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

Abstract

We present a lattice calculation of the hadronic vacuum polarization and the lowest-order hadronic contribution (HLO) to the muon anomalous magnetic moment, a µ = (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 a model to incorporate 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 generated by the MILC Collaboration (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 HLO µ = (713 ± 15) × 10 −10 and (748 ± 21) × 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 various systematic uncertainties not eliminated in this study (including a model of vector resonances used to fit the lattice data and the omission of disconnected quark contractions in the vector-vector correlation function), 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)×10 −10 , and including the experimental decay rate of the tau lepton to hadrons, 711.0 (5.0) (0.8)(2.8)×10 −10 . We discuss several ways to improve the current lattice calculation.

Sparameter in QCD from domain wall fermions

“…Note that similar observables are used to compute hadronic contributions to the anomalous magnetic moment of the muon in Refs. [36][37][38], where one can find a more detailed discussion of the renormalization of the correlators. A similar cancellation was pointed out in Ref.…”

Muon g − 2 vs LHC in supersymmetric models

“…The evaluations of the hadronic light-by-light contribution have been improving (see ref. [65] for a recent review), and lattice calculations are in development [66][67][68][69][70][71]. If the anomaly is confirmed in future, SUSY is one of the most attractive candidates for the solution.…”

On the extraction of zero momentum form factors on the lattice

“…The subtracted form factor is introduced in order to cancel divergent contributions (see for example refs. [14][15][16][17][18] for dedicated works) and, for this reason, it is very important to have an accurate determination of Π(0). By using standard techniques, Π(0) can only be obtained by extrapolating the data obtained at p 2 > 0.…”

“…In the following we shall concentrate on the connected part. Actually, many of the lattice collaborations involved in the computation of the hadronic vacuum polarization tensor [14][15][16][17][18] have neglected (or just attempted an estimate of) disconnected contributions. The choice is due to the big computational effort required for the calculation and not because these are expected (at least in general) to be negligible.…”