Electric dipole moments of charged leptons at one loop in the presence of massive neutrinos

Violation of $CP$ invariance is a quite relevant phenomenon that is found in the Standard Model, though in small amounts. This has been an incentive to look for high-energy descriptions in which $CP$ violation is increased, thus enhancing effects that are suppressed in the Standard Model, such as the electric dipole moments of elementary particles. In the present investigation, we point out that charged currents in which axial couplings are different from vector couplings are able to produce one-loop contributions to electric dipole moments of charged leptons if neutrinos are massive and if these currents violate $CP$. We develop our discussion around charged currents involving heavy neutrinos and a $W^{\prime }$ gauge boson coupling to Standard Model charged leptons. Using the most stringent bound on the electron electric dipole moment, provided by the ACME Collaboration, we determine that the upper bound on the difference between axial and vector currents lies within $\sim {10}^{-10}$ and $\sim {10}^{-7}$ for heavy-neutrino masses between 0.5 TeV and 6 TeV and if the $W^{\prime }$ mass is within 0.45 TeV–7 TeV. This possibility is analyzed altogether with the anomalous magnetic moments of charged leptons, among which we estimate, for the $\tau$ lepton, an anomalous magnetic moment contribution between $\sim {10}^{-8}$ and $\sim {10}^{-10}$ for neutrino masses ranging from 0.5 TeV to 6 TeV and a $W^{\prime }$ mass between 0.45 TeV and 7 TeV. The general charged currents are also used to calculate the branching ratio for $\mu \to e\gamma$, which gets suppressed if the set of masses of heavy neutrinos is quasidegenerate. In a scenario of nondegenerate neutrino masses, we find that regions of neutrino and $W^{\prime }$ masses in which the contributions to this flavor-changing branching ratio are lower than the current upper bound exist. We show that such regions can be widened if the $W^{\prime }$ gauge boson mass is larger.

Figure 1

One-loop diagrams contributing to the flavor-changing electromagnetic vertex.

Figure 2

Behavior of $z_{1,j}$ and $z_{2,j}$ for mixed $m_{W^{\prime }}$ and as a function of $m_j$. The units used in the $m_j$ axis are TeVs.

Figure 3

Intersection of regions in which ${\mu }_e<0$, ${\mu }_{\mu }>0$, and ${\mu }_{\tau }<0$ hold.

Figure 4

Regions in the $({\kappa }_1,{\kappa }_N)$ plane in which $\text{Br}(\mu \to e\gamma )<5.7\times {10}^{-13}$, barring mixing dependence. The width of each region is determined by the mass $m_{W^{\prime }}$.