© CAMBRIDGE UNIVERSITY PRESS 1999

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(_e)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(_µ)< 0.17 MeV (90% C.L.) and m() < 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 = m() / (92 h² eV) < ₀. There is a small window for an unstable with mass ~ 10-24 MeV, which could have many astrophysical and cosmological consequences: relaxing the Big-Bang Nucleosynthesis bound on _b and N, 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 _µ -> _e oscillations followed by _e + p -> n + e⁺, n + p -> D + , with coincident detection of e⁺ and the 2.2 MeV neutron-capture -ray in the Liquid Scintillator Neutrino Detector (LSND) experiment at Los Alamos suggests that m²_eµ |m(_µ)² - m(_e)²| > 0 (Athanassopoulos et al. 1995, 1996). The analysis of the LSND data through 1995 strengthens the earlier LSND signal for _µ -> _e oscillations. Comparison with exclusion plots from other experiments implies a lower limit m²_µe |m(_µ)² - m(_e)²| 0.2 eV², implying in turn a lower limit m 0.45 eV, or 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 (_* 0.004 (Peebles 1993, eq. 5.150). More data and analysis are needed from LSND's _µ -> _e channel before the initial hint (Caldwell 1995) that m²_µe 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 m²_µe 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 _µ -> oscillations ⁽²⁾ occur with an oscillation length comparable to the height of the atmosphere, implying that m²_µ ~ 10^-2 eV² - which in turn implies that if either _µ or have large enough mass ( 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 _µ -> oscillations will be confirmed and extended. Starting in 1997 there will be a long-baseline neutrino oscillation disappearance experiment to look for _µ -> with a beam of _µ 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 e deficit	m2ex = 10-5 eV2, sin2 2ex small
Atm µ deficit	m2µy 10-2 eV2, sin2 2µy ~ 1
	Kamiokande E > 1.3 GeV
Reactor e	probably excludes y = e, so atm µ -> or s
BBN	excludes µ -> s with large mixing, so y =
LSND	m2µe 1-10 eV2, sin2 2µe small
	excludes x = µ, so solar e -> s
Cold + Hot Dark Matter	m 5 h502 eV

Evidence for non-zero neutrino mass evidently favors CHDM, but it also disfavors low- 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 and would be incompatible with a cold dark matter density _c as small as 0.3 (PHKC95). Allowing 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 0.2 and h 0.5 and COBE normalization (corresponding to ₈ 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 shared between N = 2 or 3 neutrino species, the linear power spectra are identical on large and small scales to the N = 1 case; the only difference is on the cluster scale, where the power is reduced by ~ 20% (Holtzman 1989, PHKC95, Pogosyan & Starobinsky 1995a, 1995b).