Data-based determination of the isospin-limit light-quark-connected contribution to the anomalous magnetic moment of the muon

TL;DR

This paper presents a data-driven dispersive method to determine the isospin-limit light-quark-connected contribution to the muon's anomalous magnetic moment, addressing discrepancies between lattice and dispersive results.

Contribution

It introduces a novel dispersive approach using recent exclusive-mode data to estimate the light-quark-connected contribution, clarifying lattice-dispersive tensions.

Findings

Determined $a_\mu^{lqc; IL}$ as approximately 635-638 × 10^{-10}.

Provided a small EM correction estimate from lattice results.

Highlighted potential resolution of lattice-dispersive discrepancies.

Abstract

We describe how recent determinations of exclusive-mode contributions to $a_\mu^{\rm LO,HVP}$, the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, can be used to provide, up to small electromagnetic (EM) corrections accessible from the lattice, a data-based dispersive determination of $a_\mu^{\rm lqc;\, IL}$, the isospin-limit, light-quark-connected contribution to $a_\mu^{\rm LO,HVP}$. Such a determination is of interest in view of the existence of a number of lattice results for this quantity, emerging evidence for a tension between lattice and dispersive determinations of $a_\mu^{\rm LO,HVP}$, and the desire to clarify the source of this tension. Taking as input for the small EM correction that must be applied to the purely data-driven dispersive determination the result $-0.93(58)\times 10^{-10}$ obtained in a recent BMW lattice study, we find $a_\mu^{\rm lqc;\, IL}$ to be $635.0(2.7)\times 10^{-10}$ if the results of Keshavarzi, Nomura and Teubner are used for the exclusive-mode contributions and $638.4(4.1)\times 10^{-10}$ if instead those of Davier, H\"ocker, Malaescu and Zhang are used.