# Long-distance reconstruction of QED corrections to the hadronic vacuum polarization for the muon g-2

## TL;DR

This paper introduces a novel method to accurately compute long-distance QED corrections to the hadronic vacuum polarization, crucial for precise muon g-2 predictions, using lattice QCD+QED data reconstruction techniques.

## Contribution

It presents a new reconstruction approach for long-distance QED corrections in lattice QCD+QED, improving precision in muon g-2 calculations.

## Key findings

- Reconstructed finite-volume contributions from lattice data.
- Established relations between pion-photon diagram contributions.
- Demonstrated method with lattice data at specific parameters.

## Abstract

The long-distance contribution of QED corrections to the hadronic vacuum polarization is particularly challenging to compute in lattice QCD+QED. Currently, it is one of the limiting factors towards matching the precision of the recent result by the Fermilab E989 experiment for the muon g-2. In this work, we present a method for obtaining high-precision results for this contribution by reconstructing exclusive finite-volume state contributions. We find relations between the pion-photon contributions of individual diagrams and demonstrate the reconstruction method with lattice QCD+QED data at a single lattice spacing of $a^{-1} \approx 1.73$ GeV and $m_\pi \approx 275$ MeV.