# Higher-order hadronic-vacuum-polarization contribution to the muon $g-2$ from lattice QCD

## Abstract

We introduce a new method for calculating the O(α3) hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ab initio lattice QCD. We first derive expressions suitable for computing the higher-order contributions either from the renormalized vacuum polarization function Π^(q2) or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously published results for the Taylor coefficients of Π^(q2) that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain 1010aμHVP,HO=-9.3(1.3) in agreement with, but with a larger uncertainty than, determinations from e+e-→hadrons data plus dispersion relations.

- Authors:

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)

- Contributing Org.:
- Fermilab Lattice, HPQCD, and MILC Collaborations

- OSTI Identifier:
- 1481454

- Alternate Identifier(s):
- OSTI ID: 1467057; OSTI ID: 1481732

- Report Number(s):
- arXiv:1806.08190; FERMILAB-PUB-18-287-T; JLAB-THY-18-2779; DOE/OR/23177-4511

Journal ID: ISSN 2470-0010; PRVDAQ; 094503

- Grant/Contract Number:
- PHY13-16222; AC02-07CH11359

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Chakraborty, B., Davies, C. T. H., Koponen, J., Lepage, G. P., Van de Water, R. S., and Fermilab Lattice, HPQCD, and MILC Collaborations. Higher-order hadronic-vacuum-polarization contribution to the muon g − 2 from lattice QCD. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.094503.
```

```
Chakraborty, B., Davies, C. T. H., Koponen, J., Lepage, G. P., Van de Water, R. S., & Fermilab Lattice, HPQCD, and MILC Collaborations. Higher-order hadronic-vacuum-polarization contribution to the muon g − 2 from lattice QCD. United States. https://doi.org/10.1103/PhysRevD.98.094503
```

```
Chakraborty, B., Davies, C. T. H., Koponen, J., Lepage, G. P., Van de Water, R. S., and Fermilab Lattice, HPQCD, and MILC Collaborations. Fri .
"Higher-order hadronic-vacuum-polarization contribution to the muon g − 2 from lattice QCD". United States. https://doi.org/10.1103/PhysRevD.98.094503.
```

