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

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 $e^{+}{e}^{-}\to {\rm Y}(nS)\to$ ${\tau }^{+}{\tau }^{-}$, $n=1,2,3$. $\text{Re}{F}_2^{\text{eff}}$ 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 $a_{\tau }$.

arXiv comment9 pages, 2 figures; journal version

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