The QCD Adler function and the muon $g-2$ anomaly from renormalons

TL;DR

This paper introduces a novel resurgent transseries approach to the QCD Adler function, enabling more accurate predictions of the muon g-2 anomaly and aligning with recent lattice results.

Contribution

It develops a new resurgent framework for the Adler function using Borel-Ecalle resummation, improving agreement with experimental and lattice data.

Findings

The new method matches current Adler function determinations.

It suggests the muon g-2 discrepancy can be explained within the Standard Model.

The approach is compatible with recent lattice QCD results.

Abstract

We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon's anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for the muon's anomalous magnetic moment and the experimental value obtained by the most recent muon g-2 collaboration. The latter shows that the Adler function's new representation can also be consistent with recent lattice determinations.