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Towards absolute neutrino masses
Petr Vogel, Caltech
NOW 2006, Otranto, September 2006
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:
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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?
Summary of methods of neutrino mass
determination and (optimistic) sensitivities::
Neutrino oscillations: 12 (U12), m12  m22 , 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)
Double beta decay:
0.01 eV
(only for Majorana)
<mb>2 = S mi2 |Uei|2
<mbb> = |S mi |Uei|2 ei|
Observational cosmology: M = S m
i
0.1 eV (independent of
Dirac vs. Majorana)
(Majorana phases)
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.
<t>signal -<t>reference
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)
The two-body decays, like p+ -> 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.
Relation between <mbb> and other neutrino mass observables
as constrained by the oscillation results.
Possible interval
(unconfirmed)
from 0nbb decay
blue shading:
normal hierarchy,
Dm231 > 0.
red shading:
inverted hierarchy
Dm231 < 0
shading:best fit
parameters, lines
95% CL errors.
Limits of sensitivity
in near future
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.
<mbb>
(eV)
0.1
0.01
Planck +SDSS
sensitivity
Katrin
sensitivity
Three regions of <mbb> of interest:
i) Degenerate mass region where all mi >> Dm312. There <mbb> > 0.1 eV.
T1/2 for 0nbb decay < 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 < Dm312. However,
quasidenegerate normal hierarchy is also possible for
<mbb> ~ 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, <mbb> < 20 meV. It would be necessary to
use ~100 ton experiments. There are no realistic ideas how to
do it.
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
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
For a fixed <mbb> there is a continuum of solutions, some
with the same Smi and other with different Smi.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
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
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.)
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:
1) 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.
2) Even though the 0nbb decay is caused by the exchange
of the light Majorana neutrinos the relation between the
decay rate and <mbb> 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.
Light Majorana neutrino,
only Standard Model
weak interactions
Heavy Majorana neutrino
interacting with WR.
Model extended to include
right-handed current
interactions.
Light or heavy Majorana
neutrino. Model extended
to include right-handed WR.
Mixing extended between
the left and right-handed
neutrinos.
Supersymmetry with
R-parity violation.
Many new particles
invoked. Light
Majorana neutrinos exist
also.
It is well known that the amplitude for the light neutrino
exchange scales as <mbb>. On the other hand, if heavy
particles of scale L are involved the amplitude scales as 1/L5.
The relative size of the heavy (AH) vs. light particle (AL)
exchange to the decay amplitude is (a crude estimate)
AL ~ GF2 mbb/<k2>,
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.
AL/AH ~ mbb L5/ <k2> MW4
Thus for mbb = 0.2 eV, <k2> = 502 MeV2, and AL/AH~ 1
L5 ~ 502x1012x804x1036/0.2 eV ~ 5x1059 eV
L ~ 1012 eV = 1 TeV
Clearly, the heavy particle mechanism could
compete with the light Majorana neutrino
exchange only if the heavy scale L is between
about 1 - 5 TeV. Smaller L are already
excluded and larger ones will be unobservable
due to the fast L5 scale dependence.
In the following I suggest that the Lepton Flavor violation (LFV)
involving charged leptons provides a “diagnostic tool” for establishing
the mechanism of 0nbb 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.
Consider the well studied LFV processes:
If
then
SM extensions with high (GUT) scale LNV,
are essentially the only possibility.
On the other hand if
~ O(1) >> 10-2 then
it is possible that SM extensions with low ( TeV) scale
LNV exist.
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?
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?
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Slowly and smoothly decreasing (except 96Zr) with A
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
What are the causes for the spread of the QRPA
calculated values of M0n?
M0n = <f|O|i>
There are two sources of spread:
1) Differences in the way |i> and |f> 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.
2) 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.
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
Comparison of M0n of Rodin et al. (RQRPA) and
the shell model results reported by A. Poves at NDM06
Nucleus
76Ge
82Se
96Zr
100Mo
116Cd
130Te
136Xe
RQRPA
2.3-2.4
1.9-2.1
0.3-0.4
1.1-1.2
1.2-1.4
1.3
0.6-1.0
Poves
Poves/1.3
ratio
2.35
2.26
1.80
1.74
1.3
1.3
2.13
1.77
1.64
1.36
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.
0.8
0.6
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 <mbb> 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:
a) Relation of <mbb> and the absolute mass (rather clear already,
becoming less uncertain with better oscillation results).
b) Mechanism of the decay (exploring LFV, models of LNV, running of
LHC to explore the ~TeV mass particles).
c) 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).
Spares:
Illustration I: RPV SUSY [R = (-1)3(B-L) + 2s ]
Spares:
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
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
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).

Without short range correction
P(r)
With short range correction
Pairing part
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.
Broken pairs part
r (fm)