Abstract
We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from {the} connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from $a \approx 0.06$ to~0.15~fm. The up- and down-quark masses in our simulations have equal masses $m_l$. We obtain, in this world where all pions have the mass of the $\pi^0$, $10^{10} a_\mu^{ll}({\rm conn.}) = 637.8\,(8.8)$, in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total $\mathcal{O}(\alpha^2)$ hadronic vacuum polarization to the muon's anomalous magnetic moment is~$10^{10}a_\mu^{\rm HVP,LO} = 699(15)_{u,d}(1)_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both {\it ab-initio} lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is $1.3\sigma$ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $a_\mu$ with theoretical calculations of the other contributions.
Highlights
On the three newer ensembles analyzed in this work, we employ in addition a cost-effective variance-reduction technique called the truncated solver method (TSM) [40]
Our numerical calculation of alμlðconn:Þ and the slope and curvature of the renormalized vacuum-polarization function described in the previous section is with equal up- and down-quark masses, and without electromagnetism
It is useful to compare the available lattice-QCD results for alμlðconn:Þ, Πl1lðconn:Þ, and Πl2lðconn:Þ before putting in the corrections for isospinbreaking and electromagnetism, in order to pin down the source of any disagreements among calculations
Summary
In the absence of direct evidence for new particles or forces that are not present in the Standard Model, it becomes. The first lattice-QCD calculation of auμdðconn:Þ, the light-quark connected contribution to aHμ VP;LO that included physical-mass u=d quarks was presented in Ref. All of these results were obtained in the isospin-symmetric limit, but the calculations differ in the quark formulation used, the lattice spacings and volumes available, and in the treatment of statistical errors and finite-volume effects. The lattice-QCD results for auμdðconn:Þ are spread over a range of several percent, with uncertainties at the same level These errors are several times larger than those obtained using the experimental information from cross sections for eþe− → hadrons. This section discusses the prospects for further improvements from lattice QCD that will allow significant input to be made to the Standard-Model value for aμ ahead of new experimental results
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