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Generating Sizable Real and Imaginary $τ$ Electric Dipole Moment

Zhong-Lv Huang, Xin-Yu Du, Xiao-Gang He, Chia-Wei Liu, Zi-Yue Zou

Abstract

The CP-violating electric dipole moment~(EDM) of a fermion provides a powerful probe of new physics beyond the Standard Model~(SM). Among the charged leptons, the $τ$ EDM remains the least constrained. When the photon has timelike momentum, the EDM develops an imaginary part. It imposes stronger constraints on new physics~(NP) than the real part. Although the current experimental bounds are several orders of magnitude above the Standard Model prediction, new physics can generate significantly larger values. Our analysis shows that an axion-like coupling of the $τ$ lepton in the two-Higgs-doublet model can induce sizable real and imaginary components of the EDM, despite the stringent constraints imposed by current axion-like particle experiments. The predicted EDM values may approach the present experimental sensitivities, making them accessible to future measurements at Belle II and the Super Tau-Charm Facility.

Generating Sizable Real and Imaginary $τ$ Electric Dipole Moment

Abstract

The CP-violating electric dipole moment~(EDM) of a fermion provides a powerful probe of new physics beyond the Standard Model~(SM). Among the charged leptons, the EDM remains the least constrained. When the photon has timelike momentum, the EDM develops an imaginary part. It imposes stronger constraints on new physics~(NP) than the real part. Although the current experimental bounds are several orders of magnitude above the Standard Model prediction, new physics can generate significantly larger values. Our analysis shows that an axion-like coupling of the lepton in the two-Higgs-doublet model can induce sizable real and imaginary components of the EDM, despite the stringent constraints imposed by current axion-like particle experiments. The predicted EDM values may approach the present experimental sensitivities, making them accessible to future measurements at Belle II and the Super Tau-Charm Facility.

Paper Structure

This paper contains 15 equations, 3 figures.

Figures (3)

  • Figure 1: One-loop Feynman diagrams contributing to the $\tau$ EDM. The left diagram yields $d_\tau(q^2)$ in the spacelike region ($q^2 < 0$), while the right diagram corresponds to the timelike region ($q^2 > 4m_\tau^2$).
  • Figure 2: Results of Re$(d_\tau(q^2))$ and Im$(d_\tau(q^2))$ of the ALP with $a_ab_a=10^{-3}$. For different values of $a_ab_a$, one can simply scale the EDM by $a_ab_a/10^{-3}$. Here, the values of $m_a$ are chosen for illustration and are convenient for later discussions. The black dashed lines correspond to $q^2 = 0$ and $q^2 = 4m_\tau^2$.
  • Figure 3: The colored regions represent the parameter space excluded by different experiments. The parameter space above the Belle experimental bound has been ruled out Belle:2021ybo. The curves corresponding to STCF and Belle-II indicate the expected bounds from future experimental sensitivities He:2025ewkLu:2025heu. The gray region is excluded by $\gamma^* \to a \gamma$ limits from BESIII BESIII:2022rzz and $a\to \gamma \gamma$ limit from OPAL Knapen:2016moh.