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The sources of $W + n$-jet events in hadron collisions are higher-order QCDprocesses, but also multiple-parton interactions. A subprocess producing a $W +k$-jet final state, followed by one producing $l$ jets in the samenucleon-nucleon interaction, will result in a $W + n$-jet event if $k + l = n$.In the simplest case a $W + 2$-jet event can be produced by a quark-antiquarkannihilation into $W$ and a 2-jet event occurring in the same proton-antiprotoninteraction. We compute that this happens at the 10% level of the higher-orderQCD processes for the type of cuts made by the Tevatron experiments. For jet$p_T$ values of order $5{\sim}10$ GeV, multiple-parton interactions dominatehigher-order QCD-processes. The emergence of this new source of $W + n$-jetevents towards lower $p_T $ simulates the running of $\alpha_s$; it isimperative to remove these processes from the event sample in order to extractinformation on the strong coupling constant. Also, BFKL studies of low-$p_T$jet cross sections are held hostage to a detailed understanding of themultiple-parton interactions. We perform the calculations required to achievethese goals. A detailed experimental analysis of the data may, for the firsttime, determine the effective areas occupied by quarks and gluons in thenucleon. These are not necessarily identical. We also compute themultiple-parton contribution to $Z + n$-jet events.Comment: Revtex, 14 pages, uses epsf.sty, 11 postscript figures include

Associated production of weak bosons and jets by multiple parton interactions