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Radiative Corrections

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

equation428

where tex2html_wrap_inline1412 are the hadronic variables obtained from

equation436

also tex2html_wrap_inline1414 and tex2html_wrap_inline1416 . If tex2html_wrap_inline1418 is the electron energy after radiation, tex2html_wrap_inline1420 . tex2html_wrap_inline1422 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

equation449

where tex2html_wrap_inline1046 is the EM scale, equal to tex2html_wrap_inline1046 for DIS or tex2html_wrap_inline1428 for resonances. The splitting function has a singularity at z=1, corresponding to low energy photons, which we cut off at tex2html_wrap_inline1432 , for tex2html_wrap_inline1434 . The minimum z value is given by the kinematic limit, ie. the minimum of

equation457

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; tex2html_wrap_inline1438 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.



Douglas M. Gingrich
Fri Mar 29 09:41:51 MST 1996