Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II

Abstract

The arguably most promising avenue towards testing physics beyond the Standard Model in the anomalous magnetic moment of the $\tau$ proceeds via suitably constructed asymmetries in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ in the presence of a polarized electron beam. Such a program, as could be realized at Belle II assuming a polarization upgrade of the SuperKEKB $e^{+}{e}^{-}$ collider, crucially relies on a careful consideration of radiative corrections. In this work, we present the complete one-loop result for the fully polarized $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ process and its implementation in the Monte-Carlo integrator McMule. As an application, we discuss projections relevant for measurements at Belle II, both with and without electron polarization, and outline the necessary steps for a generalization to next-to-next-to-leading order.

32 pages, 9 figures, expressions for one-loop diagrams provided as Mathematica notebook; journal version

References in corpus (37)

• Measurement of the fine-structure constant as a test of the Standard Model
• 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
• Automation of next-to-leading order computations in QCD: the FKS subtraction
• Measurement of the Electron Magnetic Moment
• Towards a data-driven analysis of hadronic light-by-light scattering
• The muon $g$-2 and $\Delta \alpha$ connection
• A new approach to evaluate the leading hadronic corrections to the muon g-2
• Mixed QCD-electroweak O(α_sα) corrections to Drell-Yan processes in the resonance region: pole approximation and non-factorizable corrections
• Data-driven evaluations of Euclidean windows to scrutinize hadronic vacuum polarization
• QED at NNLO with McMule
• Tau anomalous magnetic moment form factor at Super B/Flavor factories
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Muon-electron scattering at NNLO
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Observation of $\gamma \gamma$ $\to$ $\tau \tau$ in proton-proton collisions and limits on the anomalous electromagnetic moments of the $\tau$ lepton
• Bhabha scattering at NNLO with next-to-soft stabilisation
• Charge asymmetry in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ process
• Radiative corrections to the forward-backward asymmetry in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$
• Tau spin correlations and the anomalous magnetic moment
• An optimized basis for hadronic light-by-light scattering
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Dispersion relations for hadronic light-by-light scattering in triangle kinematics
• The LBK theorem to all orders
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Dispersion relations for the hadronic VVA correlator
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Lepton Electric Dipole Moment and Strong CP Violation
• Model Independent Tests of the Hadronic Vacuum Polarization Contribution to the Muon $g$$-$$2$
• LHC tau-pair production constraints on $a_{\tau }$ and $d_{\tau }$
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Improved evaluation of the electroweak contribution to muon $g-2$
• Lepton pair production at NNLO in QED with EW effects
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Electron-positron, parton-parton and photon-photon production of $\tau$-lepton pairs: anomalous magnetic and electric dipole moments spin effects
• Spin correlations in $\tau$-lepton pair production due to anomalous magnetic and electric dipole moments
• Strategy to measure tau $g-2$ via photon fusion in LHC proton collisions

Cited by in corpus (4)

• 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
• Characterizing Dark Bosons at Chiral Belle
• Linearly Polarized Photon Fusion as a Precision Probe of the Tau Lepton Dipole Moments at Lepton Colliders