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We study the neutron electric dipole moment in the presence of the $CP$-violating operators up to dimension five in terms of the QCD sum rules. It is found that the operator product expansion calculation is robust when exploiting a particular interpolating field for a neutron, while there exist some uncertainties on the phenomenological side. By using input parameters obtained from the lattice calculation, we derive a conservative limit for the contributions of the $CP$-violating operators. We also show the detail of the derivation of the sum rules.
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Hisano et al. (2012) studied this question.
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