Non-factorisable two-loop contribution to $t$-channel single-top production

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.