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We present a detailed calculation of next-to-leading order QCD corrections tothe $tW$ associated production using the one cutoff phase space slicing method.Such QCD corrections have been calculated independently by two groups already,however, a number of differences were found. It is desirable to have a thirdparty calculation to make a crossing check. In this note, we present ourcomplete results of the virtual corrections which are not shown in theliterature so far. The numerical comparison will be presented in theforthcoming paper. As a demonstration of the one cutoff phase space slicingmethod, we also show in details how to organize the color ordered amplitudesand how to slice the soft and collinear phase space regions.

Demonstration of One Cutoff Phase Space Slicing Method: Next-to-Leading Order QCD Corrections to the $tW$ Associated Production in Hadron Collision