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

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 $a≈0.06$ to 0.15 fm. The up- and down-quark masses in our simulations have equal masses ml. We obtain, in this world where all pions have the mass of the $π^0$, $$10^{10}a_μ^{ll}(conn.)=637.8(8.8)$$, 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 $O(α^2)$ hadronic-vacuum polarization to the muon’s anomalous magnetic moment is $$10^{10}a_μ^{HVP,LO}=699(15)_{u,d}(1)_{s,c,b}$$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both ab-initio lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is $1.3σ$ below the “no new physics” value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $$a_μ$$ with theoretical calculations of the other contributions.

Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Contributing Org.:
[Fermilab Lattice, HPQCD, and MILC Collaborations]
OSTI Identifier:
1600067
Alternate Identifier(s):
OSTI ID: 1529343
Report Number(s):
[FERMILAB-PUB-19-064-T]
[Journal ID: ISSN 2470-0010; PRVDAQ; 034512]
Grant/Contract Number:  
[AC02-07CH11359; FG02-13ER41976; SC0009998; SC0010005; SC0010120; SC0015655; TG-MCA93S002]
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
[Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 3]; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice field theory; Quantum chromodynamics; Muons; Magnetic moment; Ab initio calculations; Lattice QCD

Citation Formats

Davies, C. T. H., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Hatton, D., Kronfeld, A. S., Laiho, J., Lepage, G. P., Liu, Yuzhi, Mackenzie, P. B., McNeile, C., Neil, E. T., Primer, T., Simone, J. N., Toussaint, D., Van de Water, R. S., Vaquero, A., and Fermilab Lattice, HPQCD, and MILC Collaborations. Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.101.034512.
Davies, C. T. H., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Hatton, D., Kronfeld, A. S., Laiho, J., Lepage, G. P., Liu, Yuzhi, Mackenzie, P. B., McNeile, C., Neil, E. T., Primer, T., Simone, J. N., Toussaint, D., Van de Water, R. S., Vaquero, A., & Fermilab Lattice, HPQCD, and MILC Collaborations. Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD. United States. doi:10.1103/PhysRevD.101.034512.
Davies, C. T. H., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Hatton, D., Kronfeld, A. S., Laiho, J., Lepage, G. P., Liu, Yuzhi, Mackenzie, P. B., McNeile, C., Neil, E. T., Primer, T., Simone, J. N., Toussaint, D., Van de Water, R. S., Vaquero, A., and Fermilab Lattice, HPQCD, and MILC Collaborations. Tue . "Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD". United States. doi:10.1103/PhysRevD.101.034512.
@article{osti_1600067,
title = {Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD},
author = {Davies, C. T. H. and DeTar, C. and El-Khadra, A. X. and Gámiz, E. and Gottlieb, Steven and Hatton, D. and Kronfeld, A. S. and Laiho, J. and Lepage, G. P. and Liu, Yuzhi and Mackenzie, P. B. and McNeile, C. and Neil, E. T. and Primer, T. and Simone, J. N. and Toussaint, D. and Van de Water, R. S. and Vaquero, A. and Fermilab Lattice, HPQCD, and MILC Collaborations},
abstractNote = {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 $a≈0.06$ to 0.15 fm. The up- and down-quark masses in our simulations have equal masses ml. We obtain, in this world where all pions have the mass of the $π^0$, $10^{10}a_μ^{ll}(conn.)=637.8(8.8)$, 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 $O(α^2)$ hadronic-vacuum polarization to the muon’s anomalous magnetic moment is $10^{10}a_μ^{HVP,LO}=699(15)_{u,d}(1)_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both ab-initio lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is $1.3σ$ below the “no new physics” value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $a_μ$ with theoretical calculations of the other contributions.},
doi = {10.1103/PhysRevD.101.034512},
journal = {Physical Review D},
number = [3],
volume = [101],
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevD.101.034512

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Works referenced in this record:

( g − 2) μ and α( M 2 Z ) re-evaluated using new precise data
journal, June 2011

  • Hagiwara, Kaoru; Liao, Ruofan; Martin, Alan D.
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 38, Issue 8
  • DOI: 10.1088/0954-3899/38/8/085003

Review of Particle Physics
journal, October 2016


Calculation of the Hadronic Vacuum Polarization Contribution to the Muon Anomalous Magnetic Moment
journal, July 2018


Hadronic Vacuum Polarization Contribution to the Anomalous Magnetic Moments of Leptons from First Principles
journal, July 2018


New class of variance-reduction techniques using lattice symmetries
journal, November 2013


Finite-volume effects in the muon anomalous magnetic moment on the lattice
journal, March 2016


Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass
journal, September 2016


Strange and charm HVP contributions to the muon (g − 2) including QED corrections with twisted-mass fermions
journal, October 2017

  • Giusti, D.; Lubicz, V.; Martinelli, G.
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)157

Complete Tenth-Order QED Contribution to the Muon g 2
journal, September 2012


ϒ and ϒ leptonic widths, a μ b , and m b from full lattice QCD
journal, April 2015


Final report of the E821 muon anomalous magnetic moment measurement at BNL
journal, April 2006


Calculation of the Hadronic Vacuum Polarization Disconnected Contribution to the Muon Anomalous Magnetic Moment
journal, June 2016


Leading hadronic contribution to ( g 2 ) μ from lattice QCD with N f = 2 + 1 flavors of O ( a ) improved Wilson quarks
journal, July 2019


Best Error Bounds for Padé Approximants to Convergent Series of Stieltjes
journal, May 1969

