Nuclear Double Beta Decay and Derivation of Neutrino Mass

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Nuclear Double Beta Decay and Derivation of
Neutrino Mass

• Sabin Stoica
• IFIN-HH

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Outline

• General view on ßß decay process
• Nuclear Models for Nuclear Matrix Elements
• Derivation of m?
• Conclusions

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Introduction Double-beta decay

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• Large interest for ßß experiments
• Present results from ?- oscillation experiments ?
  ? 0
• Normal hierarchy
• Inverted hierarchy
• Evidence claimed for 0?ßß in a 76Ge measurement
  (Klapdor et al., 2001) gt 0.35
  eV
• These are very exciting results for ??-decay
  experiments because several of such future
  experiments aim at reaching this sensitivity.
• ??-decay experiments have a broader potential
• Decide whether ? is a Majorana or a Dirac
  particle.
• Connection to beyond SM physics

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• ßß provides a broader potential to search for
  beyond SM physics
• Lepton number non-conservation
• Existence of RH components in the weak
  interaction (?, ?) 10-5
• L-R theories 0??? mediated by heavy RH W
  bosons. Absence of 0???
• provides a lower mass limit for these bosons.
• SUSY theories 0??? occurs via exchange of
  supersymmetric
• particles and can be used to restrict R parity
  violating SUSY models
• Majoron 0??? may appear by a spontaneous
  breaking of a global symmetry due to a Majoron (a
  light or massless boson which can couple to ?)
• Leptoquarks (bosons carrying both lepton and
  baryon number) appearing in some GUTs scenarious
  could mediate 0???
• Compositeness possible substructure of quarks
  and leptons at an energy scale of TeV. A
  possible low energy manifestation of
  compositeness could be 0??? mediated by a
  composite heavy Majorana ?.
• Reliability of these constraints depends on our
  ability to evaluate the nuclear matrix elements
  mediating these decay mechanisms

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Sensitivity to the ? mass of planned experiments
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2?ßß

?M M(parent) M(daughter)
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0?ßß
Light neutrino mechanism ?T0?1/2 ?-1 Cmm
(?m?? / me)2 C?? ???2 C?? ???2 2 Cm?
(?m?? / me) ??? 2 Cm? (?m?? / me) lt?gt
2 C?? lt?gtlt?gt Cij are products between various NME
and the corresponding phase space factors
Mass mechanism
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Nuclear structure methods QRPA-based
pnQRPA higher-order QRPA Used for most nuclei
decaying double-beta Characteristics all Nh?
s.p. states but
limited g.s. correlations Shell model (ShM)
calculations for 48Ca, 76Ge, 82Se, 100Mo,
136Xe Characteristics limited (0h?) s.p.
states but all
g.s. correlations
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(pn)QRPA
Pairing (pp, nn, np)
Quasi-Boson - Approximation
Drawback a sever dependence of the nuclear
matrix elements for the 2??? mode on the
particle-particle strengh parameter (gpp).
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we need g_pp well fixed in order to get reliable
estimations of the NME for 0??? Unharmonicities
gt Higher order pnQRPA
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• Higher-order QRPA methods SQRPA, RQRPA
• SQRPA unharmonicities are introduced through
  the
• boson expansion method

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RQRPA unharmonicities are introduced by taking
into account additional
one-quasiparticle scattering terms
in the commutation relations for
fermion pairs to the QB
approximation - selfconsistent
iteration of the QRPA equations
J. Suhonen and colab.
D
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Other improvements on pnQRPA Proton-neutron
pairing Extension of the QRPA equations to
include explicitly p-n pairing, as an additional
type of correlations goal get a smooth model
dependence of the NME Results p-n pairing is
not expected to become dominantly in the cases of
interest for ßß in treating these correlations
self-consistently the effect is not
important Restore the particle-number
non-conservation (shortcoming of BCS procedure)
-gt by particle-number projection Effect minor
for medium-heavy and heavy nuclei Continuum
QRPA take into account states in
continuum Results M2? almost not affected
M0? affected (but the pairing not fully
accounted for)
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Other approximations for NME

• SU(4) Wigner symmetry
• the strong suppression of the NME is expected to
  be produced by the SU(4) selection rules which
  prohibit the transitions between members of bands
  with different total spin S and isospin T
• Closure approximation
• Related to the possibility of defining an
  effective 2-body transition operator from the
  initial to the final nucleus that implies the
  replacement of the energy denominators apprearing
  in the expressions of the NME by an average
  value gt allows the sum over the intermediate
  states can be carried out exactly
• Bad for 2?ßß due to the sensitivity of the NME on
  the chosen set of intermediate virtual states
• Good for 0?ßß

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Other ßß transitions
bb
Physics involved very rich Description of the
structure of the excited states Single beta and
electromagnetic transitions Most favored
transitions to the 01
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Other ßß transitions
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Shell Model Significant qualitative and
quantitative progress
i) a good valence space ii) an effective
interaction adapted to it
iii) a ShM code capable to cope the secular
problem i) diagonalization of matrices
109 ii) new NN interaction 2-body
3-body - 2-body
derived from realistic potentials
- 3-body monopole 3 body forces
iii) Lanczos tridiagonal construction

