Data-driven evaluations of Euclidean windows to scrutinize hadronic vacuum polarization

TL;DR

This paper explores how Euclidean time windows can help identify the sources of discrepancies in calculating the hadronic vacuum polarization contribution to the muon's magnetic moment, comparing lattice QCD and experimental data.

Contribution

It introduces a framework for using Euclidean time windows to analyze and compare HVP evaluations, providing phenomenological data and discussing optimization strategies.

Findings

Provides phenomenological comparison numbers for window quantities.

Highlights the importance of covariance matrix precision in lattice QCD.

Suggests modifications to window parameters for better energy dependence analysis.

Abstract

In this paper, we discuss how windows in Euclidean time can be used to isolate the origin of potential conflicts between evaluations of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon in lattice QCD and from $e^+e^-\to\text{hadrons}$ cross-section data. We provide phenomenological comparison numbers evaluated from $e^+e^-\to\text{hadrons}$ data for the window quantities most commonly studied in lattice QCD, complete with the correlations among them. We discuss and evaluate modifications of window parameters that could be useful in dissecting the energy dependence of tensions in the HVP integral and emphasize that further optimizations require a precise knowledge of the full covariance matrix in lattice-QCD calculations as well.