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 .
In the case of solar neutrinos, e µ and/or oscillations are preferred, though some admixture of e sterile cannot be excluded. After SNO , 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 , as seen in Fig. 8.
We heard at this meeting of a possible indication for neutrinoless double- decay, corresponding to 0.11 eV < <m> < 0.56 eV  (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 , 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 12 and the Tritium -decay observable <m> that would be imposed if 0.11 eV < <m> < 0.56 eV (thin lines) or 0.05 eV < <m> < 0.84 eV (thick lines) . The ranges of 12 favoured by the LMA (LOW) solutions are shaded between thin solid (dashed) lines.
Tritium -decay experiments are largely complementary to neutrinoless double- decay experiments , since they measure a different observable:
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
As we also heard at this meeting, there are ambitious ideas for a next-generation experiment called KATRIN , 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:
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 .
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 . Also starting to take data is the KamLAND experiment , which should provide a conclusive test of the LMA interpretation of the solar neutrino data. Shortly, we can also expect important data from BOREXINO , that will also help pin down the interpretation of solar neutrinos.
Long-baseline neutrino experiments  are now swinging into action to probe the interpretation of atmospheric neutrinos, led by K2K . 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 , in parallel with the CNGS beam and the OPERA detector in Europe . 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 , 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 . A longer-standing concept is that of a neutrino factory based on the decays of muons in a storage ring . 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 , 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 . The intense proton source would provide other particle physics opportunities, for example using stopped or slow muons , as well as opportunities in other areas of physics . 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 . Back.