# The hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD

## TL;DR

This paper calculates the hadronic vacuum polarization contribution to the muon g-2 using lattice QCD with dynamical quarks, employing multiple methods to control infrared effects and estimate uncertainties, achieving a precise result.

## Contribution

It introduces a comprehensive lattice QCD approach with multiple techniques to accurately determine the hadronic vacuum polarization contribution to muon g-2, including finite-volume corrections and bounds on disconnected diagrams.

## Key findings

- Final result: $a_\mu^{\mathrm hvp}=(654\pm32^{+21}_{-23})\times 10^{-10}$
- Disconnection diagrams reduce the estimate by at most 2%
- Controlled infrared regime and finite-volume effects improve precision

## Abstract

We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_\mu^{\mathrm hvp}$, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Pad\'e fits, time moments and the time-momentum representation. We correct our results for finite-volume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the L\"uscher formalism. On a subset of our ensembles we have derived an upper bound on the magnitude of quark-disconnected diagrams and found that they decrease the estimate for $a_\mu^{\mathrm hvp}$ by at most 2%. Our final result is $a_\mu^{\mathrm hvp}=(654\pm32\,{}^{+21}_{-23})\cdot 10^{-10}$, where the first error is statistical, and the second denotes the combined systematic uncertainty. Based on our findings we discuss the prospects for determining $a_\mu^{\mathrm hvp}$ with sub-percent precision.