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We present first results of jet cross sections at the Tevatron $p\bar pZ + 4$ jet channel is of particular interest as a normalizer for the jet background to top quark signals, as a background to a possible flavor-changing neutral-current (FCNC) decay signal, and as a background to missing- signals from gluino pairs. We also calculate the different heavy flavor contributions to jet production. The MADGRAPH program is used to generate all leading order subprocess helicity amplitudes. We present Monte Carlo studies with separation and acceptance criteria suitable for the Tevatron experimental analyses.

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