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Linearly Polarized Photon Fusion as a Precision Probe of the Tau Lepton Dipole Moments at Lepton Colliders

Ding Yu Shao, Hao Xiang, Fang Xu, Bin Yan, Cheng Zhang

Abstract

We present a comprehensive investigation into the anomalous magnetic dipole moment ($a_τ$) and electric dipole moment ($d_τ$) of the $τ$ lepton using the $γγ\to τ^+τ^-$ process at future lepton colliders, with the Super Tau-Charm Facility serving as a benchmark. By employing transverse-momentum-dependent factorization, we introduce novel observables derived from $\cos2φ$, $\sin2φ$, and $\cos4φ$ azimuthal asymmetries to precisely probe the $τ$ lepton's electromagnetic structure. Our analysis significantly enhances the precision of $a_τ$ constraints within the photon-photon fusion process, yielding $\mathrm{Re}(a_τ) \in [-4.6, 7.0] \times 10^{-3}$ at the $2σ$ confidence level, which approaches the precision of the Standard Model prediction. These findings highlight the considerable potential of azimuthal asymmetry measurements for high-precision determinations of fundamental particle properties at future lepton colliders.

Linearly Polarized Photon Fusion as a Precision Probe of the Tau Lepton Dipole Moments at Lepton Colliders

Abstract

We present a comprehensive investigation into the anomalous magnetic dipole moment () and electric dipole moment () of the lepton using the process at future lepton colliders, with the Super Tau-Charm Facility serving as a benchmark. By employing transverse-momentum-dependent factorization, we introduce novel observables derived from , , and azimuthal asymmetries to precisely probe the lepton's electromagnetic structure. Our analysis significantly enhances the precision of constraints within the photon-photon fusion process, yielding at the confidence level, which approaches the precision of the Standard Model prediction. These findings highlight the considerable potential of azimuthal asymmetry measurements for high-precision determinations of fundamental particle properties at future lepton colliders.

Paper Structure

This paper contains 4 sections, 14 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Theoretical Formalism
  3. Phenomenology and Discussions
  4. Conclusions

Figures (4)

  • Figure 1: Production of a $\tau^+ \tau^-$ pair via photon-photon fusion at $e^+ e^-$ colliders. The blue dots represent the effective $\gamma \tau^+ \tau^-$ vertices.
  • Figure 2: Theoretical predictions for (a) $\hbox{cos}2\phi$, (b) $\hbox{sin}2\phi$, and (c) $\hbox{cos}4\phi$ azimuthal asymmetries from form factors $F_2$ and $F_3$ in $\gamma\gamma\to \tau^+ \tau^-$ at an $e^+ e^-$ collider with $\sqrt{S_{ee}} = 7$ GeV. The black square indicates the prediction from the SM.
  • Figure 3: The expected sensitivity of the $\hbox{cos}2\phi$ asymmetry to $\tau$ dipole moments for four benchmark scenarios: (a) $\mathrm{Re}(a_\tau), \mathrm{Re}(d_\tau)\neq 0$, (b) $\mathrm{Re}(a_\tau), \mathrm{Im}(a_\tau)\neq 0$, (c) $\mathrm{Re}(d_\tau), \mathrm{Im}(d_\tau)\neq 0$, (d) $\mathrm{Im}(a_\tau), \mathrm{Im}(d_\tau)\neq 0$. The green and yellow regions correspond to $1\sigma$ and $2\sigma$ CL, respectively. The black dots indicate SM predictions, while the blue (CMS) CMS:2024qjo, purple (DELPHI) DELPHI:2003nah, and red (Belle) Belle:2021ybo error bars represent current experimental constraints at $2\sigma$ CL.
  • Figure 4: The expected sensitivity of the (a) $\hbox{sin}2\phi$ and (b) $\hbox{cos}4\phi$ asymmetries to $\tau$ dipole moments, with green and yellow regions correspond to $1\sigma$ and $2\sigma$ CL, respectively. The black dots indicate SM predictions, while the red error bars indicate current experimental constraints at $2\sigma$ CL from Belle Belle:2021ybo.