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

We investigate CP-violating interactions involving the Higgs boson and gluons within an effective field theory approach, focusing on the specific class of new-physics scenarios where the Yukawa couplings of light quarks are zero or strongly suppressed compared to the standard-model expectations. We compute the contributions of the most relevant higher-dimensional operators of Weinberg type to the electric dipole moment of the neutron (nEDM), which are induced by Feynman diagrams that involve an effective CP-violating Higgs-gluon coupling and top-quark loops. The resulting nEDM sensitivities and prospects are discussed and compared to the existing and expected LHC bounds. We find that future nEDM searches can set non-trivial constraints on CP-violating Higgs-gluon interactions even if the Higgs only couples to the third generation of quarks.