The matrix element for 
has the general structure
with
To obtain the matrix element for 
, one replaces 
by
The processes (3.1)
and (3.2) thus involve the four 
form factors
, 
which depend on
the square of the four momentum transfer to the leptons.
Let 
or 
.
is referred to as the vector form factor, because
it specifies the P-wave projection of the crossed channel matrix elements
.
The S-wave projection is described by the scalar form factor
Analyses of 
data frequently assume a linear dependence
For a discussion of the validity of this approximation see [24,3]
and references cited therein. Eq. (3.8) leads to a constant
,
The form factors 
are analytic functions in the complex
t-plane cut along the positive real axis. The cut starts at 
. In our phase convention, the form factors are real in the physical
region
The kinematics of (spin averaged) 
decays needs two variables, for
which we choose
In the K rest frame, y (z) is proportional to the charged lepton (pion) energy,
The physical region for y and z is
or, equivalently,
