  The single-top production is an important process at the LHC to test the
Standard Model (SM) and search for the new physics beyond the SM. Although the
complete next-to-next-to-leading order (NNLO) QCD correction to the single-top
production is crucial, this calculation is still challenging at present. In
order to efficiently reduce the NNLO single-top amplitude, we improve the
auxiliary mass flow (AMF) method by introducing the $\epsilon$ truncation. For
demonstration we choose one typical planar double-box diagram for the $tW$
production. It is shown that one coefficient of the form factors on its
amplitude can be systematically reduced into the linear combination of 198
scalar integrals.
