# The leading hadronic contribution to $(g-2)_\mu$ from lattice QCD with $N_{\rm f}=2+1$ flavours of O($a$) improved Wilson quarks

## TL;DR

This paper calculates the leading hadronic contribution to the muon's anomalous magnetic moment using lattice QCD with Wilson quarks, achieving a precise result that includes systematic uncertainties and finite-size corrections.

## Contribution

It presents a novel lattice QCD computation of $(g-2)_$ with improved discretization and multiple lattice spacings, incorporating finite-size and isospin-breaking effects.

## Key findings

- Final result: $a_^{
m hvp}=(720.0\u00b1 12.4_{
m stat} 9.9_{
m syst}) imes 10^{-10}$
- Includes quark-disconnected diagrams and systematic error estimates
- Uses combined chiral and continuum extrapolation to physical point.

## Abstract

The comparison of the theoretical and experimental determinations of the anomalous magnetic moment of the muon $(g-2)_\mu$ constitutes one of the strongest tests of the Standard Model at low energies. In this article, we compute the leading hadronic contribution to $(g-2)_\mu$ using lattice QCD simulations employing Wilson quarks. Gauge field ensembles at four different lattice spacings and several values of the pion mass down to its physical value are used. We apply the O($a$) improvement programme with two discretizations of the vector current to better constrain the approach to the continuum limit. The electromagnetic current correlators are computed in the time-momentum representation. In addition, we perform auxiliary calculations of the pion form factor at timelike momenta in order to better constrain the tail of the isovector correlator and to correct its dominant finite-size effect. For the numerically dominant light-quark contribution, we have rescaled the lepton mass by the pion decay constant computed on each lattice ensemble. We perform a combined chiral and continuum extrapolation to the physical point, and our final result is $ a_\mu^{\rm hvp}=(720.0\pm12.4_{\rm stat}\,\pm9.9_{\rm syst})\cdot10^{-10}$. It contains the contributions of quark-disconnected diagrams, and the systematic error has been enlarged to account for the missing isospin-breaking effects.