Towards testing the magnetic moment of the tau at one part per million

TL;DR

This paper predicts the BSM-induced deviations in the tau lepton's magnetic moment and proposes experimental methods at Belle II to measure these effects with high precision, advancing the search for new physics beyond the Standard Model.

Contribution

It provides the first complete two-loop prediction of the tau's Pauli form factor at high energies and discusses experimental strategies to measure BSM effects on the tau magnetic moment.

Findings

Predicted the two-loop value of the tau's Pauli form factor at 100 GeV^2.

Proposed using polarized electron beams to measure asymmetries in tau pair production.

Estimated sensitivity of Belle II to BSM effects in tau magnetic moment at 10^{-6} level.

Abstract

If physics beyond the Standard Model (BSM) explains the $4.2\sigma$ difference between the Standard-Model and measured muon anomalous magnetic moment, $a_{\mu}$, minimal flavor violation predicts a shift in the analog quantity for the $\tau$ lepton, $a_{\tau}$, at the $10^{-6}$ level, and even larger effects are possible in generic BSM scenarios such as leptoquarks. We show that this produces equivalent BSM deviations in the Pauli form factor, $F_2(s)$, at $s=(10\,\text{GeV})^2$, and report the first complete two-loop prediction of $\text{Re}\, F_2^\text{eff}(100\,\text{GeV}^2)=-268.77(50)\times 10^{-6}$ for resonant $\tau$-pair production in $e^+e^-\rightarrow \Upsilon(nS) \rightarrow$ $\tau^+\tau^-$, $n=1,2,3$. $\text{Re}\, F_2^\text{eff}$ can be measured from $e^-$-helicity-dependent transverse and longitudinal asymmetries in $\tau$-pair events, which requires a longitudinally polarized $e^-$ beam. We discuss how Belle II asymmetry measurements could probe $a_{\tau}^\text{BSM}$ at $10^{-6}$, assuming such a polarization upgrade of the SuperKEKB $e^+e^-$ collider, and conclude by outlining the next steps to be taken in theory and experiment along this new avenue for exploring realistic BSM effects in $a_\tau$.