  We report on a recent computation of the non-factorisable contribution to the
two-loop helicity amplitude for $t$-channel single-top production
arXiv:2108.09222. This is the last missing piece of the two-loop virtual
corrections to this process. We perform analytic integration-by-parts reduction
to master integrals and use the auxiliary mass flow method for their fast
numerical evaluation. The impact of the non-factorisable corrections to
single-top production on experimentally measured observables is estimated.
