Higher-order QCD and electroweak corrections for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover accent="true"> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>H</mml:mi>

We calculate higher-order soft-gluon corrections for the associated production of a top-antitop quark pair and a Higgs boson ( t t ¯ H production) using resummation in one-particle-inclusive (1PI) kinematics. By adding these corrections to NLO QCD and NLO electroweak (EW) results, we present cross sections through approximate N 3 LO (aN 3 LO) in QCD and NLO in EW for t t ¯ H production at LHC energies. These aN 3 LO QCD + NLO EW results provide significant enhancements over lower orders and a reduced scale dependence. Based on our results and current experimental data, we derive a constraint on the deviation of the top quark Yukawa coupling from the Standard Model value which is a probe of new physics beyond it. We also calculate top-quark differential distributions in transverse momentum and rapidity.