Models for the Electric Dipole Moment and Anomalous Magnetic Moment of the Tau Lepton

TL;DR

This work analyzes radiatively generated tau mass models as a source of sizable tau EDM and g-2, focusing on two benchmarks with distinct hypercharge assignments: MF with neutral fermions and charged scalars, and RS with a charged fermion and neutral scalars. The tau dipole moments arise from CP-violating phases in the new Yukawa couplings and mixing, with $m_\tau^{\rm rad}$ governed by $m_\tau^{\rm rad} = \dfrac{y_\phi y_\eta}{16\pi^2}\mathcal{F}_{\rm mdl}$ (MF) or $m_\tau^{\rm rad} = \dfrac{y_\phi y_\eta}{16\sqrt{2}\pi^2}\mathcal{F}_{\rm RS}$ (RS). Numerical studies show MF can yield $a_\tau \sim \mathcal{O}(10^{-5})$ and $|d_\tau| \gtrsim 10^{-19}\,e\,\mathrm{cm}$ in viable regions, while RS produces similar $|a_\tau|$ but typically smaller $|d_\tau|$ and opposite sign for $a_\tau$, all within constraints from Higgs decays, collider searches, LFU, and electroweak precision data. These benchmark scenarios provide targeted signatures for upcoming tau dipole-moment measurements and related EDM constraints, highlighting the potential to probe CP-violating new physics through tau observables.

Abstract

The Belle II experiment and other ongoing and projected lepton facilities are expected to greatly enhance the sensitivity to the electric dipole moment (EDM) and anomalous magnetic moment ($g-2$) for the tau lepton, making it timely to explore models that predict these observables. We present a class of models that generate a sizable EDM and $g-2$ of the tau lepton via radiative tau mass generation. Two benchmark models with different hypercharge assignments are investigated. The first model contains neutral fermions and charged scalars. We find that the model can predict a large signal of the tau EDM, $d_τ = \mathcal{O}(10^{-19}) \, e \, {\rm cm}$, and $g-2$, $a_τ = \mathcal{O}(10^{-5})$, which are within the reach of future updates of their measurements. In contrast, the second model, containing a charged fermion and neutral scalars, yields a similar magnitude for the $g-2$ but predicts a comparatively smaller EDM signal. Our models serve as benchmarks for new physics generating sizable EDM and $g-2$ of the tau lepton.

Figures (4)

• Figure 1: Diagrams relevant to $C_T (q^2)$ and $C_{T'} (q^2)$. $q = p_f - p_i$ is the four-momentum of the photon, and $\varphi_j$ and $\psi_a$ are mass eigenstates for the exotic particles.
• Figure 2: Additional diagram related to $Z \to \tau^+ \tau^-$ decay process for the RS model. Due to the $Z$ boson coupling structure, only $j \neq k$ cases contribute to the decay process.
• Figure 3: Numerical predictions of $a_{\tau}$ (left panel) and $|d_{\tau}|$ (right panel) in the MF model with Eq. \ref{['eq:ParamsMF']} and $(150 \, {\rm GeV})^2 \leq M_{\eta}^2 \leq (450 \, {\rm GeV})^2$ and $5 \, {\rm GeV} \leq m_{LL} \leq 150 \, {\rm GeV}$. Each black contour shows the predictions of $a_{\tau}$ and $|d_{\tau}|$, while the gray dashed line is the contour for the combination of Yukawa couplings, $y_{\phi} y_{\eta}$. The shaded regions are excluded by the LEP bound (red), $y_{\phi} y_{\eta} > 4 \pi$ (gray) and the LFU constraint (cyan) by setting $y_{\phi} = y_{\eta}$.
• Figure 4: Numerical predictions of $a_{\tau}$ (left panel) and $|d_{\tau}|$ (right panel) in the RS model with Eq. \ref{['eq:RSpara']}. Each black contour shows the predictions of $a_{\tau}$ and $|d_{\tau}|$, while the gray dashed lines are the contours for the combination of Yukawa couplings, $y_{\phi} y_{\eta}$. The shaded regions are excluded by the $h^0 \to \tau^+ \tau^-$ bound (magenta), the LEP bound (red), $y_\phi y_\eta>4\pi$ (gray) and the LFU constraint (cyan).