The LSND results [33], if confirmed, would almost certainly imply a fourth,
sterile, neutrino (the
lineshape does not allow a fourth light active neutrino),
in which one or two of the neutrinos are separated from the others by
eV.
There could be even more sterile neutrinos.
In the schemes,
is heavier or lighter than
by
, with the splittings between the
latter controlled by
and
.
This case has generally been considered excluded by limits from
and
disappearance. However, small recent changes in the LSND
favored range (to lower
)
imply that these schemes are barely allowed for
, and possibly for
.
The
case may offer a theoretical advantage over
schemes
in that the
is more distinct from the active neutrinos.
In the schemes,
one has two pairs of mass eigenstates
and
, with
eV
,
eV
(MSW) or
eV
(vacuum), and
eV
,
where
.
The reactor data imply that
must be largely restricted to one of the
pairs. The cases
and
are referred to
as hierarchical and inverted, respectively. The inverted case, and to a
somewhat lesser extent the hierarchical case, are quasi-degenerate, and
may be unstable under radiative corrections [28].
The and some versions of the
models involve a
significant hot or warm neutrino component to the dark matter.
The extra sterile neutrino may be of importance for big bang nucleosynthesis.
The versions with
in the heavier group may give significant
contributions to
, although there may be major cancellations
for large mixing.
The recent SuperKamiokande [19] and MACRO [34] atmospheric neutrino data
exclude the pure
case, in which the atmospheric neutrino results
are associated with
, while Super-K solar neutrino data [35]
probably eliminates
the pure
(i.e.,
) explanation for the solar neutrinos. These were the simplest and perhaps most
plausible cases. However, more general mixing schemes with significant
admixtures in the solar and atmospheric neutrinos are
possible [18,30,36].