  We present first results of $Z+4$ jet cross sections at the Tevatron $p\bar
p$ collider with heavy quark flavor identification. The $Z + 4$ jet channel is
of particular interest as a normalizer for the $W +4$ jet background to top
quark signals, as a background to a possible $t\to cZ$ flavor-changing
neutral-current (FCNC) decay signal, and as a background to missing-$p_T$
signals from gluino pairs. We also calculate the different heavy flavor
contributions to $W+4$ 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.
