There is mounting astrophysical and laboratory data suggesting that neutrinos oscillate from one species to another [27], which can only happen if they have non-zero mass. Of these experimental results, the ones that are regarded as probably most secure are those concerning atmospheric neutrino oscillations from Super-Kamiokande (see the chapter by John Learned) and solar neutrinos from several experiments (see the chapter by Wick Haxton). But the experimental results that are most relevant to neutrinos as hot dark matter are from the Liquid Scintillator Neutrino Detector (LSND) experiment at Los Alamos (see the chapter by David Caldwell).
Older Kamiokande data
[83]
showed that, for events attributable
to atmospheric neutrinos with visible energy E > 1.3 GeV, the deficit
of µ increases with
zenith angle. The
Super-Kamiokande detector has confirmed and extended the results of its
smaller predecessor
[84]. These
data imply that
µ
->
oscillations occur with a
large mixing angle
sin2 2
> 0.82 and an
oscillation length several times the
height of the atmosphere, which implies that 5 x 10-4 <
m2
µ < 6 x 10-3
eV2 (90% CL). (Neutrino
oscillation experiments measure not the masses, but rather the
difference of the squared masses, of the oscillating species, here
m
µ2
|m(
)2
- m(
µ)2|.) This in
turn implies that if other data requires either
µ or
to have large enough mass
(
1 eV) to be a hot dark matter
particle, then they must be nearly equal in mass, i.e., the hot dark
matter mass would be shared between these two neutrino species. Both
the new Super-Kamiokande atmospheric
e data and the lack of a
deficit of
e in the CHOOZ
reactor experiment
[85]
make it quite unlikely that the atmospheric neutrino oscillation is
µ
->
e. If the oscillation
were instead to a
sterile neutrino, the large mixing angle implies that this sterile
species would become populated in the early universe and lead to too
much 4He production during the Big Bang Nucleosynthesis epoch
[86].
(Sterile neutrinos are discussed further below.) It may be
possible to verify that
µ
->
oscillations
occur via a long-baseline neutrino oscillation experiment. The K2K
experiment is looking for missing
µ due to
µ ->
oscillations with a beam of
µ from the Japanese KEK
accelerator directed at the Super-Kamiokande detector, with more
powerful Fermilab-Soudan and CERN-Gran Sasso long-baseline experiments
in preparation, the latter of which will look for
appearance.
The observation by LSND 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, suggests
that
mµ
e2 > 0
[87].
The independent LSND data
[88]
suggesting that
µ
->
e oscillations are also
occurring is consistent with, but has less statistical weight than, the
LSND signal for
µ
->
e oscillations.
Comparison of the latter with exclusion plots from other experiments
allows two discrete values of
m2µ
e, around 10.5 and 5.5
eV2, or a range 2 eV2
m2µ
e
0.2 eV2.
The lower limit in turn implies a lower limit
m
0.5 eV, or
0.01 (0.65 /
h)2. This would imply that the
contribution of hot dark matter to the cosmological density is at least
as great as that of all the visible stars
*
0.0045
(0.65 / h)
[89].
Such an important conclusion requires
independent confirmation. The KArlsruhe Rutherford Medium Energy
Neutrino (KARMEN) experiment has added shielding to decrease its
background so that it can probe a similar region of
m2µ
e and neutrino mixing angle; the KARMEN results exclude a significant
portion of the LSND parameter space, and the numbers quoted above take
into account the current KARMEN limits. The Booster Neutrino
Experiment (BOONE) at Fermilab should attain greater sensitivity.
The observed deficit of solar electron neutrinos in three different
types of experiments suggests that some of the
e undergo
Mikheyev-Smirnov-Wolfenstein matter-enhanced oscillations
e
->
x to another species of
neutrino
x with
me x2
10-5
eV2 as they travel through the
sun [90],
or possibly ``Just-So'' vacuum oscillations with even smaller
me
x2
[91].
The LSND
µ
->
e signal with a much larger
me
µ2 is inconsistent with x = µ,
and the Super-Kamiokande
atmospheric neutrino oscillation data is inconsistent with x =
. Thus
a fourth neutrino species
s is required if all these
neutrino
oscillations are actually occurring. Since the neutral weak boson
Z0 decays only to three species of neutrinos, any additional
neutrino species
s could
not couple
to the Z0, and is called
``sterile.'' This is perhaps distasteful, although many modern
theories of particle physics beyond the standard model include the
possibility of such sterile neutrinos. The resulting pattern of
neutrino masses would have
e and
s very light, and
m(
µ)
m(
)
(
me
µ2)1/2,
with the
µ and
playing the role of the hot dark
matter particles if their masses are high enough
[92]. This
neutrino spectrum might also explain how heavy elements are synthesized
in core-collapse supernova explosions
[93].
Note that the required solar neutrino mixing angle is very small,
unlike that required to explain the atmospheric
µ deficit, so a
sterile neutrino species would not be populated in the early universe and
would not lead to too much 4He production.
Of course, if one or more of the indications of neutrino oscillations
are wrong, then a sterile neutrino would not be needed and other
patterns of neutrino masses are possible. But in any case the
possibility remains of neutrinos having large enough mass to be hot dark
matter. Assuming that the Super-Kamiokande data on atmospheric
neutrinos are really telling us that
µ oscillates to
,
the two simplest possibilities regarding neutrino masses are as follows:
A) Neutrino masses are hierarchical like all the other
fermion masses, increasing with generation, as in see-saw models. Then
the Super-Kamiokande
m2
0.003 implies
m(
)
0.05 eV, corresponding to
![]() | (11) |
This is not big enough to affect galaxy formation significantly, but it is another puzzling cosmic coincidence that it is close to the contribution to the cosmic density from stars.
B) The strong mixing between the mu and tau neutrinos
implied by the Super-Kamiokande data suggests that these neutrinos are
also nearly equal in mass, as in the Zee model
[94] and many
modern models
[91,
92]
(although such strong mixing can
also be explained in the context of hierarchical models based on the
SO(10) Grand Unified Theory
[95]). Then the above
is just a lower limit. An upper limit is given by
cosmological structure formation. In Cold + Hot Dark Matter (CHDM)
models with
m = 1,
we saw in the previous section that if
is greater than about 0.2 the voids are too big and there
is not enough early structure. In the next section we consider the
upper limit on
if
m
0.4, which is favored
by a great deal of data.