  • Baker, George A.
  • Journal of Mathematical Physics, Vol. 10, Issue 5
  • DOI: 10.1063/1.1664911

Strange and charm quark contributions to the anomalous magnetic moment of the muon
journal, June 2014

  • Chakraborty, Bipasha; Davies, C. T. H.; Donald, G. C.
  • Physical Review D, Vol. 89, Issue 11
  • DOI: 10.1103/PhysRevD.89.114501

Light-quark contribution to the leading hadronic vacuum polarization term of the muon g 2 from twisted-mass fermions
journal, December 2018


Light quark vacuum polarization at the physical point and contribution to the muon g 2
journal, January 2020


XSEDE: Accelerating Scientific Discovery
journal, September 2014

  • Towns, John; Cockerill, Timothy; Dahan, Maytal
  • Computing in Science & Engineering, Vol. 16, Issue 5
  • DOI: 10.1109/MCSE.2014.80

Analysis of systematic error in hadronic vacuum polarization contribution to muon g-2
conference, May 2019

  • Shintani, Eigo; Kuramashi, Yoshinobu
  • Proceedings of The 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)
  • DOI: 10.22323/1.334.0060

Quark disconnected diagrams in chiral perturbation theory
journal, November 2010

  • Della Morte, Michele; Jüttner, Andreas
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)154

High-precision scale setting in lattice QCD
journal, September 2012

  • Borsányi, Szabolcs; Dürr, Stephan; Fodor, Zoltán
  • Journal of High Energy Physics, Vol. 2012, Issue 9
  • DOI: 10.1007/JHEP09(2012)010

muon g-2/EDM experiment at J-PARC
conference, November 2017

  • Sato, Yutaro
  • Proceedings of The 3rd International Symposium on “Quest for the Origin of Particles and the Universe" — PoS(KMI2017)
  • DOI: 10.22323/1.294.0006

The electroweak contributions to ( g 2 ) μ after the Higgs-boson mass measurement
journal, September 2013


Highly improved staggered quarks on the lattice with applications to charm physics
journal, March 2007


Slope and curvature of the hadronic vacuum polarization at vanishing virtuality from lattice QCD
journal, October 2017


The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD
journal, October 2017

  • Morte, M. Della; Francis, A.; Gülpers, V.
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)020

Nonperturbative comparison of clover and highly improved staggered quarks in lattice QCD and the properties of the ϕ meson
journal, October 2017


Charm and bottom quark masses: An update
journal, October 2009


ρ 0–γ mixing in the neutral channel pion form factor $F^{(e)}_{\pi}(s)$ and its role in comparing e + e − with τ spectral functions
journal, May 2011


Lattice computation of the electromagnetic contributions to kaon and pion masses
journal, February 2019


Erratum to: Lattice calculation of the leading strange quark-connected contribution to the muon g − 2
journal, May 2017

  • Blum, T.; Boyle, P. A.; Del Debbio, L.
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)034

Hadronic vacuum polarization contribution to a μ from full lattice QCD
journal, August 2017

  • Chakraborty, Bipasha; Davies, C. T. H.; de Oliveira, P. G.
  • Physical Review D, Vol. 96, Issue 3
  • DOI: 10.1103/PhysRevD.96.034516

Muon $$g-2$$ g - 2 estimates: can one trust effective Lagrangians and global fits?
journal, December 2015


Constrained curve fitting
journal, March 2002


Lattice QCD ensembles with four flavors of highly improved staggered quarks
journal, March 2013


Higher order hadronic and leptonic contributions to the muon g − 2
journal, January 2016


Strong-Isospin-Breaking Correction to the Muon Anomalous Magnetic Moment from Lattice QCD at the Physical Point
journal, April 2018


Connected and Leading Disconnected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment with a Physical Pion Mass
journal, January 2017


Model-independent parametrization of the hadronic vacuum polarization and g -2 for the muon on the lattice
journal, September 2012


Muon g – 2 theory: The hadronic part
journal, January 2018


Lattice calculation of the leading strange quark-connected contribution to the muon g − 2
journal, April 2016

  • Blum, T.; Boyle, P. A.; Del Debbio, L.
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)063

Vector correlators in lattice QCD: Methods and applications
journal, November 2011


Muon g 2 and α ( M Z 2 ) : A new data-based analysis
journal, June 2018


Recent developments in the comparison between theory and experiments in quantum electrodynamics
journal, May 1972


Four-flavour leading-order hadronic contribution to the muon anomalous magnetic moment
journal, February 2014

  • Burger, Florian; Feng, Xu; Hotzel, Grit
  • Journal of High Energy Physics, Vol. 2014, Issue 2
  • DOI: 10.1007/JHEP02(2014)099

The bounding properties of the multipoint Padé approximant to a series of Stieltjes on the real line
journal, March 1973

  • Barnsley, Michael
  • Journal of Mathematical Physics, Vol. 14, Issue 3
  • DOI: 10.1063/1.1666314

V u s from π and K decay constants in full lattice QCD with physical u , d , s , and c quarks
journal, October 2013


Precision tests of the J / ψ from full lattice QCD: Mass, leptonic width, and radiative decay rate to η c
journal, November 2012


Electromagnetic and strong isospin-breaking corrections to the muon g 2 from lattice QCD + QED
journal, June 2019


Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
journal, June 2014


Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD
journal, April 2016


Hadronic light-by-light scattering contribution to the muon g – 2 on the lattice
journal, January 2018