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• No Core Shell Model Calculations (J. Vary et al.,
  Iowa Univ.)
• First calculations for the A48 mass nuclei (Ca,
  Sc, Ti)
• Limited goals
• - to see the limitations of an ab-intio NCSM in
  this region
• - by introducing phenomenological adjustments to
  see how far we still
• are from a good spectroscopic description of
  these nuclei before
• addressing ßß decay calculations
• to be prepared for future larger scale NCSM
  calculations
• Ingredients
• We adopted a NCSM approach and approximate the
  full with a 2-body cluster
  truncation all nucleons are treated on the same
  2-body H derived from realistic NN interaction
  including Coulomb interaction between nucleon
  pairs

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• For 48Ca we evaluate both the positive (
  ) and negative ( )
• spectra with the same
• We provide a baseline for further improvements
  to such as the
• inclusion of real and effective 3-body forces
• Main results
• With the ab-initio NCSM, with
  , we obtained that the trend of e-e and
  o-o nuclear binding energies matches well the
  expt. but the binding energies are underbinded by
  0.4 MeV/nucleon, Also, we obtain the corect
  Jp0 g.s. spin and parity for e-e nuclei, while
  for o-o nuclei generally we do not obtain the
  corect Jp.
• The overal picture improved considerably when
  adding phenomenological terms
  
  
• accurate BE/A for 8 nuclei with A48
• reasonable low energy spectra for the 3
  nuclei

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• Uncertainties in QRPA- and ShM-based methods
• QRPA
• Residual NN interactions schematic zero-range
  or realistic
• interactions (Bonn, Argonne, etc.)
• Renormalizations
• - pairing channel ? gpair
• - particle-hole channel ? gph
• - particle-particle ? gpp ? how to fix it?
  From single or double beta
• 
  decay
• - renormalization depends on the basis size

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• ShM
• 0h? model space is not enough for 0?ßß
• 0?ßß-transitions via negative parity
  intermediate states (dipole,
• spin-dipole, multipoles, etc.) are missing
  while it is shown by QRPA
• that these transitions give a significant
  contribution to 0?ßß NME
• in some calculations even some GT strength is
  missing (ISR is
• violated)
• several spin-orbit partners are missing even in
  0h? model space

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- Systematic effort from the groups involved in
NME calculation for ßß decay - Alternative
calculations with both QRPA- and ShM based
methods - Other ideas of improvement the methods
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Direct measurements of the neutrino mass 1)
Tritium decay ?-mass is measured by measurement
of the energy of end point part of the
beta-spectrum of tritium 3H
? 3H e- ?e Advantages ?- decay is
superallowed ? nuclear matrix elements are
constant and the electron spectrum is determined
by only the phase space Energy released E0
and T1/2 12.3 yr are convenable
quantities Inconvenient reduced sensibility
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Present results ? from experiments Mainz and
Troitsk
m? lt 1.8 eV Future
experiment (KATRIN) designed to measure the
mass of the electron neutrino directly with a
sensitivity of m? 0.2 eV. It is a next
generation tritium beta-decay experiment scaling
up the size and precision of previous experiments
by an order of magnitude as well as the intensity
of the tritium beta source. Observation What
one measures in the tritiu experiment is the
quantity m?
? Uei2 mi Normal Hierarchy m? 0.012eV
Inverted m? 0.05eV
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ßß decay Effective Majorana neutrino mass
Direct measurements
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• Determination of neutino mass
• More stringent limits for m? when ßß
  information is used in combination with
  constraints from neutrino oscillation experiments
  and cosmological data
• If one considers CP conservation (e?(i)
  ?1) and taking into account the oscillation
  results one obtains
• ? m??? ? Uei2 m1 ? ? Uei2 ( m1 ?m122 )1/2
  and gets
• Normal hierachy ? m??? several meV
• Inverted hierarchy ? m??? several tens of meV
• Degenerate hierarchy ? m??? gt 50 meV
• The most sensitive present experiment
• Heidelberg-Moscow gt ? m??? 0.35 eV
• EXO, NEMO, GEM, Majorana, etc. gt aim at
  reaching such sensitivities
• 
  

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Conclusions

• In latest years there were impressive
  experimental results in favor
• of ?- oscillation interpretation gt neutrinos
  have mass and mix
• - Absolute m? ?
• - Nature of ? Dirac or Majorana?
• ?? decay - key position to answer to these
  issues
• ?? decay has a broader potetial to investigate
  physics beyond SM
• - mass hierarchy
• - the mechanism of ? mass
  generation
• - test of GUTs by assuming
  different mechanisms of ocuring
• NME systematic effort for clarifying and
  eliminate the uncertainties
• alternative calculations with QRPA
  and ShM besed models
• - ?? decay experiments
  decisive progress
• - large baseline neutrino oscillation experiments
  gt in understanding