Dispersion relation for hadronic light-by-light scattering: pion pole

Abstract

The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon $(g-2{)}_{\mu }$ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for $(g-2{)}_{\mu }$ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space- and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the correct high- and low-energy limits, and proves convenient for the evaluation of the $(g-2{)}_{\mu }$ loop integral. We concentrate on the systematics of the fit to $e^{+}{e}^{-}\to 3\pi$ data, which are key in constraining the isoscalar dependence, as well as the matching to the asymptotic limits. In particular, we provide a detailed account of the pion transition form factor at low energies in the time- and space-like region, including the error estimates underlying our final result for the pion-pole contribution, $a_{\mu }^{{\pi }^0\text{-pole}}=62.6_{-2.5}^{+3.0}\times 10^{-11}$, and demonstrate how forthcoming singly-virtual measurements will further reduce its uncertainty.

55 pages, 16 figures, result for the space-like pion transition form factor attached as ancillary material; journal version

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• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• The mass-degenerate SM-like Higgs and anomaly of $(g-2{)}_{\mu }$ in $\mu$-term extended NMSSM
• Contribution of exclusive $({\pi }^0{\pi }^0,{\pi }^0\eta ,\eta \eta )\gamma$ channels to the leading order HVP of the muon $g-2$
• Light new physics and the $\tau$ lepton dipole moments: prospects at Belle II
• Contributions to the Muon $g-2$ from a Three-Form Field
• Leptonic probes of Alternative Left-Right Symmetric Models
• Pion observables calculated in Minkowski and Euclidean spaces with Ansätze for quark propagators
• The Radiative Flavor Template at the LHC: Lepton non-universality and g-2
• On-shell Renormalization with Vector-like Leptons, One-loop Muon-Higgs Coupling and Muon g-2
• Model-independent extrapolation of MUonE data with Padé and D-Log approximants
• Flavour anomalies meet flavour symmetry
• Muon $g-2$ Anomaly from a Massive Spin-2 Particle
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• Analytic Properties of Triangle Feynman Diagrams in Quantum Field Theory
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• A pedagogical review on muon $g-2$
• Unitarity bounds on extensions of Higgs sector
• Fermiophobic $Z^{\prime }$ model for simultaneously explaining the muon anomalies $R_{K^{(\ast )}}$ and $(g-2{)}_{\mu }$
• $(g-2{)}_{e,\mu }$ and decays $e_b\to e_a\gamma$ in a $ \mbox{SU}(4)_L \otimes \mbox{U}(1)_X$ model with inverse seesaw neutrinos
• Tau data-driven evaluation of the Hadronic Vacuum Polarization
• Systematic analysis of search strategies for $L_{\mu }-L_{\tau }$ gauge bosons at Belle II
• GM2Calc-2 for the 2HDM
• Fractionary Charged Particles Confronting Lepton Flavor Violation and the Muon's Anomalous Magnetic Moment
• Graph Reinforcement Learning for Exploring BSM Model Spaces
• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$
• Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model
• Explaining the hints for lepton flavour universality violation with three $S_2$ leptoquark generations
• Thermal Leptophilic Light Vector Dark Matter with Spinor Mediator and Muon (g-2) Anomaly
• New high-statistics measurement of the ${\pi }^0\to e^{+}{e}^{-}\gamma$ Dalitz decay at the Mainz Microtron
• Theory of Muon g-2
• Probing the muon $g-2$ with future beam dump experiments
• Flavour anomalies in supersymmetric scenarios with non-minimal flavour violation
• From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models
• Aligned Zee-Grimus-Neufeld model for $(g-2{)}_{\mu }$