Consistency of hadronic vacuum polarization between lattice QCD and the R ratio

Abstract

There are emerging tensions for theory results of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment both within recent lattice QCD calculations and between some lattice QCD calculations and R-ratio results. In this paper we work towards scrutinizing critical aspects of these calculations. We focus in particular on a precise calculation of Euclidean position-space windows defined by RBC/UKQCD that are ideal quantities for cross-checks within the lattice community and with R-ratio results. We perform a lattice QCD calculation using physical up, down, strange, and charm sea quark gauge ensembles generated in the staggered formalism by the MILC collaboration. We study the continuum limit using inverse lattice spacings from a −1 ≈ 1.6 GeV to 3.5 GeV, identical to recent studies by FNAL/HPQCD/MILC and Aubin et al. and similar to the recent study of BMW. Our calculation exhibits a tension for the particularly interesting window result of a ud,conn.,isospin,W µ from 0.4 fm to 1.0 fm with previous results obtained with a different discretization of the vector current on the same gauge configurations. Our results may indicate a difficulty related to estimating uncertainties of the continuum extrapolation that deserves further attention. In this work we also provide results for a ud,conn.,isospin µ , a s,conn.,isospin µ , a SIB,conn. µ for the total contribution and a large set of windows. For the total contribution, we find a HVP LO µ = 714(27)(13)10 −10 , a ud,conn.,isospin µ = 657(26)(12)10 −10 , a s,conn.,isospin µ = 52.83(22)(65)10 −10 , and a SIB,conn. µ = 9.0(0.8)(1.2)10 −10 , where the first uncertainty is statistical and the second systematic. We also comment on finite-volume corrections for the strong-isospin-breaking corrections.

Muon g−2 and Δα connection

“…When considering the current 3.8σ tension between the KNT19 dispersive result for a had;VP μ [23] and the recent lattice QCD evaluation of the BMW Collaboration that indicates agreement with a exp μ [85], this could suggest that the lattice calculation may have captured contributions below ∼0.7 GeV that are absent from the hadronic data (see, e.g., [144]). A study comparing the results from BMW Collaboration with the dispersive results is beyond the scope of this work and a detailed discussion can be found in [1,86]. However, it has been found here that the size of the missed contributions required to bridge the muon g − 2 discrepancy (or the BMW-KNT19 discrepancy) would need to be improbably large given the robust status of the hadronic cross section measurements.…”

“…An extensive comparison with the lattice results of the BMW Collaboration [85] is beyond the scope of this paper. For an up-to-date discussion, see [1] and [86].…”

Inclusive Semileptonic Decays from Lattice QCD

“…One may instead use analyticity and the optical theorem to relate the total rate to another quantity that is calculable on the lattice. This approach has been followed in simple cases, such as the e þ e − → qq processes [12][13][14][15] and τ-lepton decays [16,17], while the application to B meson semileptonic decays is much more complicated [9].…”

Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2

“…The BMW Collaboration [80] obtained recently from lattice calculation significantly higher values for the had(1)-contribution, 10 10 × a had (1) µ;latt = 712.4 ± 4.5 [80], which would indicate that the deviation between a dir.exp µ and a (SM) µ reduces to about 1σ and that no new physics beyond QCD (beyond SM) is needed for the explanation of the deviation. However, the results of lattice calculation by another group [81] indicates that higher statistical uncertainties appear in a had (1) µ;latt than assumed in [80]. This would then ease tension with the results Eq.…”