In order to do a cross section measurement at a collider experiment the luminosity has to be determined. In order to do so the rate of a process with a well known cross section is measured. This process also has to have a high cross section to be used online so that the beam optics can be modified for maximum luminosity. At HERA the hard photon bremsstrahlung produced in the Bethe-Heitler process [20] is used.
The ZEUS luminosity monitor ( LUMI) consists of two calorimeters, one, for detecting the scattered photon is placed near the proton beam pipe at , the other one, for detecting the scattered positron is placed at . The acceptance for photon detection is for . The positron acceptance is more difficult to estimate because the positrons have to traverse several magnets before reaching the calorimeter, but it is about for . The coincidence rate of the two calorimeters is used as a cross check for the luminosity determined from the photon counter only.
The luminosity detector of ZEUS and its operation are described in detail in [21,22].
The data used for this thesis is the positron-proton data
of 
, for which HERA delivered
a luminosity of
.
Of this luminosity, ZEUS could
trigger
, the difference being mainly due to
the time necessary for the beam conditions to stabilize at the
beginning of each run. Some losses were due to miscellaneous
detector problems.