Model-independent extrapolation of MUonE data with Pad\'e and D-Log approximants

TL;DR

This paper introduces a model-independent approach using Padé and D-Log Padé approximants to reliably extrapolate MUonE data for calculating the muon g-2 hadronic contribution, ensuring accurate results with minimal external input.

Contribution

It presents a novel, systematic method employing Padé approximants for extrapolating MUonE data, enabling precise determination of the muon g-2 contribution without relying heavily on external models.

Findings

The method provides reliable bounds for $a_\mu^{\mathrm{HVP,\,LO}}$.

Demonstrated effectiveness on toy data mimicking MUonE statistics.

Achieves competitive uncertainty with minimal external assumptions.

Abstract

The MUonE experiment is designed to extract the hadronic contribution to the electromagnetic coupling in the space-like region, $\Delta \alpha_{\rm had}(t)$, from elastic $e\mu$ scattering. The leading order hadronic vacuum polarization contribution to the muon $g-2$, $a_\mu^{\mathrm{HVP, \,LO}}$, can then be obtained from a weighted integral over $\Delta \alpha_{\rm had}(t)$. This, however, requires knowledge of $\Delta \alpha_{\rm had}(t)$ in the whole domain of integration, which cannot be achieved by experiment. In this work, we propose to use Pad\'e and D-Log Pad\'e approximants as a systematic and model-independent method to fit and reliably extrapolate the future MUonE experimental data, extracting $a_\mu^{\mathrm{HVP,\,LO}}$ 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 $a_\mu^{\mathrm{HVP,\,LO}}$ and provides lower and upper bounds for the result for $a_\mu^{\mathrm{HVP,\,LO}}$. We demonstrate the reliability of the method using toy data sets generated from a model for $\Delta \alpha_{\rm had}(t)$ reflecting the expected statistics of the MUonE experiment.