Light new physics and the $\boldsymbolτ$ lepton dipole moments: prospects at Belle II

TL;DR

The paper investigates how light versus heavy New Physics (NP) can affect the tau lepton's electric and magnetic dipole moments, using asymmetries in $e^+e^-\to\tau^+\tau^-$ to access the electromagnetic form factors $F_2(s)$ and $F_3(s)$ at center-of-mass energy $s$. It shows that for heavy NP the dipole moments map cleanly to $\text{Re}\,F_{2,3}(0)$ via an EFT decoupling argument, while for light NP the contributions are momentum-dependent and can acquire imaginary parts above threshold, making some effects observable even without electron polarization. The analysis covers spin-0 and spin-1 mediators, finding that scalar mediators decouple more slowly (logarithmically) than vectors, and that imaginary parts provide a polarization-free handle on NP at Belle II; threshold enhancement and radiative-return strategies can further improve sensitivity. A concrete toy model with Yukawa-like couplings illustrates the decoupling behavior and EFT matching, highlighting the role of logarithms and the potential Higgs-like analogy with $\Lambda$ playing the role of the new-physics cutoff. Overall, the work motivates targeted Belle II measurements of normal asymmetries to probe light NP in the tau sector and maps out the model-dependent connections to $a_\tau$ and $d_\tau$.

Abstract

While electron and muon dipole moments are well-established precision probes of physics beyond the Standard Model, it is notoriously challenging to test realistic New-Physics (NP) scenarios for the $τ$ lepton. Constructing suitable asymmetries in $e^+e^-\toτ^+τ^-$ has emerged as a promising such avenue, providing access to the electric and magnetic dipole moment once a polarized electron beam is available, e.g., with the proposed polarization upgrade of the SuperKEKB $e^+e^-$ collider. However, this interpretation relies on an effective-field-theory (EFT) argument that only applies if the NP scale is large compared to the center-of-mass energy. In this Letter we address the consequences of the asymmetry measurements in the case of light NP, using light spin-0 and spin-1 bosons as test cases, to show how results can again be interpreted as constraints on dipole moments, albeit in a model-dependent manner, and how the decoupling to the EFT limit proceeds in these cases. In particular, we observe that the imaginary parts generated by light new particles can yield non-vanishing asymmetries even without electron polarization, presenting opportunities for NP searches that can be realized already with present data at Belle II.

Figures (3)

• Figure 1: Representative Feynman diagrams contributing to $a_\tau$. Square dots denote insertions of NP couplings, $\phi$ and $X$ refer to new spin-$0$ and spin-$1$ particles, respectively.
• Figure 2: Comparison of the sensitivity of the Belle II experiments to light NP affecting $a_\tau$ for $\Lambda = 1\,\text{TeV}$. The choice of $c_{\gamma\gamma} = -\alpha_\text{em}/(4\pi) \,c_P^\tau$ corresponds to the minimal coupling present in the case of a derivatively coupled axion-like particle, being unavoidably generated in passing from the derivative to the non-derivative basis. The choice of $C_A = c_A^\tau/(6\pi^2)$ is dictated by the requirement of gauge anomaly cancellation. Left (Right): Bounds obtained assuming a sensitivity on $\text{Re}\, F_2^\text{eff} (\text{Im}\, F_2^\text{eff})= 10^{-6}$ as a function of the mass of the NP mediator.
• Figure 3: Comparison of the sensitivity of the Belle II experiment to light NP affecting $a_\tau$ just above the $\tau^+\tau^-$ threshold, $s_{\tau\tau} = 4(1.78\,\text{GeV})^2$ (same notation as in Fig. \ref{['fig:Money_Plots']}). No loss in luminosity has been assumed for either of the two cases. Realistic projections should of course take it into account and rescale accordingly the results displayed here.