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

The MUonE experiment is designed to extract the hadronic contribution to the electromagnetic coupling in the spacelike region Δαhad(t) from elastic eμ scattering. The leading-order hadronic vacuum polarization contribution to the muon g-2, aμHVP,LO, can then be obtained from a weighted integral over Δαhad(t). This, however, requires knowledge of Δαhad(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 aμHVP,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 aμHVP,LO and provides lower and upper bounds for the result for aμHVP,LO. We demonstrate the reliability of the method using toy datasets generated from a model for Δαhad(t) reflecting the expected statistics of the MUonE experiment.