# Hadronic vacuum polarization contribution to the muon $g-2$ with 2+1 flavor lattice QCD on a larger than (10 fm$)^4$ lattice at the physical point

## TL;DR

This study assesses systematic uncertainties in lattice QCD calculations of the hadronic vacuum polarization contribution to muon g-2, focusing on finite volume, cutoff effects, and integration schemes, providing a precise estimate at the physical point.

## Contribution

It presents a comprehensive analysis of systematic effects in lattice QCD for muon g-2, using large-volume simulations at the physical point to improve accuracy.

## Key findings

- Finite volume effects are quantified at different lattice sizes.
- Cutoff effects are compared using local and conserved vector currents.
- The HVP contribution to muon g-2 is estimated as 737(9)(+13-18)×10^{-10}.

## Abstract

We study systematic uncertainties in the lattice QCD computation of hadronic vacuum polarization (HVP) contribution to the muon $g-2$. We investigate three systematic effects; finite volume (FV) effect, cutoff effect, and integration scheme dependence. We evaluate the FV effect at the physical pion mass on two different volumes of (5.4 fm$)^4$ and (10.8 fm$)^4$ using the PACS10 configurations at the same cutoff scale. For the cutoff effect, we compare two types of lattice vector operators, which are local and conserved (point-splitting) currents, by varying the cutoff scale on a larger than (10 fm$)^4$ lattice at the physical point. For the integration scheme dependence, we compare the results between the coordinate- and momentum-space integration schemes at the physical point on a (10.8 fm$)^4$ lattice. Our result for the HVP contribution to the muon $g-2$ is given by $a_\mu^{\rm hvp} = 737(9)(^{+13}_{-18})\times 10^{-10}$ in the continuum limit, where the first error is statistical and the second one is systematic.