An extended parton model for the effective w and z approximation

Abstract

Exact expressions for the effective off-shell IVB distributions of fermions and for fermion decay widths to fermion plus IVB are developed. We consider the simple example of heavy fermion production to one loop in order to display the method and to check the results against an exact Feynman diagram calculation. The correct handling of energy conservation is shown to yield results identical to that of the appropriate Feynman diagram result. The off-shell widths derived are related to observed widths, so that the later may be used in such a calculation. The methods is valid for all angles and all energies. It can be extended to find the off-shell corrections for any other vertices as well. The utilization of these structure functions with appropriate off-shell correction factors at vertices and exact energy conservation will yield results with a much wider range of validity than is obtained from the usual parton model. Furthermore one can use the results of this work to explore the range of validity of the usual parton model calculation. In some cases the procedure may be modified less drastically than is necessary to obtain the usual parton calculation and the validity of the modification will be more clearly understood. The modified procedure will be simpler than the Feynman diagram calculation with a range of validity in energy and angle which is much larger than that of the simple parton model.