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1.5.3 Hot Dark Matter: Data on Neutrino Mass

The upper limit on the electron neutrino mass is roughly 10-15 eV; the current Particle Data Book (Barnett et al. 1996) notes that a more precise limit cannot be given since unexplained effects have resulted in significantly negative measurements of m(nue)2 in recent precise tritium beta decay experiments. The (90% C.L.) upper limit on an effective Majorana neutrino mass 0.65 eV from the Heidelberg-Moscow 76Ge neutrinoless double beta decay experiment (Balysh et al. 1995). The upper limits from accelerator experiments on the masses of the other neutrinos are m(nuµ)< 0.17 MeV (90% C.L.) and m(nutau) < 24 MeV (95% C.L.). Since stable neutrinos with such large masses would certainly ``overclose the universe'' (i.e., prevent it from attaining its present age), the cosmological upper limits follow from the neutrino contribution to the cosmological density Omeganu = m(nu) / (92 h2 eV) < Omega0. There is a small window for an unstable nutau with mass ~ 10-24 MeV, which could have many astrophysical and cosmological consequences: relaxing the Big-Bang Nucleosynthesis bound on Omegab and Nnu, allowing BBN to accommodate a low (less than 22%) primordial 4He mass fraction or high deuterium abundance, improving significantly the agreement between the CDM theory of structure formation and observations, and helping to explain how type II supernovae explode (Gyuk & Turner 1995).

But there is mounting astrophysical and laboratory data suggesting that neutrinos oscillate from one species to another, and therefore that they have non-zero mass. The implications if all these experimental results are taken at face value are summarized in Table 1.5. Of these experiments, the ones that are most relevant to neutrinos as hot dark matter are LSND and the higher energy Kamiokande atmospheric (cosmic ray) neutrinos. But the experimental results that are probably most secure are those concerning solar neutrinos, suggesting that some of the electron neutrinos undergo MSW oscillations to another species of neutrino as they travel through the sun (see, e.g., Hata & Langacker 1995, Bahcall 1996).

The recent observation of events that appear to represent nubarµ -> nubare oscillations followed by nubare + p -> n + e+, n + p -> D + gamma, with coincident detection of e+ and the 2.2 MeV neutron-capture gamma-ray in the Liquid Scintillator Neutrino Detector (LSND) experiment at Los Alamos suggests that Delta m2 ident |m(nuµ)2 - m(nue)2| > 0 (Athanassopoulos et al. 1995, 1996). The analysis of the LSND data through 1995 strengthens the earlier LSND signal for nubarµ -> nubare oscillations. Comparison with exclusion plots from other experiments implies a lower limit Delta m2µe ident |m(nuµ)2 - m(nue)2| gtapprox 0.2 eV2, implying in turn a lower limit mnu gtapprox 0.45 eV, or Omeganu gtapprox 0.02 (0.5/h)2. This implies that the contribution of hot dark matter to the cosmological density is larger than that of all the visible stars (Omega* approx 0.004 (Peebles 1993, eq. 5.150). More data and analysis are needed from LSND's nuµ -> nue channel before the initial hint (Caldwell 1995) that Delta m2µe approx 6 eV2 can be confirmed. Fortunately the KARMEN experiment has just added shielding to decrease its background so that it can probe the same region of Delta m2µe and mixing angle, with sensitivity as great as LSND's within about two years (Kleinfeller 1996). The Kamiokande data (Fukuda 1994) showing that the deficit of E > 1.3 GeV atmospheric muon neutrinos increases with zenith angle suggests that nuµ -> nutau oscillations (2) occur with an oscillation length comparable to the height of the atmosphere, implying that Delta m2tauµ ~ 10-2 eV2 - which in turn implies that if either nuµ or nutau have large enough mass (gtapprox 1 eV) to be a hot dark matter particle, then they must be nearly degenerate in mass, i.e., the hot dark matter mass is shared between these two neutrino species. The much larger Super-Kamiokande detector is now operating, and we should know by about the end of 1996 whether the Kamiokande atmospheric neutrino data that suggested nuµ -> nutau oscillations will be confirmed and extended. Starting in 1997 there will be a long-baseline neutrino oscillation disappearance experiment to look for nuµ -> nutau with a beam of nuµ from the KEK accelerator directed at the Super-Kamiokande detector, with more powerful Fermilab-Soudan, KEK-Super-Kamiokande, and possibly CERN-Gran Sasso long-baseline experiments later.

Table 5. Data Suggesting Neutrino Mass

Solar nue deficit Delta m2ex = 10-5 eV2, sin2 2thetaex small
Atm nuµ deficit Delta m2µy appeq 10-2 eV2, sin2 2thetaµy ~ 1
Kamiokande Enu > 1.3 GeV
Reactor nue probably excludes y = e, so atm nuµ -> nutau or nus
BBN excludes nuµ -> nus with large mixing, so y = tau
LSND Delta m2µe approx 1-10 eV2, sin2 2thetaµe small
excludes x = µ, so solar nue -> nus
Cold + Hot Dark Matter Sigma mnu approx 5 h502 eV

Evidence for non-zero neutrino mass evidently favors CHDM, but it also disfavors low-Omega models. Because free streaming of the neutrinos damps small-scale fluctuations, even a little hot dark matter causes reduced fluctuation power on small scales and requires substantial cold dark matter to compensate; thus evidence for even 2 eV of neutrino mass favors large Omega and would be incompatible with a cold dark matter density Omegac as small as 0.3 (PHKC95). Allowing Omeganu and the tilt to vary, CHDM can fit observations over a somewhat wider range of values of the Hubble parameter h than standard or tilted CDM (Pogosyan & Starobinsky 1995a, Liddle et al. 1996b). This is especially true if the neutrino mass is shared between two or three neutrino species (Holtzman 1989; Holtzman & Primack 1993; PHKC95; Pogosyan & Starobinsky 1995b; Babu, Schaefer, & Shafi 1996), since then the lower neutrino mass results in a larger free-streaming scale over which the power is lowered compared to CDM. The result is that the cluster abundance predicted with Omeganu approx 0.2 and h approx 0.5 and COBE normalization (corresponding to sigma8 approx 0.7) is in reasonable agreement with observations without the need to tilt the model (Borgani et al. 1996) and thereby reduce the small-scale power further. (In CHDM with a given Omeganu shared between Nnu = 2 or 3 neutrino species, the linear power spectra are identical on large and small scales to the Nnu = 1 case; the only difference is on the cluster scale, where the power is reduced by ~ 20% (Holtzman 1989, PHKC95, Pogosyan & Starobinsky 1995a, 1995b).


2 The Kamiokande data is consistent with atmospheric nuµ oscillating to any other neutrino species y with a large mixing angle thetaµy. But as summarized in Table 1.5 (see further discussion and references in, e.g., Primack et al. 1995, hereafter PHKC95; Fuller, Primack, & Qian 1995) nuµ oscillating to nue with a large mixing angle is probably inconsistent with reactor and other data, and nuµ oscillating to a sterile neutrino nus (i.e., one that does not interact via the usual weak interactions) with a large mixing angle is inconsistent with the usual Big Bang Nucleosynthesis constraints. Thus, by a process of elimination, if the Kamiokande data indicating atmospheric neutrino oscillations is right, the oscillation is nuµ -> nutau. Back.

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