Model-independent extrapolation of MUonE data with Padé and D-Log approximants

Abstract

The MUonE experiment is designed to extract the hadronic contribution to the electromagnetic coupling in the space-like region, $\Delta {\alpha }_{\mathrm{had}}(t)$, from elastic $e\mu$ scattering. The leading order hadronic vacuum polarization contribution to the muon $g-2$, $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$, can then be obtained from a weighted integral over $\Delta {\alpha }_{\mathrm{had}}(t)$. This, however, requires knowledge of $\Delta {\alpha }_{\mathrm{had}}(t)$ in the whole domain of integration, which cannot be achieved by experiment. In this work, we propose to use Padé and D-Log Padé approximants as a systematic and model-independent method to fit and reliably extrapolate the future MUonE experimental data, extracting $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$ with a conservative but competitive uncertainty, using no, or very limited, external information. The method relies on fundamental analytic properties of the two-point correlator underlying $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$ and provides lower and upper bounds for the result for $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$. We demonstrate the reliability of the method using toy data sets generated from a model for $\Delta {\alpha }_{\mathrm{had}}(t)$ reflecting the expected statistics of the MUonE experiment.

32 pages, 8 figures. App. B removed. Results unchanged. Matches published version

References in corpus (14)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• 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
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm
• A new approach to evaluate the leading hadronic corrections to the muon g-2
• On the extraction of spectral densities from lattice correlators
• Vector Meson Dominance as a first step in a systematic approximation: the pion vector form factor
• A New Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to $(g-2{)}_{\mu }$
• Status of the MUonE experiment
• Conformal and Uniformizing Maps in Borel Analysis
• $\tau$ data-driven evaluation of Euclidean windows for the hadronic vacuum polarization
• Spectral-weight sum rules for the hadronic vacuum polarization
• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
• Hadronic Vacuum Polarization and the MUonE proposal

Cited by in corpus (2)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution