Non-factorisable contribution to t-channel single-top production

We compute the non-factorisable ${\cal O}(\alpha_s^2)$ corrections to $t$-channel single-top quark production at LHC. These peculiar arise because of interactions between heavy- and light-quark lines appear for very first time next-to-next-to-leading order in perturbative QCD. find that change cross section relevant kinematic distributions this process by about half a percent.