Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair

The associated production of a Higgs boson and a top-quark pair is important for probing the Yukawa coupling of the top quark, and calls for better theoretical modeling. In this paper, we calculate the two-loop infrared divergences in $t\bar{t}H$ production at hadron colliders. To do that we compute the one-loop amplitudes to higher orders in the dimensional regulator $\epsilon$. Numeric results for the infrared poles are given as a reference at several representative phase-space points. The result in this work servers as a part of the ongoing efforts towards the $t\bar{t}H$ cross sections at the next-to-next-to-leading order.