Coordinate-space calculation of the window observable for the hadronic vacuum polarization contribution to $(g-2)_\mu$

TL;DR

This paper introduces a coordinate-space method to compute the hadronic vacuum polarization contribution to the muon's anomalous magnetic moment, aiming to cross-validate lattice QCD results with data-driven approaches.

Contribution

It presents a Lorentz-covariant coordinate-space calculation of the intermediate window quantity, providing an independent check against traditional time-momentum representation methods.

Findings

Results agree with recent TMR-based lattice calculations.

Calculation performed in continuum and infinite-volume limits.

Uses four different lattice spacings for validation.

Abstract

The `intermediate window quantity' of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon allows for a high-precision comparison between the data-driven approach and lattice QCD. The existing lattice results, which presently show good consistency among each other, are in strong tension with the data-driven determination. In order to check for a potentially common source of systematic error of the lattice calculations, which are all based on the time-momentum representation (TMR), we perform a calculation using a Lorentz-covariant coordinate-space (CCS) representation. We present results for the isovector and the connected strange-quark contributions to the intermediate window quantity at a reference point in the $(m_\pi,m_K)$ plane, in the continuum and infinite-volume limit, based on four different lattice spacings. Our results are in good agreement with those of the recent TMR-based Mainz-CLS publication.