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We present new results for the light-quark connected part of the leadingorder hadronic-vacuum-polarization (HVP) contribution to the muon anomalousmagnetic moment, using $2+1+1$ staggered fermions. We have collected morestatistics on previous ensembles, and we added two new ensembles. This allowsus to reduce statistical errors on the HVP contribution and related windowquantities significantly. We also calculated the current-current correlator tonext-to-next-to-leading order (NNLO) in staggered chiralperturbation theory, sothat we can correct to NNLO for finite-volume, pion-mass mistuning andtaste-breaking effects. We discuss the applicability of NNLO chiralperturbation theory, emphasizing that it provides a systematic EFT approach tothe HVP contribution, but not to short- or intermediate-distance windowquantities. This makes it difficult to assess systematic errors on the standardintermediate-distance window quantity that is now widely considered in theliterature. In view of this, we investigate a longer-distance window, for whichEFT methods should be more reliable. Our most important conclusion is that newhigh-statistics computations at lattice spacings significantly smaller than0.06 fm are indispensable. The ensembles we use have been generously providedby MILC and CalLat.

The muon anomalous magnetic moment: is the lattice spacing small enough?