The role of Pad\'e and D-Log Pad\'e approximants in the context of the MUonE Experiment

TL;DR

This paper explores how Padé and D-Log Padé approximants, leveraging the correlator's analyticity, can improve the precision of hadronic contribution extraction in the MUonE experiment, addressing current discrepancies in muon g-2 calculations.

Contribution

It introduces the application of Padé and D-Log Padé approximants to enhance the accuracy of hadronic contribution measurements in the MUonE experiment.

Findings

Padé approximants effectively model the correlator's analytic structure.

D-Log Padé approximants improve convergence in the low-energy region.

Method shows potential to reduce uncertainties in muon g-2 calculations.

Abstract

In the context of the anomalous magnetic moment of the muon, the hadronic contribution plays a crucial role, especially given its large contribution to the final error. Currently, lattice QCD simulations are in disagreement with dispersive calculations based on $e^+e^-$ hadronic cross sections. The new MUonE experiment intends to shed light on this situation extracting the hadronic contribution to the running of the electromagnetic coupling in the space-like region, $\Delta \alpha_{\rm had}(t)$, from elastic $e\mu$ scattering. Still, due to the limited kinematic range that can be covered by the experiment, a powerful method must be devised to accurately extract the desired hadronic contribution from a new experiment of this type. In this work, we show how Pad\'e and D-Log Pad\'e approximants profiting from the analyticity of the correlator governing the hadronic contribution can be a powerful tool in reaching the required precision.