Within the QED structure function approach [5,6],
successfully applied nowadays to the evaluation
of the electromagnetic corrections to various high--energy
reactions of experimental interest, the cross section of a
annihilation including initial state radiation is
written, according to a QCD analogy to the
Drell--Yan process, as convolution of the following form:
Eq. (9) is based on the factorization theorems [7] of the
infrared and collinear singularities: actually,
is the hard--scattering cross section
(at the reduced energy scale 
) containing
the details of the short--range interaction and 
represents the
probability of finding inside a parent electron (positron) an
electron (positron) with a
momentum fraction x and virtualness s. Therefore,
the structure functions 
contain the long--distance (universal)
logarithmic contributions, due to the soft and/or
collinear photon radiation, which are naturally resummed
to all orders when solving the Renormalization Group
equation satisfied by the structure function
in the non singlet approximation.
In the following, we describe the theoretical ingredients needed to treat, in the framework of QED structure function method, two experimental configurations of typical experimental interest:
