Electric dipole moment of the electron and of the neutron

Abstract

It is shown that if Higgs-boson exchange mediates CP violation a significant electric dipole moment for the electron can result. Analogous effects can contribute to the neutron's electric dipole moment at a level competitive with Weinberg's three-gluon operator.PACS numbers: 13.40.Fn, ll.30.Er, 12.15.Cc Ever since the discovery of CP violation' a quarter of a century ago, experimentalists have steadily improved the bounds on the electron dipole moments of the electron 2,3 and of the neutron. 4 In the standard model, these moments are rather small and well below the present experimental bounds. Recently, Weinberg 5 pointed out that in models with CP or T violation carried by Higgs fields, a class of graphs neglected previously by theorists may contribute to the electric dipole moment of the neutron at a level just an order of magnitude below the present bound. Inspired by Weinberg's work, we have found a class of graphs, also neglected previously, which may contribute significantly to the electric dipole moment of the electron. Furthermore, a similar class of graphs competes with and may even dominate Weinberg's effect for the neutron electric dipole moment.In the standard model, the electron electric dipole moment is predicted to be 6 ;SlO~3 8 ecm, which is much smaller than the present bound of 3 ( -1.5 ±5.5 ± 1.5) xlO -26 ecm, as to make experimentalists despair. Indeed, a survey of the literature 7 shows that even in nonstandard models the electron electric dipole moment tends to be very small, typically less than (and usually much less than) 10 ~2 6 cm. To cheer up the experimentalists, one of us has designed a model 8 specifically to produce a large electron dipole moment, perhaps as large as 10~2 5 -10~2 6 ecm. This model requires exotic scalar particles coupling the electron to the r. It is also possible to have a large electron dipole moment in left-rightsymmetric models. 9 In contrast, in this Letter we will stick to the more conservative possibility envisioned by Weinberg 5,10 that there is some CP violation mediated by Higgs-boson exchange. This is possible in the two-Higgs-doublet standard model. l! Encouragingly we find a typical value for d e le which is typically of order 10 ~2 6 cm. Experimentalists are currently working towards limits of a few x 10~2 7 cm, and hope to reach limits near 10~2 8 cm in the future.One of our graphs involves a top quark just as does Weinberg's graph, except that we have pulled the Higgs field "out of the top-quark loop," which reduces what would otherwise have been at least a three-loop effect to a two-loop one. The point is that since a factor of m e is required by chirality in any case, we may as well let an explicit Higgs-boson coupling flip the chirality. We can understand the behavior of this graph by considering the limit m t^> rriH, in which we have in the effective theory (for energies ;Sm/y) the operators v ~l0F llv F^v and v~x()>F^vF^v. By dimension counting, the coefficient of the operator is proportional to the Yukawa coupling of the top quark divided by...

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