Two-loop amplitudes for $ t\overline{t}H $ production: the quark-initiated N$_f$-part

We present numerical results for the two-loop virtual amplitude entering the
NNLO corrections to Higgs boson production in association with a top quark pair at the
LHC, focusing, as a proof of concept of our method, on the part of the quark-initiated
channel containing loops of massless or massive quarks. Results for the UV renormalised
and IR subtracted two-loop amplitude for each colour structure are given at selected phase-
space points and visualised in terms of surfaces as a function of two-dimensional slices of
the full phase space.