Matching Matrix Elements and Parton Showers with HERWIG and PYTHIA

We report on our exploration of matching matrix element calculations with the parton-shower models contained in the event generators HERWIG and Pythia. We describe results for e+e- collisions and for the hadroproduction of W bosons and Drell--Yan pairs. We compare methods based on (1) a strict implementation of ideas proposed by Catani, et al., (2) a generalization based on using the internal Sudakov form factors of HERWIG and Pythia, and (3) a simpler proposal of M. Mangano. Where appropriate, we show the dependence on various choices of scales and clustering that do not affect the soft and collinear limits of the predictions, but have phenomenological implications. Finally, we comment on how to use these results to state systematic errors on the theoretical predictions.