We examine the two-loop contributions to the dimension-8, $J^{\mathrm{PC}}=0^{-+}$, gluonic operators in the multi-Higgs-boson extension of the standard model with $\mathrm{CP}$ violation occurring either in the neutral or in the charged scalar mesons sectors. Our calculational procedure is based on the background field method. We discuss the contribution to the nucleon electric dipole moment by means of an effective chiral Lagrangian approach. This is used to evaluate the basic hadronic matrix elements of the dimension-8 operators as well as the pion loop corrections. The discussion of numerical results encompasses the complete set of dimension-5, -6, and -8 $\mathrm{CP}$-violating operators. It is found that the dimension-8 operators, through the contributions of the two-loop irreducible Feynman diagrams involving the bottom quark, are likely to dominate over the dimension-6 operators and to be comparable to the dimension-5 operators.

• Received 30 November 1992

DOI:https://doi.org/10.1103/PhysRevD.48.283