Towards%20absolute%20neutrino%20masses

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Towards absolute neutrino masses
Petr Vogel, Caltech NOW
2006, Otranto, September 2006
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Thanks to the recent triumphs of neutrino physics
we know that neutrinos are massive and mixed.
However, in order to better delineate the path
toward the New Standard Model we would like to
know more

• Are neutrinos Majorana particles?
• What is the pattern of neutrino masses?
• What is the absolute mass scale?
• Is CP invariance violated in the lepton sector?
• Is there a relation between all of this and the
  baryon
• excess in the Universe?

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Summary of methods of neutrino mass determination
and (optimistic) sensitivities
Neutrino oscillations ?12 (U12),
, etc. observed 10-5 eV2 (only mass square
differences, independent
of Dirac vs. Majorana)
Single beta decay 0.2 eV (independent of Dirac
vs. Majorana)
ltmbgt2 S mi2 Uei2
Double beta decay 0.01 eV (only for Majorana)
ltmbbgt S mi Uei2 ei
(Majorana phases)
Observational cosmology 0.1 eV (independent of
Dirac vs. Majorana)
M S mi
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Note that conceptually simple methods of neutrino
mass determination, like TOF, are not sensitive
enough

• The time delay, with respect to massless
  particle, is
• Dt(E) 0.514 (m/E)2D, where m is in eV, E in
  MeV, D in 10 kpc,
• and Dt in sec.
• But there are no massless particles emitted by SN
  at the same
• time as neutrinos. Alternatively, we might look
  for a time delay
• between the charged current signal (i.e. ne) and
  the neutral current
• signal (dominated by nx). In addition , one might
  look for a
• broadening of the signal, and rearrangement
  according to the
• neutrino energy.

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lttgtsignal -lttgtreference for several mass
values Lower part shows the range of the deduced
masses. The dashed lines are 10 and 90
CL. See, Beacom P.V., Phys.Rev.D58,053010(1998)
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The two-body decays, like p -gt m nm are even
simpler conceptually, in the rest frame of the
pion mn2 mp2 mm2 - 2mpEm , but the
sensitivity is only to mn 170 keV with
little hope of a substantial improvement.
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Relation between ltmbbgt and other neutrino mass
observables as constrained by the oscillation
results.
Possible interval (unconfirmed) from 0nbb decay
blue shading normal hierarchy, Dm231 gt 0. red
shading inverted hierarchy Dm231 lt
0 shadingbest fit parameters, lines 95 CL
errors.
Limits of sensitivity in near future
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The degenerate mass region will be explored by
the next generation of 0nbb experiments and also
probed by ways independent on Majorana nature of
neutrinos.
ltmbbgt (eV)
0.1
0.01
Katrin sensitivity
Planck SDSS sensitivity
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• Three regions of ltmbbgt of interest
• i) Degenerate mass region where all mi gtgt Dm312.
  There ltmbbgt gt 0.1 eV.
• T1/2 for 0nbb decay lt 1026-27 y in this
  region. This region will be
• explored during the next 3-5 years with 0nbb
  decay experiments
• using 100 kg sources . Moreover, most if not
  all of that mass region
• will be explored also by study of ordinary b
  decay and by the
• observational cosmology. These latter
  techniques are independent of
• whether neutrinos are Majorana or Dirac
  particles.
• ii) Inverted hierarchy region where m3 could be lt
  Dm312. However,
• quasidenegerate normal hierarchy is also
  possible for
• ltmbbgt 20-100 meV. T1/2 for 0nbb decay is
  1027-28 years here, and
• could be explored with ton size experiments.
  Proposals for such
• experiments, with timeline 10 years, exist.
• iii) Normal mass hierarchy, ltmbbgt lt 20 meV. It
  would be necessary to
• use 100 ton experiments. There are no
  realistic ideas how to
• do it.

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However, life is not simple. Even with infinite
precision and with two independent mass
determinations, we cannot decide which hierarchy
is the correct one. We still need a long
baseline experiment with matter effects. For
example
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For a fixed ltmbbgt there is a continuum of
solutions, some with the same Smi and other with
different Smi.
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Combined results of the claimed 76Ge 0nbb
discovery and the most restrictive observational
cosmology constraint. There is a clear conflict

in this case.
From Fogli et al, hep-ph/0608060
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Leaving aside the all important question whether
the 0nbb experimental evidence will withstand
further scrutiny and whether the
cosmological constraint is reliable and model
independent, lets discuss various possible
scenarios suggested by this test of consistency.
Possibility 1 Both neutrino mass determination
give a positive and consistent result (the
results intersect on the expected band and both
suggest a degenerate mass pattern. (Everybody is
happy, even though somewhat surprised since the
degenerate scenario is a bit unexpected.)
Possibility 2 0nbb will not find a positive
evidence (the present claim will be shown to be
incorrect) but observational cosmology will give
a positive evidence for a degenerate mass
scenario, i.e., a situation opposite to the
previous slide. (This will also be
reluctantly accepted as an evidence that
neutrinos are not Majorana but Dirac.)
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• Possibility 3 The situation on the previous
  slide is confirmed.
• The positive evidence stemming from 0nbb decay is
  confronted with
• a lack of evidence from observational cosmology.
  What now?
• Is there a possible scenario that would
  accommodate such
• a possibility?
• The answer is yes and deserves a more detailed
  explanation.
• Actually, this can happen for two reasons
• The 0nbb decay is not caused by the exchange of
  the light
• Majorana neutrinos, but by some other
  mechanism. The obvious
• question then is how can we tell which
  mechanism is responsible
• for the 0nbb decay.
• Even though the 0nbb decay is caused by the
  exchange
• of the light Majorana neutrinos the
  relation between the
• decay rate and ltmbbgt is rather different
  than what we thought,
• i.e. the nuclear matrix elements we used
  are incorrect. The
• obvious question then is how uncertain the
  nuclear matrix
• elements really are.

