| © CAMBRIDGE UNIVERSITY PRESS 1999
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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(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 m2eµ |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 m2µe |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 m2µe 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 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 µ -> oscillations (2) occur with an oscillation length comparable to the height of the atmosphere, implying that m2µ ~ 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.
Solar e deficit | m2ex = 10-5 eV2, sin2 2ex small | ||||||||||||
Atm µ deficit | m2µy 10-2 eV2, sin2 2µy ~ 1 | ||||||||||||
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
|
| 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).
2 The
Kamiokande data is consistent with atmospheric µ oscillating
to any other neutrino species y with a large mixing angle
µy. 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)
µ oscillating to
e with a large mixing
angle is probably inconsistent with
reactor and other data, and µ oscillating to a sterile
neutrino s (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 µ ->
. Back.