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 $a_{\tau }$.

9 pages, 2 figures; journal version

References in corpus (38)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The anomalous magnetic moment of the muon in the Standard Model
• Measurement of the fine-structure constant as a test of the Standard Model
• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• The Muon Magnetic Moment and Supersymmetry
• Leptoquark model to explain the $B$-physics anomalies, $R_K$ and $R_D$
• Hadronic vacuum polarization: $(g-2{)}_{\mu }$ versus global electroweak fits
• Towards a data-driven analysis of hadronic light-by-light scattering
• The muon $g$-2 and $\Delta \alpha$ connection
• Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 experiment
• B-decay Anomalies in a Composite Leptoquark Model
• Constraints on the two-pion contribution to hadronic vacuum polarization
• Consistency of hadronic vacuum polarization between lattice QCD and the R-ratio
• $(g-2{)}_{\mu }$, Lepton Flavour Violation and $Z$ Decays with Leptoquarks: Correlations and Future Prospects
• Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab
• With or without U(2)? Probing non-standard flavor and helicity structures in semileptonic B decays
• Consequences of chirally enhanced explanations of $(g-2{)}_{\mu }$ for $h\to \mu \mu$ and $Z\to \mu \mu$
• Impact of correlations between $a_{\mu }$ and ${\alpha }_{QED}$ on the EW fit
• Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative
• Correlating $h\to {\mu }^{+}{\mu }^{-}$ to the Anomalous Magnetic Moment of the Muon via Leptoquarks
• Probing low energy scalar leptoquarks by the leptonic $W$ and $Z$ couplings
• Anomalous electromagnetic moments of $\tau$ lepton in $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ reaction in Pb+Pb collisions at the LHC
• Hadronic vacuum polarization and vector-meson resonance parameters from $e^{+}{e}^{-}\to {\pi }^0\gamma$
• Tau anomalous magnetic moment form factor at Super B/Flavor factories
• Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab
• Lepton-flavour non-universality of $\bar{B}\to D^{\ast }\ell \bar{\nu }$ angular distributions in and beyond the Standard Model
• Scalar Leptoquarks in Leptonic Processes
• Unveiling Hidden Physics at the LHC
• Mounting Evidence for the Violation of Lepton Flavor Universality
• Novel method for the direct measurement of the tau lepton dipole moments
• Tau spin correlations and the anomalous magnetic moment
• Interplay of New Physics Effects in $(g-2{)}_{\ell }$ and $h\to {\ell }^{+}{\ell }^{-}$ -- Lessons from SMEFT
• CP violation and electric-dipole-moment at low energy $\tau$ production with polarized electrons
• The Forward-Backward Asymmetry in $B\to D^{\ast }\ell \nu$: One more hint for Scalar Leptoquarks?
• From B-meson anomalies to Kaon physics with scalar leptoquarks
• Precision measurement of the $\mathcal{B}({\rm Y}(3S)\to {\tau }^{+}{\tau }^{-})/\mathcal{B}({\rm Y}(3S)\to {\mu }^{+}{\mu }^{-})$ ratio

Cited by in corpus (22)

• Anomalies in Particle Physics
• Observation of $\gamma \gamma$ $\to$ $\tau \tau$ in proton-proton collisions and limits on the anomalous electromagnetic moments of the $\tau$ lepton
• Opportunities for new physics searches with heavy ions at colliders
• Observation of $\tau$ lepton pair production in ultraperipheral lead-lead collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Model Independent Tests of the Hadronic Vacuum Polarization Contribution to the Muon $g$$-$$2$
• LHC tau-pair production constraints on $a_{\tau }$ and $d_{\tau }$
• Collider and astrophysical signatures of light scalars with enhanced $\tau$ couplings
• Flavor Physics at the CEPC: a General Perspective
• Lepton pair production at NNLO in QED with EW effects
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Strategy to measure tau $g-2$ via photon fusion in LHC proton collisions
• A compact frozen-spin trap for the search for the electric dipole moment of the muon
• Spin correlations in $\tau$-lepton pair production due to anomalous magnetic and electric dipole moments
• Vector leptoquark contributions to lepton dipole moments
• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• Constraints on $\tau$ electromagnetic moments via tau pair production at the Muon colliders
• Light new physics and the $\tau$ lepton dipole moments: prospects at Belle II
• Probing the Tau Anomalous Magnetic Moment at Colliders: From Ultra-Peripheral Collisions to the Precision Frontier
• Electric and Magnetic Tau Dipole Moments Revisited
• Linearly Polarized Photon Fusion as a Precision Probe of the Tau Lepton Dipole Moments at Lepton Colliders
• Characterizing Dark Bosons at Chiral Belle
• From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models