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We investigate CP-violating interactions involving the Higgs boson and gluonswithin an effective field theory approach, focusing on the specific class ofnew-physics scenarios where the Yukawa couplings of light quarks are zero orstrongly suppressed compared to the standard-model expectations. We compute thecontributions of the most relevant higher-dimensional operators of Weinbergtype to the electric dipole moment of the neutron (nEDM), which are induced byFeynman diagrams that involve an effective CP-violating Higgs-gluon couplingand top-quark loops. The resulting nEDM sensitivities and prospects arediscussed and compared to the existing and expected LHC bounds. We find thatfuture nEDM searches can set non-trivial constraints on CP-violatingHiggs-gluon interactions even if the Higgs only couples to the third generationof quarks.

Bounds on CP-violating Higgs-gluon interactions: the case of vanishing light-quark Yukawa couplings