The CKM quark mixing matrix is the transformation
between the strong interaction quark eigenstates
and the weak interaction quark eigenstates,
The transformation between these strong and weak mass eigenstates
takes the form:
A test of the unitarity of the CKM matrix would serve to limit certain extensions
to the current Standard Model of elementary particles. This test can be performed
most reliably by a measure of the sum of the elements of the top row of the matrix:
. If the sum 
is
equal to unity, then the matrix is unitary. Using the accepted value for
and the limits on 
, in combination with the value of 
extracted from nuclear beta decay, one finds the result
. This value
includes the most reliable nuclear structure dependent corrections, and is lower
than the Standard Model prediction by 
.
A second evaluation of , using the value for extracted from
neutron beta decay, brings the value of 
up to 
, which is higher than the Standard Model prediction
by 
[15].
A precise extraction of is needed to resolve the discrepancy
between these two calculations of . This will be accomplished with
the measurement of the pion beta decay rate 
, as
where 
is the weak vector coupling constant.