Hadronic vacuum polarization contribution to aμ from full lattice QCD

Abstract

We determine the contribution to the anomalous magnetic moment of the muon from the α 2 QED hadronic vacuum polarization diagram using full lattice QCD and including u/d quarks with physical masses for the first time. We use gluon field configurations that include u, d, s and c quarks in the sea at multiple values of the lattice spacing, multiple u/d masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for a HVP,LO µ of 667(6)(12) × 10 −10 , where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of aµ and the Standard Model of 3σ.

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

“…We have also performed a sanity check by comparing our prediction for finite-size effects to the direct lattice QCD data in [39], where at one set of quark masses, results for a hvp µ at three volumes are available: within the uncertainties, our estimate for the volumedependence of dΠ dQ 2 | Q 2 =0 is fully consistent with the numerical data. In the comparison, we assume that finite-size effects are dominated by the iso-vector contribution to a hvp µ , since the iso-scalar ω and φ resonances are extremely narrow.…”

“…While this is consistent with similar estimates based on effective field theories (see, for instance, refs. [39,40,78,94]), a direct calculation, performed at sufficiently large m π L, which demonstrates that finite-volume effects are under control is still lacking. Based on the Gounaris-Sakurai model, we estimate that finite-volume effects are below the percent level when m π L 6.…”

“…This concerns both a hvp µ , studied in [28][29][30][31][32][33][34][35][36][37][38][39][40], as well as a hlbl µ [41][42][43][44][45][46][47][48][49]. Lattice calculations of a hvp µ proceed by evaluating a convolution integral over Euclidean momenta Q 2 [28,50].…”

“…We add that our results are in good agreement with those of refs. [33,39] which were performed for N f = 2+1+1 flavours.…”

“…Thus, our way of employing time moments differs from the procedures applied in refs. [34,39], where the subtracted vacuum polarization functionΠ(Q 2 ) is constructed from time moments within the entire momentum interval. In order to guarantee a smooth transition between the low-momentum representation and the actual data forΠ(Q 2 ) = 4π 2 (Π(Q 2 ) − Π 0 ) we have chosen Q 2 cut so as to minimize the difference between the Padé approximation ofΠ(Q 2 ) and the data within the interval Q 2 = 0.1 − 0.5 GeV 2 .…”