Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis

Abstract

The two-pion low-energy contribution to the anomalous magnetic moment of the muon, $a_{\mu }\equiv (g-2{)}_{\mu }/2$, expres sed as an integral over the modulus squared of the pion electromagnetic form fac tor, brings a relatively large contribution to the theoretical error, since the low accuracy of experimental measurements in this region is amplified by the drastic increase of the integration kernel. We derive stringent constraints on the two-pion contribution by exploiting analyticity and unitarity of the pion electromagnetic form factor. To avoid the poor knowledge of the modulus of this function, we use instead its phase, known with high precision in the elastic region from Roy equations for pion-pion scattering via the Fermi-Watson theorem. Above the inelastic threshold we adopt a conservative integral condition on the modulus, determined from data and perturbative QCD. Additional high precision data on the modulus in the range $0.65-0.71$ GeV, obtained from $e^{+}{e}^{-}$ annihilation and $\tau$-decay experiments, are used to improve the predictions on the modulus at lower energies by means of a parametrization-free analytic extrapolation. The results are optimal for a given input and do not depend on the unknown phase of the form factor above the inelastic threshold. The present work improves a previous analysis based on the same technique, including more experimental data and employing better statistical tools for their treatment. We obtain for the contribution to $a_{\mu }$ from below 0.63 GeV the value $(133.258\pm 0.723)\times 10^{-10}$, which amounts to a reduction of the theoretical error by about $6\times 10^{-11}$.

13 pages, latex using revtex 4, 8 figures; revised version includes two additional references, improved discussions, figures touched up

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Cited by in corpus (20)

• The anomalous magnetic moment of the muon in the Standard Model
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Two-pion contribution to hadronic vacuum polarization
• Three-pion contribution to hadronic vacuum polarization
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• Kaon electromagnetic form factors in dispersion theory
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• The branching ratio $\omega \to {\pi }^{+}{\pi }^{-}$ revisited
• Nucleon matrix elements of the antisymmetric quark tensor
• Electromagnetic charge radius of the pion at high precision
• Non-Perturbative Effects in $\mu \to e\gamma$
• A Call for New Physics : The Muon Anomalous Magnetic Moment and Lepton Flavor Violation
• Dispersion relations for the hadronic VVA correlator
• Test of analyticity and unitarity for the pion form-factor data around the $\rho$ resonance
• Model-independent constraints on hadronic form factors with above-threshold poles
• A Simple Parametrisation of the Pion Form Factor
• Study of pion vector form factor and its contribution to the muon $(g-2)$
• Momentum-dependence of $\rho -\omega$ mixing in the pion vector form factor and its effect on $(g-2{)}_{\mu }$
• Structure-dependent radiative corrections to $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ in the GVMD approach