There is no compelling laboratory evidence for non-zero neutrino mass. The direct limits from kinematic searches for the masses yield the upper limits [11]
where the upper limit on 
is a recent result
from ALEPH [12], which makes use of both the invariant mass and
the visible energy in the events.
All of these are much smaller than the
corresponding charged lepton masses. One disturbing feature is that the
tritium 
decay experiments all yield
negative 
values, with a weighted average
,
suggesting a common systematic or theoretical uncertainty in the
experiments. Until this is understood the precise upper limit must be
considered somewhat questionable.
Searches for neutrinoless double beta decay (
) are
sensitive to the combination of Majorana masses
,
where it is assumed that the 
is a superposition
of mass eigenstates. 
is
a CP phase, allowing for cancellations between the different terms,
as occurs for a Dirac neutrino. Currently, the most stringent upper
limit is 
eV from the Heidelberg-Moscow
Ge experiment [13]. There is some uncertainty in the
precise value of the upper limit, since it depends on a theoretical
calculation of a nuclear matrix element.
There have been many accelerator and reactor searches for neutrino
oscillations. None have reported a compelling positive signal.
The Los Alamos LSND experiment has recently reported [14]
9 candidate events for 
oscillations. However, an alternative analysis [15]
of the same data with
somewhat more stringent cuts obtains no signal above background.
If the LSND results are confirmed, values
for the mass-squared difference
would be required.