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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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• In the following I suggest that the Lepton Flavor
  violation (LFV)
• involving charged leptons provides a diagnostic
  tool for establishing
• the mechanism of ???? decay or Lepton Number
  Violation (LNV).

This assertion is 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.
The basic idea is that while the two processes,
LFV and LNV are, generally, governed by different
mass scales, one can establish (with some fine
tuning exceptions) a relation between these
scales.
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Consider the well studied LFV processes
then
If
SM extensions with high (GUT) scale LNV,

are essentially the only possibility.
O(1) gtgt 10-2
On the other hand if
then
it is possible that SM extensions with low (?
TeV) scale LNV exist.
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Nuclear matrix elements
A provocative question Do we know at all how
large the matrix elements really are? Or, in
other words, why there is so much variation among
the published calculated matrix elements?
from Bahcall et al
hep-ph/0403167 , spread of published values of
squared nuclear matrix element for 76Ge
This suggests an uncertainty of as much as a
factor of 5. Is it really so bad?
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In contrast, Rodin et al, nucl-th/0503063 suggest
that the uncertainty is much less, perhaps only
30 (within QRPA and its generalizations,
naturally). So, who is right?
Slowly and smoothly decreasing (except 96Zr) with
A
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(No Transcript)
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Nuclear matrix elements for the 2n decay deduced
from measured halflives. Note the pronounced
shell dependence.
1/T1/2 G(E,Z) (MGT2n)2
easily calculable phase space factor
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• What are the causes for the spread of the QRPA
• calculated values of M0n?
• M0n ltfOigt
• There are two sources of spread
• Differences in the way igt and fgt are obtained,
• often related to the difference in which the
• effective hamiltonian is chosen. In
  particular,
• the choice of the effective neutron-proton
• coupling constant gpp.
• Differences in the way the operator O is
• handled. In particular whether the
  correction
• for the short range nucleon-nucleon
  repulsion
• is made and how.

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In QRPA the 0n matrix element depends on the
number of s.p. states included. However, that
dependence is drastically reduced if we adjust
the coupling strength gpp accordingly (from the
2n decay here).
Calculation by F.Simkovic
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Comparison of M0n of Rodin et al. (RQRPA) and the
shell model results reported by A. Poves at
NDM06 Nucleus RQRPA
Poves Poves/1.3 ratio 76Ge
2.3-2.4
2.35 1.80 1.3 82Se

1.9-2.1 2.26 1.74
1.3 96Zr
0.3-0.4 100Mo
1.1-1.2
116Cd
1.2-1.4 130Te
1.3
2.13 1.64 0.8 136Xe
0.6-1.0
1.77 1.36 0.6 Note that the
SM calculations include the reduction caused
by the s.r.c. but not by the induced currents
(about 30 reduction). Also note that the
previous (tentative and preliminary) results as
privately communicated by F. Nowacki in 2004
included a rather small values for 100Mo and
96Zr, similar to the hole for 96Zr in QRPA. It
remains to be seen whether this feature persists.
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Summary and/or Conclusions

• Study of 0nbb decay entered a new era. No longer
  is the aim just to
• push the sensitivity higher and the background
  lower, but to explore
• specific regions of the ltmbbgt values.
• In agreement with the phased program the plan
  is to explore the
• degenerate region (0.1-1 eV) first, with 100
  kg sources, and
• prepare the study of inverted hierarchy
  (0.01-0.1eV) region
• with ton sources that should follow later.
• In this context it is important to keep in mind
  the questions I discussed
• Relation of ltmbbgt and the absolute mass (rather
  clear already, becoming less uncertain with
  better oscillation results).
• Mechanism of the decay (exploring LFV, models of
  LNV, running of
• LHC to explore the TeV mass particles).
• Nuclear matrix elements (exploring better, and
  agreeing on, the
• reasons for the spread of calculated
  values, and deciding on the
• optimum way of performing the calculations,
  while pursuing vigorously
• also the application of the shell model).

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Illustration I RPV SUSY R (-1)3(B-L) 2s
Spares
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Illustration II Left-Right Symmetric Model
Spares
SU(2)L ? SU(2)R ? U(1)B-L ? SU(2)L ? U(1)Y
? U(1)EM
?
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Spares
Two-nucleon probability distribution, with and
without correlations, MC with realistic
interaction. O. Benhar - private communication
no s.r.c.
nuclear matter, saturation density
nuclear matter, half of the saturation density
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Spares
The integrand of M0n, M0n
P(r) dr based
on a semirealistic, exactly solvable model, see
J. Engel and P.V., PRC69,034304 (2004).
There is essentially no effect of short range on
the broken pairs part One can see that
the partial cancellation between the two parts
enhances the effect of short range correction.
Without short range correction
With short range correction
P(r)
Pairing part
Broken pairs part
r (fm)