Why obtain different groups different 0nbb
  matrix elements ? 
• 2. How reliable are the different many body
  methods for the double beta decay, for other LFV
  and LNV rare decays and for dark matter cross
  sections? 
• 3. Influence of Deformation.
• 4. What is the leading mechanism for the 0nbb
  decay ?
•  
• 5. What is the connection of the 0nbb decay with
  other lepton number (LNV) and lepton flavor
  (LFV) violating processes like (m,e) conversion
  and rare heavy meson decays ?
• 6. What can one learn from neutrino oscillations
  for the double beta decay?

THE END