Leading logarithmic initial state bremsstrahlung in the collinear approximation has been implemented. The radiative differential cross-section measured using lepton variables (x,y) is given by
where are the hadronic variables
obtained from
also and
.
If
is the electron energy after radiation,
.
is the Born cross-section in
terms of the hadronic variables.
The form of the splitting function for the hard bremsstrahlung contribution is given by
where is the EM scale, equal to
for DIS or
for resonances.
The splitting function has a singularity at z=1,
corresponding to low energy photons, which we cut off at
, for
.
The minimum z value is given by the kinematic limit, ie.
the minimum of
For the soft photon contribution, which has not been
calculated, we pick a form that keeps the total radiative
contribution finite.
A constant is chosen since soft photons at this energy will
not be detected in most detectors; MeV is used.
During the calculation of the total cross-section the soft photon part is calculated analytically, but numerically during the importance sampling stage.