  We study higher-order QCD corrections for the production of a top-antitop
quark pair ($t{\bar t}$ production) at the Large Hadron Collider in the
Standard Model Effective Field Theory. We consider effects of new physics
parametrized by the top-quark chromomagnetic dipole operator. We calculate new
physics contributions to the total cross section at approximate NNLO, with
second-order soft-gluon corrections added to the complete NLO result, including
uncertainties from scale dependence and from parton distributions. We also
calculate new physics contributions at approximate NNLO for differential
distributions in top-quark transverse momentum.
