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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.13638 |
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Table of Contents:
- The MUonE experiment is designed to extract the hadronic contribution to the electromagnetic coupling in the space-like region, $Δα_{\rm had}(t)$, from elastic $eμ$ scattering. The leading order hadronic vacuum polarization contribution to the muon $g-2$, $a_μ^{\mathrm{HVP, \,LO}}$, can then be obtained from a weighted integral over $Δα_{\rm had}(t)$. This, however, requires knowledge of $Δα_{\rm had}(t)$ 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 $a_μ^{\mathrm{HVP,\,LO}}$ 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 $a_μ^{\mathrm{HVP,\,LO}}$ and provides lower and upper bounds for the result for $a_μ^{\mathrm{HVP,\,LO}}$. We demonstrate the reliability of the method using toy data sets generated from a model for $Δα_{\rm had}(t)$ reflecting the expected statistics of the MUonE experiment.