TY - JOUR

T1 - Hadronic-vacuum-polarization contribution to the muon's anomalous
magnetic moment from four-flavor lattice QCD

AU - Davies, CTH

AU - DeTar, C

AU - El-Khadra, AX

AU - Gamiz, E

AU - Gottlieb, S

AU - Hatton, D

AU - Kronfeld, AS

AU - Laiho, J

AU - Lepage, GP

AU - Liu, Y

AU - Mackenzie, PB

AU - McNeile, C

AU - Neil, ET

AU - Primer, T

AU - Simone, JN

AU - Toussaint, D

AU - Water, RSVD

AU - Vaquero, A

PY - 2020/2/18

Y1 - 2020/2/18

N2 - 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.

AB - 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.

KW - hep-lat

KW - hep-ph

U2 - 10.1103/PhysRevD.101.034512

DO - 10.1103/PhysRevD.101.034512

M3 - Article

SN - 1550-2368

VL - 0

JO - Physical Review D: Particles, Fields, Gravitation and Cosmology

JF - Physical Review D: Particles, Fields, Gravitation and Cosmology

IS - 0

ER -