$t\bar{t}H$ production at NNLO: the flavour off-diagonal channels

We consider QCD radiative corrections to the associated production of a heavy-quark pair ( $$Q{{\bar{Q}}}$$ ) with a generic colourless system F at hadron colliders. We discuss the resummation formalism for the production of the $$Q{{\bar{Q}}}F$$ system at small values of its total transverse momentum $$q_T$$ . We present the results of the corresponding resummation coefficients at next-to-leading and, partly, next-to-next-to-leading order. The perturbative expansion of the resummation formula leads to the explicit ingredients that can be used to apply the $$q_T$$ subtraction formalism to fixed-order calculations for this class of processes. We use the $$q_T$$ subtraction formalism to perform a fully differential perturbative computation for the production of a top-antitop quark pair and a Higgs boson. At next-to-leading order we compare our results with those obtained with established subtraction methods and we find complete agreement. We present, for the first time, the results for the flavour off-diagonal partonic channels at the next-to-next-to-leading order.