Light new physics and the $τ$ lepton dipole moments

TL;DR

The paper addresses how light New Physics (NP) that couples to taus can modify the tau electromagnetic form factors $F_2(q^2)$ and $F_3(q^2)$, and hence the anomalous magnetic moment $a_\tau$ and the electric dipole moment $d_\tau$, beyond the heavy-NP EFT paradigm. It develops analytic expressions for loop-induced contributions from light spin-0 and spin-1 mediators (scalars, pseudoscalars, and tauphilic vectors), including CP-violating effects, imaginary parts above thresholds, and energy-dependent behavior relevant to Belle II. A key contribution is the detailed mapping between NP-induced $F_{2,3}$ and observable asymmetries in $e^+e^- \to \tau^+\tau^-$, enabling extraction of both real and imaginary parts of the form factors—without and with polarized beams—and illustrating the complementarity between indirect form-factor constraints and direct collider probes. The authors apply this framework to tauphilic vector bosons, offering Belle II-specific strategies, and discuss how such light states can be probed or constrained in conjunction with UV-complete models, including implications for explanations of anomalies and future experimental prospects. Overall, the work provides a comprehensive toolkit for testing light NP scenarios that predominantly couple to the third generation via both loop-level indirect constraints and targeted direct searches at Belle II.

Abstract

Testing New-Physics (NP) scenarios that couple predominantly to the third generation is notoriously difficult experimentally, as exemplified by comparing limits for the $τ$ lepton dipole moments to those of electron and muon. In this case, extracting limits from processes such as $e^+e^-\toτ^+τ^-$ often relies on effective-field-theory (EFT) arguments, which allows for model-independent statements, but only applies if the NP scale is sufficiently large compared to the center-of-mass energy. In this work we offer a comprehensive analysis of light NP contributions to the $τ$ dipole moments, providing a detailed account of the interpretation of asymmetry measurements in $e^+e^-\toτ^+τ^-$ that are tailored towards the extraction of dipole moments, for the test cases of new light spin-$0$ and spin-$1$ bosons. Moreover, we study the decoupling to the EFT limit in these scenarios and discuss the complementarity to constraints from other related processes, such as production in $e^+e^-$ reactions. While covering a wide range of light NP scenarios, as specific case study we present a detailed discussion of a tauphilic gauge vector boson at Belle II.

Figures (18)

• Figure 1: Feynman diagrams contributing to the $\tau$ magnetic (first two diagrams) and electric (last diagram) dipole moments. Blue dots represent an insertion of the operator $\phi \bar{\tau}\tau$, while red dots represent insertions of the operator $\phi \bar{\tau}\gamma_5\tau$.
• Figure 2: Left: Contributions to $a_\tau$ induced by a $CP$-violating scalar with only Yukawa interactions to $\tau$ leptons. Its contributions to the electromagnetic form factor $F_2$ are reported as well. In the limit of a very large scalar mass, form factors tend to the value of the corresponding dipole moments. Right: In the simultaneous presence of $c_P^\tau$ and $c_S^\tau$ a contribution to $d_\tau$ is generated as well. In the figure we report the corresponding predictions for the choice $c_P^\tau = c_S^\tau$.
• Figure 3: Feynman diagrams contributing to the ALP-mediated effects to $a_\tau$ and $d_\tau$ as induced by the exchange of a virtual scalar. Blue and red dots denote insertions of effective operators with opposite $CP$-transformation properties. The contributions in which the two EFT vertices are swapped need to be included as well.
• Figure 4: Left: Comparison between the contributions to AMM and EDM as induced by pure Yukawa couplings and by the presence of mixed couplings. Right: The same but for the form factors $F_2$ and $F_3$.
• Figure 5: Feynman diagram contributing to the $\tau$ magnetic dipole moment.