Vanishing Contribution to Quark Electric Dipole Moment in the 2HD Model with CKM CP Violation

TL;DR

This paper demonstrates that in a two Higgs doublet extension of the Standard Model with CKM CP violation, the charged Higgs contribution to the quark electric dipole moment vanishes at two-loop order, similar to the Standard Model.

Contribution

It provides a detailed calculation showing the vanishing of the charged Higgs contribution to quark EDM at two loops, clarifying the underlying symmetry reasons.

Findings

Charged Higgs contribution to quark EDM vanishes at two-loop order.

The vanishing is related to the structure of Yukawa couplings in gauge theories.

Results extend the understanding of CP violation effects in extended Higgs models.

Abstract

In the standard model (SM) of electroweak interactions, CP noninvariance arises from the nonzero phase in the CKM matrix. Its contribution to the quark electric dipole moment (EDM) vanishes surprisingly at two loop order. This makes the quark EDM extremely small in the SM. In this paper, we consider the two Higgs doublet extension of the SM and assume that CP noninvariance is still encoded in the CKM matrix. We calculate the charged Higgs boson contribution to the quark EDM which naively should be of order $eG_F^2\tilde{\delta}(4\pi)^{-4}m_{u(d)}m_t^2m_b^2m_H^{-2}$ for the up (down) quark with possible enhancement factors of $\tan^2\beta$. Here $\tilde{\delta}$ is the rephasing invariant of CP violation. However, contrary to the above naive expectation, we find that the charged Higgs boson contribution vanishes strictly at two loop order. We show explicitly how this comes about and explains how it is related to the general form of Yukawa couplings in a spontaneously broken gauge theory.