Intermediate window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from O$(a)$ improved Wilson quarks

TL;DR

This paper calculates the intermediate distance window contribution to the muon g-2 using lattice QCD with improved Wilson quarks, aiming to clarify discrepancies between phenomenological and lattice estimates.

Contribution

It provides a detailed lattice QCD calculation of the intermediate window contribution employing multiple lattice spacings and discretizations, and compares results with data-driven estimates.

Findings

Result shows a 3.9 sigma tension with data-driven evaluations.

Employs six lattice spacings below 0.1 fm and physical pion masses.

Uses two discretizations and independent improvement coefficients for robustness.

Abstract

Following the publication of the new measurement of the anomalous magnetic moment of the muon, the discrepancy between experiment and the theory prediction from the $g-2$ theory initiative has increased to $4.2\,\sigma$. Recent lattice QCD calculations predict values for the hadronic vacuum polarization contribution that are larger than the data-driven estimates, bringing the Standard Model prediction closer to the experimental measurement. Euclidean time windows in the time-momentum representation of the hadronic vacuum polarization contribution to the muon $g-2$ can help clarify the discrepancy between the phenomenological and lattice predictions. We present our calculation of the intermediate distance window contribution using $N_\mathrm{f}=2+1$ flavors of O$(a)$ improved Wilson quarks. We employ ensembles at six lattice spacings below $0.1\,$fm and pion masses down to the physical value. We present a detailed study of the continuum limit, using two discretizations of the vector current and two independent sets of improvement coefficients. Our result at the physical point displays a tension of $3.9\,\sigma$ with a recent evaluation of the intermediate window based on the data-driven method.