Higher-order QCD and electroweak corrections for $t\bar{t}H$ production

We calculate higher-order soft-gluon corrections for the associated production of a top-antitop quark pair and a Higgs boson ($t\bar{t}H$ 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 $t\bar{t}H$ 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.