Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks

TL;DR

This paper reports a lattice QCD calculation of the hadronic vacuum polarization contribution to the muon g-2 using improved staggered quarks, achieving results consistent with experimental estimates and discussing potential improvements.

Contribution

First lattice calculation using 2+1 flavors of improved staggered fermions with detailed systematic uncertainty analysis for muon g-2.

Findings

Calculated a_^{HLO} = (713 b1 15) imes 10^{-10} (linear extrapolation)

Calculated a_^{HLO} = (748 b1 21) imes 10^{-10} (quadratic extrapolation)

Results agree with experimental-based estimates within uncertainties.

Abstract

We present a lattice calculation of the hadronic vacuum polarization and the lowest-order hadronic contribution to the muon anomalous magnetic moment, a_\mu = (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to the low-q^2 region of the vacuum polarization is necessary to accurately extract the muon g-2. To obtain this fit, we use staggered chiral perturbation theory, including the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the relative contributions of the pions and vector mesons. Using a single lattice spacing ensemble (a=0.086 fm), light quark masses as small as roughly one-tenth the strange quark mass, and volumes as large as (3.4 fm)^3, we find a_\mu^{HLO} = (713 \pm 15) \times 10^{-10} and (748 \pm 21) \times 10^{-10} where the error is statistical only and the two values correspond to linear and quadratic extrapolations in the light quark mass, respectively. Considering systematic uncertainties not eliminated in this study, we view this as agreement with the current best calculations using the experimental cross section for e^+e^- annihilation to hadrons, 692.4 (5.9) (2.4)\times 10^{-10}, and including the experimental decay rate of the tau lepton to hadrons, 711.0 (5.0) (0.8)(2.8)\times 10^{-10}. We discuss several ways to improve the current lattice calculation.