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We calculate the one-loop corrections to the soft anomalous dimensionmatrices for the production of a top-antitop quark pair in association with ajet at hadron colliders. This is a step forward towards implementing aprocedure for the resummation of soft-gluon emission logarithms for the$t\bar{t}j + X$ hadroproduction process, that will enable the improvement ofthe accuracy of the $t\bar{t} j + X$ cross sections, beyond the current degreeof knowledge. The latter, so far, has reached the next-to-leading order (NLO)level, complemented by the accuracy of the Shower Monte Carlo approaches usedin matching the NLO computations to parton showers (PS) and by merging withmatrix elements with a different number of light jets.

One-loop soft anomalous dimension matrices for $t\bar t j$ hadroproduction