As described in Section 2 many theories with coupling constant unification, such as grand unified theories, predict a seesaw-type mass [7,9]
where 
is the mass of a superheavy neutrino, 
, c, t are
the up-type quarks, and 
is a radiative correction. The general
range suggested by the solar neutrinos is consistent with the
GUT-seesaw range. In particular, in the string motivated models one
expects the heavy mass to be a few orders of magnitude below the
unification scale [62]. As an example, for 
GeV one predicts
In this case one would expect MSW oscillations of 
in the
sun, and perhaps the 
is in the range relevant to hot dark
matter. If this is the case there is a good chance that 
oscillations will be observed in accelerator appearance
experiments now
underway at CERN. Alternately, for small modifications in the seesaw one
could have somewhat smaller 
masses that could lead to 
oscillations in the range relevant to the atmospheric
neutrino anomaly.
The specific predictions are highly model dependent, and one cannot make anything more than general statements at this time. It will be important to follow up all experimental possibilities. If oscillations are responsible for the atmospheric neutrino results it should possible to prove it with long baseline oscillation experiments proposed at Fermilab, Brookhaven, and elsewhere.
It is difficult to account for solar neutrinos, a component of hot dark
matter, and atmospheric neutrinos simultaneously.
There are just not
enough neutrinos to go around.
Confirmation of the LSND
events would further
complicate the situation
.
Attempts to account for all of these
effects generally invoke additional sterile neutrinos and/or nearly
degenerate neutrinos, so that the mass differences can be much smaller than
the average masses [64].
