The \( tW\overline{b} \) production contributes to the real corrections to the tW cross section. It would interfere with the top quark pair production, causing difficulties in a clear definition of the \( tW\overline{b} \) events. The subtraction of the \( t\overline{t} \) contributions has been performed in the diagram removal or diagram subtraction schemes for the tree-level processes. However, these schemes rely on the ability to identify the double resonant diagrams and thus can not be extended to loop diagrams. We propose a new scheme to subtract the \( t\overline{t} \) contributions by power expansion of the squared amplitude in the resonant region. In order to cancel the infra-red divergences of the loop amplitudes, a widely used method is to introduce the dipole counter-terms, an ingredient in calculations of the full next-to-leading order QCD corrections. In our scheme, these counter-terms are also power-expanded. As a proof of principle, we calculate the one-loop correction to the \( d\overline{d} \) → \( \overline{b} Wt \) process, and present the invariant mass distribution of the \( W\overline{b} \) system.
