Neutrinoless double beta decay and Lepton Flavor Violation

1
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 if it is ever observed
Petr Vogel, Caltech Erice, 9/20/2005
2

• Based on
• Lepton number violation without supersymmetry
• Phys.Rev.D 70 (2004) 075007
• V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and
  P.V.
• And on
• Neutrinoless double beta decay and lepton flavor
  violation
• Phys. Rev. Lett. 93 (2004) 231802
• V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf,
  and P.V.

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Observation of the 0??? decay means that
neutrinos are massive Majorana particles
Theorem due to Schechter and Valle, (1982).
Existence of the vertex causes, by the multiloop
graph shown, existence of the Majorana mass term.
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Light or heavy Majorana neutrino. Model
extended to include right-handed WR. Mixing
extended between the left and right-handed neutrin
os.
Light Majorana neutrino, only Standard Model weak
interactions
Supersymmetry with R-parity violation. Many new
particles invoked. Light Majorana neutrinos
exist also.
Heavy Majorana neutrino interacting with
WR. Model extended to include right-handed
current interactions.
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It is well known that the amplitude for the light
neutrino exchange scales as ltm??gt. On the other
hand, if heavy particles of scale ??are involved
the amplitude scales as 1/?5.

• The relative size of the 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
• mechanisms contribute equally.

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AL/AH m????5/ ltk2gt MW4

• Thus for m??? 0.2 eV, ltk2gt 502 MeV2, and
  AL/AH 1
• ?5 502x1012x804x1036/0.2 eV 5x1059 eV
• ?? 1012 eV 1 TeV

Clearly, the heavy particle mechanism could
compete with the light Majorana neutrino exchange
only if the heavy scale ? is between about 1 - 5
TeV. Smaller ? are already excluded and larger
ones will be unobservable due to the fast ?5
scale dependence.
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• APS Joint Study on the Future ofNeutrino Physics
  (2004)
• (physics/0411216)
• We recommend, as a high priority, a phased
  program
• of sensitive searches for neutrinoless double
  beta
• decay (first on the list of recommendations)
• The answer to the question whether neutrinos are
  
• their own antiparticles is of central importance,
  not
• only to our understanding of neutrinos, but also
  to
• our understanding of the origin of mass.

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It is well known that for the light neutrino
exchange mechanism knowing ltm??gt helps to fix
the absolute mass scale.
This is based on the parameters of the solar
KamLAND solution. The cross-hatched region is
for 1s errors. Arrows indicate that by
determining ltmbbgt , even crudely we can constrain
the neutrino mass pattern.
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The relation between ltm??gt and the mass hierarchy
requires a comment As one can see e.g. in the
plot of ltm??gt vs. the sum of neutrino masses the
sign of ?m2atm (i.e. normal or inverted
hierarchy) cannot be determined at all for even
if ltm??gt is accurately known in the case of the
degenerate pattern, and even in the case commonly
known as the inverted hierarchy region.
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Alternatively, plot ltm??gt versus ltm?gt
?Uei2mi21/2, the quantity that can be
determined in ordinary ? decay.
Note that these two quantities are propor- tional
to each other, except in the unreachable low
mass region. The gap in shading shows
where inverted hierarchy begins.
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• Observation of 0??? 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 ltm??gt from the
  
• rate since only then ? ltm??gt 2.
• In most cases it is impossible to decide which
  mechanism
• is responsible for 0??? since the electron
  spectra, angular
• distributions, polarizations, etc. are
  independent of it.

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There is one known exception to this statement,
the classical case of right-handed currents,
characterized by the phenomenological
parameters ? and ?. In that case, indeed,
single electron spectra are different when
compared to the light Majorana exchange.
However, the corresponding decay rate is expected
to be smaller than the rate where the
distinction cannot be made (see e.g. G.
Prezeau, M. Ramsey-Musolf P.V., Phys. Rev.
D68, 034016 (2003)).
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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 ???? decay.

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• In the standard model lepton flavor conservation
  is 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 ? -gt e ?, muon conversion ?- (Z,A) -gt e-
  (Z,A),
• or ? -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.

?
W
e
?
?
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So, why are people even looking for
LFV? Because most particle physics
models of physics beyond the Standard
Model contain LFV originating at some
high mass scale. Most of them also
contain LNV and, naturally, all
realistic models should include light
and mixed neutrinos, known to exist. If
the scales of both LFV and LNV are well
above the weak scale, then ?????? ltm??gt2 and
ltm??gt can be derived from the 0??? decay
rate. However, the dangerous case is
when both LFV and LNV scales are low (
TeV). In that case there might be an
ambiguity in interpreting the results of
0??? decay experiments.
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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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Effective theory description
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 (cont)

• 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 (cont)

• (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.

For the discussion of neutrino masses in the
R-parity violating supersymmetric models see Y.
Grossman and S. Rakshit, hep-ph/0311310
Generally, hierarchical neutrino spectrum is
predicted, but small neutrino masses require some
fine tuning.
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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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Matter fields
Higgs sector
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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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Linking LNV to LFV

• Simple criteria based on ratio

1. ?
(Need more input to discriminate)
2. ?
3. Non observation ?
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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