Quark

Vacuum polarization

Pion

Anomalous magnetic dipole moment

Lattice QCD

Nuclear physics

Particle physics

Hadron

Physics

Strange quark

Muon

Isospin

Lattice field theory

Quantum chromodynamics

Physical review. D/Physical review. D.

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 $a\ensuremath{\approx}0.06$ 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 ${\ensuremath{\pi}}^{0}$, $1{0}^{10}{a}_{\ensuremath{\mu}}^{ll}(\mathrm{conn}.)=637.8(8.8)$, 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 $\mathcal{O}({\ensuremath{\alpha}}^{2})$ hadronic-vacuum polarization to the muon's anomalous magnetic moment is $1{0}^{10}{a}_{\ensuremath{\mu}}^{\mathrm{HVP},\mathrm{LO}}=699(15{)}_{u,d}(1{)}_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both ab-initio lattice-QCD calculations and phenomenological determinations from experimental ${e}^{+}{e}^{\ensuremath{-}}$-scattering data. It is $1.3\ensuremath{\sigma}$ below the ``no new physics'' value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of ${a}_{\ensuremath{\mu}}$ with theoretical calculations of the other contributions.

Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD