Utility of a hybrid approach to the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment

TL;DR

This paper evaluates a hybrid method combining lattice QCD and experimental data to accurately compute the hadronic vacuum polarisation contribution to the muon g-2, testing the robustness of the approach and its implications for Standard Model consistency.

Contribution

It demonstrates the effectiveness of varying the separation point in the hybrid approach and supports the use of CMD-3 data, aligning with recent lattice results and reducing uncertainties.

Findings

Favors CMD-3 data over earlier experiments for $e^+e^- o ext{hadrons}$

Total LOHVP estimate consistent with BMW/DMZ results

Supports no significant discrepancy between muon g-2 experiment and Standard Model

Abstract

An accurate calculation of the leading-order hadronic vacuum polarisation (LOHVP) contribution to the anomalous magnetic moment of the muon ($a_\mu$) is key to determining whether a discrepancy, suggesting new physics, exists between the Standard Model and experimental results. This calculation can be expressed as an integral over Euclidean time of a current-current correlator $G(t)$, where $G(t)$ can be calculated using lattice QCD or, with dispersion relations, from experimental data for $e^+e^-\to\mbox{hadrons}$. The BMW/DMZ collaboration recently presented a hybrid approach in which $G(t)$ is calculated using lattice QCD for most of the contributing $t$ range, but using experimental data for the largest $t$ (lowest energy) region. Here we study the advantages of varying the position $t=t_1$ separating lattice QCD from data-driven contributions. The total LOHVP contribution should be independent of $t_1$, providing both a test of the experimental input and the robustness of the hybrid approach. We use this criterion and a correlated fit to show that Fermilab/HPQCD/MILC lattice QCD results from 2019 strongly favour the CMD-3 cross-section data for $e^+e^-\to\pi^+\pi^-$ over a combination of earlier experimental results for this channel. Further, the resulting total LOHVP contribution obtained is consistent with the result obtained by BMW/DMZ, and supports the scenario in which there is no significant discrepancy between the experimental value for $a_\mu$ and that expected in the Standard Model. We then discuss how improved lattice results in this hybrid approach could provide a more accurate total LOHVP across a wider range of $t_1$ values with an uncertainty that is smaller than that from either lattice QCD or data-driven approaches on their own.