This paper reports a new, more complete calculation for the process where a proton–proton collision makes a top–antitop pair together with a Higgs boson (pp → t t̄ H) at the LHC. The authors compute next-to-leading order (NLO) corrections from the strong force (QCD) and at the same time include a small set of possible “new physics” effects described by dimension‑6 operators in the Standard Model Effective Field Theory (SMEFT). They present results for the LHC Run III energy of √s = 13.6 TeV in the di‑lepton decay channel, where each top decays to a W boson and a b quark and the W bosons decay to an electron and a muon plus neutrinos.

The focus is on four dimension‑6 operators that can change the top–Higgs and top–gluon interactions: Otφ (which rescales the top–Higgs Yukawa coupling), OtG (a chromomagnetic dipole for the top), OφG (a loop‑induced coupling of the Higgs to gluons), and OtW (which affects the top decay Wtb vertex). The authors include these operators consistently in both the production of t t̄ H and in the subsequent top‑quark decays. They study linear and quadratic dependences on the operator strengths, account for renormalisation‑group mixing where relevant, and give both integrated and differential cross‑section predictions. They also provide a comparison between calculations with stable top quarks and calculations in which top quarks are reconstructed from their decay products.

At a high level, the calculation combines two things. First, NLO QCD corrections are needed to reduce theoretical errors and to model radiation that changes event shapes. Second, SMEFT operators parametrize how heavy, unseen particles could shift those shapes without being produced directly. Including the operators in the decays as well as in production matters because kinematic cuts and detector‑level reconstruction depend on the decay products. The authors show that these effects can change the shapes of common observables used in experiments, so they argue both production and decay effects should be treated together.