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Register a new userSlope and curvature of the hadron vacuum polarization at vanishing virtuality from lattice QCD
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We compute the slope and curvature, at vanishing four-momentum transfer squared, of the leading order hadron vacuum polarization function, using lattice QCD. Calculations are performed with 2+1+1 flavors of staggered fermions directly at the physical values of the quark masses and in volumes of linear extent larger than 6fm. The continuum limit is carried out using six different lattice spacings. All connected and disconnected contributions are calculated, up to and including those of the charm.
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We determine the contribution to the anomalous magnetic moment of the muon from the $alpha^2_{mathrm{QED}}$ 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 $a_{mu}^{mathrm{HVP,LO}}$ of $667(6)(12)$, 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 $a_{mu}$ and the Standard Model of 3$sigma$.
Recent progress in lattice QCD calculations of nucleon structure will be presented. Calculations of nucleon matrix elements and form factors have long been difficult to reconcile with experiment, but with advances in both methodology and computing resources, this situation is improving. Some calculations have produced agreement with experiment for key observables such as the axial charge and electromagnetic form factors, and the improved understanding of systematic errors will help to increase confidence in predictions of unmeasured quantities. The long-omitted disconnected contributions are now seeing considerable attention and some recent calculations of them will be discussed.
The QCD coupling appears in the perturbative expansion of the current-current two-point (vacuum polarization) function. Any lattice calculation of vacuum polarization is plagued by several competing non-perturbative effects at small momenta and by discretization errors at large momenta. We work in an intermediate region, computing the vacuum polarization for many off-axis momentum directions on the lattice. Having many momentum directions provides a way to monitor and account for lattice artifacts. Our results are competitive with, and have certain systematic advantages over, the alternate phenomenological determination of the strong coupling from the same light quark vacuum polarization produced by sum rule analyses of hadronic tau decay data.
We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_mu^{mathrm hvp}$, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Pade fits, time moments and the time-momentum representation. We correct our results for finite-volume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the Luscher formalism. On a subset of our ensembles we have derived an upper bound on the magnitude of quark-disconnected diagrams and found that they decrease the estimate for $a_mu^{mathrm hvp}$ by at most 2%. Our final result is $a_mu^{mathrm hvp}=(654pm32,{}^{+21}_{-23})cdot 10^{-10}$, where the first error is statistical, and the second denotes the combined systematic uncertainty. Based on our findings we discuss the prospects for determining $a_mu^{mathrm hvp}$ with sub-percent precision.
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 $a^{-1}approx 1.6$ 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 $a_mu^{rm ud, conn.,isospin, W}$ 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 $a_mu^{rm ud,conn.,isospin}$, $a_mu^{rm s,conn.,isospin}$, $a_mu^{rm SIB,conn.}$ for the total contribution and a large set of windows. For the total contribution, we find $a_mu^{rm HVP~LO}=714(27)(13) 10^{-10}$, $a_mu^{rm ud,conn.,isospin}=657(26)(12) 10^{-10}$, $a_mu^{rm s,conn.,isospin}=52.83(22)(65) 10^{-10}$, and $a_mu^{rm SIB,conn.}=9.0(0.8)(1.2) 10^{-10}$, where the first uncertainty is statistical and the second systematic. We also comment on finite-volume corrections for the strong-isospin-breaking corrections.
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