Larger Higgs-boson-exchange terms in the neutron electric dipole moment

The neutron electric dipole moment ($d_n$) due to Higgs-boson exchange is reconsidered, now without assuming that Higgs-boson exchange is solely responsible for $K_L^0$→2π. The dominant contribution to $d_n$ arises from a three-gluon operator, produced in integrating out top quarks and neutral Higgs bosons. The estimated results together with current experimental bounds on $d_n$ show, even for the largest plausible Higgs-boson masses, that CP is not maximally violated in neutral-Higgs-boson exchange.