Neutrinoless double beta decay and Lepton Flavor Violation

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Neutrinoless double beta decay andLepton Flavor
Violation
Or, in other words, how the study of LFV can help
us to decide what mechanism is responsible for
the 0nbb decay
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• Based on
• Lepton number violation without supersymmetry
• hep-ph/0404233, Phys.Rev.D accepted
• V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and
  P.V.
• And on
• Neutrinoless double beta decay and lepton flavor
  violation
• hep-ph/0406199,
• V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf,
  and P.V.

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• Observation of 0nbb would establish the existence
  of
• massive Majorana neutrinos. However, only if the
• process is mediated by the light neutrino
  exchange
• can one extract the effective mass ltmbbgt from the
  
• rate since only then G ltmbbgt 2.
• In most cases it is impossible to decide which
  mechanism
• is responsible for 0nbb since the electron
  spectra, angular
• distributions, polarizations, etc. are
  independent of it.

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• The relative size of heavy (AH) vs. light
  particle (AL)
• exchange to the decay amplitude is (a crude
  estimate)
• AL GF2 mbb/ltk2gt, AH GF2 MW4/L5 ,
• Where L is the heavy scale and k 50 MeV is the
• virtual neutrino momentum.
• For L 1 TeV and mbb 0.1 0.5 eV AL/AH 1,
• hence both mechanism contribute equally.

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• In the following we suggest that
• Lepton flavor violation (LFV) involving
• charged leptons provides a diagnostic
• tool for establishing the mechanism
• of 0nbb decay.

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• In the standard model lepton flavor conservation
  is as a consequence
• of vanishing neutrino masses. However, the
  observation of neutrino
• oscillations shows that neutrinos are massive and
  that the flavor is
• not conserved. Hence a more general theory must
  contain LFV
• of charged leptons generated probably at some
  high scale.
• There is a long history of searches for LFV with
  charged leptons,
• like m -gt e g, muon conversion m- (Z,A) -gt e-
  (Z,A),
• or m -gt e e e- .
• Impressive limits for the branching ratios have
  been established

lt 1.2x10-11
lt 8x10-13
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• There are ambitious new proposals with much
  better sensitivities
• MECO Bm -gte lt 5x10-17 on Al
• MEG Bm -gt eg lt 5x 10-14
• i.e. improvement by a factor of 1000 - 10000.
• The direct effect of neutrino mass is GIM
  suppressed
• by a factor of (Dmn2/MW2)2 10-50 hence
  unobservable.

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In the most popular SUSY-GUT scenario (for SU(5)
GUT) one has the branching ratios
Thus a) MEG and MECO should see an effect, and
b) m -gt e g is enhanced by a factor 1/a
compared to m -gt e conversion. The feature b)
is generic for theories with high scale LNV
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Linking LNV to LFV Summary

• SM extensions with low (? TeV) scale LNV
  ?

• SM extensions with high (GUT) scale LNV
  ?

In absence of fine-tuning or hierarchies
in flavor couplings. Important caveat!
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Linking LNV to LFV I

• Simple criteria based on ratio

1. ?
(Need more input to discriminate)
2. ?
3. Non observation ?
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Effective theory description I
Operators (omitting L ? R)
- arises at loop level
- , may arise at tree level
- Leading pieces in ci are nominally of
order (Yukawa)2
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Effective theory description II

• Phase space overlap integrals

for light nuclei

• hn are coefficients of O(1)

• Origin of large logs

one loop operator mixing
Raidal-Santamaria 97
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Effective theory description III

• (i) No tree level , ?

(ii) Tree level , ? log
enhancement and
(iii) Tree level ?
Need to show that in models with low scale LNV
Ol and/or Olq are generated at tree level.
No general proof, but two illustrations
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Illustration I RPV SUSY R (-1)3(B-L) 2s
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• Clearly, the way to avoid the connection between
  LFV
• and LNV is if l111 gtgt l211 , etc. That is if l
  is nearly
• flavor diagonal.
• Note that empirically both lijk and lijk are
  small ltlt 1.

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Illustration II Left-Right Symmetric Model
SU(2)L ? SU(2)R ? U(1)B-L ? SU(2)L ? U(1)Y
? U(1)EM
?
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hij are coupling constants of leptons and the
doubly charged Higgs
They are related to the mixing matrix KR of the
heavy neutrinos
Note that glfv vanishes for degenerate heavy
neutrinos, but hij need not.
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Within LRSM the LFV branching ratios depend only
on glfv .
Thus the present limits suggest that either the
scale is gtgt 1 TeV, or that glfv is very small,
i.e. that he heavy neutrino spectrum is
degenerate or has very little mixing.
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Conclusions

• The ratio provides insight
  into the 0nbb
• mechanism and possibility to access LNV mass
  scale
• Low scale LNV ?
• Simple criteria
• - if ?
• - if , TeV scale LNV
  is possible and thus
• more expt./th. input needed to decide
  0nbb mechanism