The partial decay rate for (5.1) is given by
The quantity is a Lorentz invariant quadratic
form in F,G,R and H. All scalar products can be expressed
in the 5 independent variables
and
,
such that
Carrying out the integrations over the remaining variables
in (5.13) gives [51]
where
The form factors F,G,R and H are independent of and
. It is therefore possible to carry out two more
integrations in
(5.15) with the result
The explicit form of is
For data analysis it is useful to represent this result in a still
different form which displays the and
dependence more clearly [52]:
One obtains
where
The definition of in (5.21) corresponds
to the combinations used by Pais and Treiman [52] (the
different sign in the terms
is due to our use of the metric
). The form factors
agree with the expressions given in [52]. We conclude that our
convention for the relative phase in the definition of the form factors
in Eq. (5.12) agrees with the one used by Pais and Treiman.
The comparison of
(5.18) with
[53, table II,] shows furthermore that it also agrees with
this reference.
The quantity can now easily be obtained from (5.19)
by integrating over
and
,