Two-pion low-energy contribution to the muon $g-2$ with improved precision from analyticity and unitarity

Abstract

The two-pion contribution from low energies to the muon magnetic moment anomaly, although small, has a large relative uncertainty since in this region the experimental data on the cross sections are neither sufficient nor precise enough. It is therefore of interest to see whether the precision can be improved by means of additional theoretical information on the pion electromagnetic form factor, which controls the leading order contribution. In the present paper we address this problem by exploiting analyticity and unitarity of the form factor in a parametrization-free approach that uses the phase in the elastic region, known with high precision from the Fermi-Watson theorem and Roy equations for $\pi \pi$ elastic scattering as input. The formalism also includes experimental measurements on the modulus in the region 0.65-0.70 GeV, taken from the most recent $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ experiments, and recent measurements of the form factor on the spacelike axis. By combining the results obtained with inputs from CMD2, SND, BABAR and KLOE, we make the predictions $a_μ^{ππ, \LO}\,[2 m_π,\, 0.30 \gev]=(0.553 \pm 0.004) \times 10^{-10}$ and $a_μ^{ππ, \LO}\,[0.30 \gev,\, 0.63 \gev]=(133. 083 \pm 0.837)\times 10^{-10}$. These are consistent with the other recent determinations, and have slightly smaller errors.

10 pages latex, using revtex, 5 figures; v2 corresponds to version to appear in Physical Review D; references added; discussions improved

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• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• Dispersive analysis of the pion transition form factor
• The anomalous magnetic moment of the muon in the Standard Model: an update
• 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
• The Role of Mesons in Muon g-2
• Nucleon matrix elements of the antisymmetric quark tensor
• Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis
• Dispersion relations for the hadronic VVA correlator
• Theoretical aspects of Chiral Dynamics
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• Model-independent constraints on hadronic form factors with above-threshold poles
• A Simple Parametrisation of the Pion Form Factor
• Structure-dependent radiative corrections to $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ in the GVMD approach