## ORCID

- McNeile, Craig: 0000-0003-0305-2028

## 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~0.06-0.15 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 $\pi^0$, $10^{10} a_\mu^{ll}({\rm conn.}) = 630.1(8.3)$, 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. We obtain for the total order $(\alpha^2)$ hadronic-vacuum polarization to the muon's anomalous magnetic moment $10^{10} a_\mu^{\rm HVP,LO} = 691(8)_{u,d}(1)_{s,c,b} (13)_{\rm other}$, where the errors are from the light-quark connected contribution, heavy-flavor connected contributions, and omitted effects listed above, respectively. Our result agrees with both $ab-initio$ lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is 1.7$\sigma$ 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.

## DOI

10.1103/PhysRevD.101.034512

## Publication Date

2020-02-18

## Publication Title

Physical Review D: Particles, Fields, Gravitation and Cosmology

## ISSN

1550-2368

## Embargo Period

2020-02-22

## Organisational Unit

School of Engineering, Computing and Mathematics

## Keywords

hep-lat, hep-ph

## Recommended Citation

Davies, C.,
DeTar, C.,
El-Khadra, A.,
Gamiz, E.,
Gottlieb, S.,
Hatton, D.,
Kronfeld, A.,
Laiho, J.,
Lepage, G.,
Liu, Y.,
Mackenzie, P.,
McNeile, C.,
Neil, E.,
Primer, T.,
Simone, J.,
Toussaint, D.,
Water, R.,
&
Vaquero, A.
(2020)
'Hadronic-vacuum-polarization contribution to the muon's anomalous
magnetic moment from four-flavor lattice QCD',
*Physical Review D: Particles, Fields, Gravitation and Cosmology*, .
Available at: https://doi.org/10.1103/PhysRevD.101.034512