In this section we report, for the sake of completeness, the lowest order
differential cross sections for the processes of fermionic pair production
(
) considered
in the first two sections of the article.
The pure photon, interference and resonant contributions in the s--channel
annihilation are given by the well--known formulae:
where is the fermion scattering angle and
the
resonant propagator:
is the fermion electric charge (in electron units),
is the ratio
of the fermion and electron coupling
and
to the
,
i.e.
. The effective couplings
can be simply derived from the measured widths
through the tree level relation:
For the process of Bhabha scattering the lowest order
contributions due to t--channel exchange
can be taken into account by adding to the previous
formulae (1)--(3) the following ones:
The above equations allow to compute the
Born cross sections
for leptonic pair production and include the inclusive
production ( line--shape) as
a particular case. Furthermore, they can also be used for
hadronic
final states provided that appropriate
and K form factors are supplied as in [4].