Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD

Understand

Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon $g-2$ serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations.

• In this paper, we present results for the intermediate time window observable computed using O($a$) improved Wilson fermions at six values of the lattice spacings below 0.1\,fm and pion masses down to the physical value.
• Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections.
• To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-L\"uscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor.