The partial decay rate is
The Dalitz plot density
is a Lorentz invariant function which contains V and A in the following form [6],
where
and
For later convenience, we note that
The indices IB, SD and INT stand respectively for the contribution from inner Bremsstrahlung, from the structure dependent part and from the interference term between the IB and the SD part in the amplitude.
To get a feeling for the magnitude of the various contributions
IB,
and 
to the decay rate, we consider
the integrated rates
where 
etc.
For the region 
we take the full phase space
for 
, and
for the Bremsstrahlung contribution. Here 
stands for the modulus of the
lepton three momentum in the kaon rest system 
.
We consider constant
form factors
V, A and write for the rates and for the corresponding branching ratios
with
The values for 
and 
are listed in table 1.1.
Table 1.1:
The quantities
.
SD
and INT
are evaluated with full phase space,
IB with
restricted kinematics (1.20).
To estimate 
and 
, we note that the form factors V,A
are of
order
From this and from the entries in the table
one concludes that for the above regions 
, the interference terms
are negligible in
, whereas they are important in 
. Furthermore,
IB is negligible for 
, because it is helicity suppressed as can
be seen from the factor 
in 
. This term
dominates however in 
.
