Now that the astrophysicists have convinced us of the necessity of dark matter, what candidates have we particle physicists to offer? Neutrinos are the prime candidates for hot dark matter, whereas there are numerous candidates for cold dark matter, including axions, supersymmetric particles such as the lightest neutralino, the axino and the gravitino, and possible superheavy metastable relics such as cryptons. Axions were not much discussed here, so I concentrate on neutrinos, supersymmetric particles and superheavy relics.
As we were reminded at this meeting, alternative interpretations of the solar and atmospheric neutrino data are not excluded, but oscillations between different neutrino mass eigenstates are very much the favoured interpretations.
In the case of atmospheric neutrinos, the favoured oscillation pattern is
µ
. There is no evidence for
oscillations involving
the e, there being
no anomaly in the atmospheric
e data, and
we also have a stronger upper limit on
e
µ oscillations
from the Chooz data. Also,
µ
sterile
oscillations are
disfavoured by the zenith-angle distributions. The central value of the
mass-squared difference
m2
~ 2.5 × 10-3 eV2, and the mixing angle is large:
sin2 2
> 0.8
[28].
In the case of solar neutrinos,
e
µ and/or
oscillations are preferred, though some admixture of
e
sterile cannot be
excluded. After SNO
[29], the data
increasingly favour the large-mixing-angle (LMA) solution, with
10-5 eV2 <
m2
< 10-4 eV2, though large mixing with a somewhat
smaller value of
m2
(the LOW solution) is also possible
[30], as seen in
Fig. 8.
|
Figure 8. Regions of 2-neutrino oscillation parameters allowed [30] by the available solar neutrino data, including those from SNO [29]. |
We heard at this meeting of a possible indication for neutrinoless
double-
decay, corresponding to 0.11 eV < <m>
< 0.56 eV
[31]
(2) .
The claimed significance is not high, around 2
, whereas 4 or 5
would be needed to
claim a discovery.
The claimed indication rests on the interpretation of one possible bump in
the energy spectrum, with some other bumps being interpreted as other
radioactive decays, and the rest resisting interpretation. However, the
analysis has been criticized
[33],
in particular because the strengths of the
other claimed radioactive decays appear to be too high. The
Heidelberg-Moscow experiment has now reached the limit of its sensitivity,
so we must wait to see what other experiments find. In a conventional
hierarchical scenario for neutrino masses, one could expect to see a
signal at the level
<m> ~ 0.01 eV, for which a future
large-scale experiment such as the GENIUS proposal will be needed.
|
Figure 9. The constraint on the neutrino
mixing angle
|
Tritium -decay
experiments are largely complementary to neutrinoless
double- decay
experiments
[34], since they
measure a different observable:
| (4) |
As we heard at this meeting, the previous problems of these experiments,
namely the tendency to prefer negative values of <m>
2 and the
appearance of a `bump' near the end of the spectrum, have now been
resolved. The former has been traced to a roughening transition in the
frozen Tritium surface layer, and the latter to plasma effects related to
particles trapped in the spectrometer. The limits accessible with the
present experiments have now been almost saturated. Each experiment
reports an upper limit ~ 2.2 eV, but a more conservative
interpretation would be
| (5) |
As we also heard at this meeting, there are ambitious ideas for a next-generation experiment called KATRIN [35], which is proposed to be 70 m long and 8 m in diameter, and able to reach a limit of 0.35 eV. This is certainly a worthwhile objective, but the question still remains: how to reach the atmospheric neutrino mass scale ~ 0.05 eV.
Combining the upper limit
(5)
from Tritium
decay
with the upper limit
<m> < 0.56 eV from
0 decay, and
recalling the lower limits:
m2
> 0.003 eV2 from atmospheric
neutrinos, 10-4 eV2 for the LMA solar solution,
one can infer the
following allowed range for the total relic neutrino density:
| (6) |
Though not conclusive, this is certainly consistent with the lack of
enthusiasm for hot dark matter indicated by studies of large-scale
structure. The CMB is relatively insensitive to
, whereas large-scale
structure is very sensitive to
[4].
We can look forward to significant advances in neutrino physics in the coming years that will check the emergent picture outlined above. The SNO experiment will soon provide important new data on the ratio of neutral- and charged-current events [29]. Also starting to take data is the KamLAND experiment [36], which should provide a conclusive test of the LMA interpretation of the solar neutrino data. Shortly, we can also expect important data from BOREXINO [37], that will also help pin down the interpretation of solar neutrinos.
Long-baseline neutrino experiments
[38]
are now swinging into
action to probe the interpretation of atmospheric neutrinos, led by K2K
[39].
The Super- KAMIOKANDE detector is currently being reconfigured after its
accident, so as to enable data-taking for the K2K experiment to restart.
Meanwhile, the NUMI beam and the MINOS detector are being prepared in the
United States
[40],
in parallel with the CNGS beam and the OPERA detector in Europe
[41].
The MINOS experiment is aimed at measurements of the oscillation
pattern, neutral- and charged-current rates, and the search for
e appearance in a
µ beam, whilst
the OPERA detector is aimed at
detecting production in a
µ beam due to
µ
oscillations. In the
longer term, the JHF is under construction
[42],
and will provide the opportunity to generate a more intense neutrino beam
that could be directed towards the SuperKAMIOKANDE detector or its
projected megaton-class successor, HyperKAMIOKANDE. The latter would
provide a first opportunity to search for CP neutrino oscillations.
The search for CP violation could be made much more precise if more
intense, pure e
and/or µ were
available. A relatively new
idea to realize this objective is to store radioactive ions whose decays
would yield pure e
and 
e beams
[43]. A
longer-standing concept is that of a neutrino factory based on the decays
of muons in a storage ring
[44].
Since this produces simultaneously
µ and
e beams, both
with
well-understood spectra, a neutrino factory is the ultimate weaqpon for
neutrino-oscillation studies. Among the objectives of this programme would
be the ultimate searches for
13 and CP
violation
[45],
and determining the sign of the neutrino mass hierarchy.
In addition to neutrino-oscillation studies, a neutrino factory would also offer interesting prospects for high-statistics studies of neutrino interactions with a short-baseline beam [46]. The intense proton source would provide other particle physics opportunities, for example using stopped or slow muons [47], as well as opportunities in other areas of physics [48]. Many accelerator laboratories around the world, including Europe, Japan and the United States, have initiated studies of neutrino factories. However, in each region it seems that the first choice for a major new accelerator facility is a linear e+e- collider. Thus there is a danger that the neutrino factory will be `always the bridesmaid, never the bride'. The priority accorded a linear e+e- collider is understandable, but a balanced accelerator programme for the world should surely also include a neutrino factory somewhere. Both machines could cast important light on the dark matter problem, in different ways.
2 The possible interpretation in the context of oscillation experiments was also discussed here [32]. Back.