```
@article{osti_1481454,
```

title = {Higher-order hadronic-vacuum-polarization contribution to the muon g − 2 from lattice QCD},

author = {Chakraborty, B. and Davies, C. T. H. and Koponen, J. and Lepage, G. P. and Van de Water, R. S. and Fermilab Lattice, HPQCD, and MILC Collaborations},

abstractNote = {We introduce a new method for calculating the O(α3) hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ab initio lattice QCD. We first derive expressions suitable for computing the higher-order contributions either from the renormalized vacuum polarization function Π^(q2) or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously published results for the Taylor coefficients of Π^(q2) that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain 1010aμHVP,HO=-9.3(1.3) in agreement with, but with a larger uncertainty than, determinations from e+e-→hadrons data plus dispersion relations.},

doi = {10.1103/PhysRevD.98.094503},

journal = {Physical Review D},

number = 9,

volume = 98,

place = {United States},

year = {2018},

month = {11}

}

https://doi.org/10.1103/PhysRevD.98.094503

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Works referenced in this record:

##
Lattice Calculation of the Lowest-Order Hadronic Contribution to the Muon Anomalous Magnetic Moment

journal, July 2003

- Blum, T.
- Physical Review Letters, Vol. 91, Issue 5

##
Mellin-Barnes approach to hadronic vacuum polarization and ${g}_{\mu}-2$

journal, April 2018

- Charles, Jérôme; de Rafael, Eduardo; Greynat, David
- Physical Review D, Vol. 97, Issue 7

##
Nonperturbative QCD simulations with $2+1$ flavors of improved staggered quarks

journal, May 2010

- Bazavov, A.; Toussaint, D.; Bernard, C.
- Reviews of Modern Physics, Vol. 82, Issue 2

##
Hadronic vacuum polarization contribution to ${a}_{\mu}$ from full lattice QCD

journal, August 2017

- Chakraborty, Bipasha; Davies, C. T. H.; de Oliveira, P. G.
- Physical Review D, Vol. 96, Issue 3

##
Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon $$g-2$$ g - 2 and $${\alpha (m_Z^2)}$$ α ( m Z 2 ) using newest hadronic cross-section data

journal, December 2017

- Davier, M.; Hoecker, A.; Malaescu, B.
- The European Physical Journal C, Vol. 77, Issue 12

##
A precise determination of the HVP contribution to the muon anomalous magnetic moment from lattice QCD

journal, January 2018

- Lehner, Christoph
- EPJ Web of Conferences, Vol. 175

##
An interpolation of the vacuum polarization function for the evaluation of hadronic contributions to the muon anomalous magnetic moment

journal, July 2002

- Groote, S.; Körner, J. G.; Pivovarov, A. A.
- The European Physical Journal C, Vol. 24, Issue 3

##
Lattice QCD ensembles with four flavors of highly improved staggered quarks

journal, March 2013

- Bazavov, A.; Bernard, C.; Komijani, J.
- Physical Review D, Vol. 87, Issue 5

##
Higher order hadronic and leptonic contributions to the muon *g* − 2

journal, January 2016

- Kurz, Alexander; Liu, Tao; Marquard, Peter
- EPJ Web of Conferences, Vol. 118

##
Hadronic vacuum polarization and gμ−2

journal, July 1969

- Bell, J. S.; de Rafael, E.
- Nuclear Physics B, Vol. 11, Issue 4

##
Calculation of the Hadronic Vacuum Polarization Contribution to the Muon Anomalous Magnetic Moment

journal, July 2018

- Blum, T.; Boyle, P. A.; Gülpers, V.
- Physical Review Letters, Vol. 121, Issue 2

##
Hadronic Vacuum Polarization Contribution to the Anomalous Magnetic Moments of Leptons from First Principles

journal, July 2018

- Borsanyi, Sz.; Fodor, Z.; Hoelbling, C.
- Physical Review Letters, Vol. 121, Issue 2

##
Strong-Isospin-Breaking Correction to the Muon Anomalous Magnetic Moment from Lattice QCD at the Physical Point

journal, April 2018

- Chakraborty, B.; Davies, C. T. H.; DeTar, C.
- Physical Review Letters, Vol. 120, Issue 15

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

journal, January 2017

- Blum, Thomas; Christ, Norman; Hayakawa, Masashi
- Physical Review Letters, Vol. 118, Issue 2

##
The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea

journal, March 2012

- Dowdall, R. J.; Colquhoun, B.; Daldrop, J. O.
- Physical Review D, Vol. 85, Issue 5

##
Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks

journal, June 2007

- Aubin, C.; Blum, T.
- Physical Review D, Vol. 75, Issue 11

##
$\mathrm{\Upsilon}$ and ${\mathrm{\Upsilon}}^{\prime}$ leptonic widths, ${a}_{\mu}^{b}$ , and ${m}_{b}$ from full lattice QCD

journal, April 2015

- Colquhoun, B.; Dowdall, R. J.; Davies, C. T. H.
- Physical Review D, Vol. 91, Issue 7

##
Final report of the E821 muon anomalous magnetic moment measurement at BNL

journal, April 2006

- Bennett, G. W.; Bousquet, B.; Brown, H. N.
- Physical Review D, Vol. 73, Issue 7

##
Calculation of the Hadronic Vacuum Polarization Disconnected Contribution to the Muon Anomalous Magnetic Moment

journal, June 2016

- Blum, T.; Boyle, P. A.; Izubuchi, T.
- Physical Review Letters, Vol. 116, Issue 23

##
Muon *g* – 2 theory: The hadronic part

journal, January 2018

- Jegerlehner, Fred
- EPJ Web of Conferences, Vol. 166

##
Improved nonrelativistic QCD for heavy-quark physics

journal, November 1992

- Lepage, G. Peter; Magnea, Lorenzo; Nakhleh, Charles
- Physical Review D, Vol. 46, Issue 9

##
Vector correlators in lattice QCD: Methods and applications

journal, November 2011

- Bernecker, David; Meyer, Harvey B.
- The European Physical Journal A, Vol. 47, Issue 11

##
Predictions for $g-2$ of the muon and ${\alpha}_{\mathrm{QED}}{(M}_{Z}^{2})$

journal, May 2004

- Hagiwara, K.; Martin, A. D.; Nomura, Daisuke
- Physical Review D, Vol. 69, Issue 9

##
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

##
Muon $g-2$ and $\alpha ({M}_{Z}^{2})$ : A new data-based analysis

journal, June 2018

- Keshavarzi, Alexander; Nomura, Daisuke; Teubner, Thomas
- Physical Review D, Vol. 97, Issue 11

##
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

##
Higher-order hadronic contributions to the anomalous magnetic moment of leptons

journal, January 1997

- Krause, Bernd
- Physics Letters B, Vol. 390, Issue 1-4

##
QCD spectrum with three quark flavors

journal, August 2001

- Bernard, Claude; Burch, Tom; Orginos, Kostas
- Physical Review D, Vol. 64, Issue 5

##
Light hadrons with improved staggered quarks: Approaching the continuum limit

journal, November 2004

- Aubin, C.; Bernard, C.; DeTar, C.
- Physical Review D, Vol. 70, Issue 9

##
Study of the reaction ${e}^{+}{e}^{-}\to {\pi}^{0}\gamma $ with the SND detector at the VEPP-2M collider

journal, May 2016

- Achasov, M. N.; Beloborodov, K. I.; Berdyugin, A. V.
- Physical Review D, Vol. 93, Issue 9

##
Precision tests of the $J/\psi $ from full lattice QCD: Mass, leptonic width, and radiative decay rate to ${\eta}_{c}$

journal, November 2012

- Donald, G. C.; Davies, C. T. H.; Dowdall, R. J.
- Physical Review D, Vol. 86, Issue 9

##
Lattice determination of the hadronic contribution to the muon $g\mathbf{-}2$ using dynamical domain wall fermions

journal, April 2012

- Boyle, Peter; Debbio, Luigi Del; Kerrane, Eoin
- Physical Review D, Vol. 85, Issue 7

##
Highly improved staggered quarks on the lattice with applications to charm physics

journal, March 2007

- Follana, E.; Mason, Q.; Davies, C.
- Physical Review D, Vol. 75, Issue 5

##
Slope and curvature of the hadronic vacuum polarization at vanishing virtuality from lattice QCD

journal, October 2017

- Borsanyi, Sz.; Fodor, Z.; Kawanai, T.
- Physical Review D, Vol. 96, Issue 7

##
Consequences of the *BABAR* and KLOE ${e}^{+}{e}^{-}\to {\pi}^{+}{\pi}^{-}$ data for the determination of model-dependent $\rho $ - $\omega $ mixing effects in ${\Pi}_{\rho \omega}({m}_{\rho}^{2})$ and $(g-2{)}_{\mu}$

journal, April 2011

- Wolfe, Carl E.; Maltman, Kim
- Physical Review D, Vol. 83, Issue 7

##
Electron and muon from vacuum polarization insertions

journal, January 1975

- Barbieri, R.; Remiddi, E.
- Nuclear Physics B, Vol. 90

##
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

##
Hadronic vacuum polarization in QCD and its evaluation in Euclidean spacetime

journal, July 2017

- de Rafael, Eduardo
- Physical Review D, Vol. 96, Issue 1

##
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

- Jegerlehner, Fred; Szafron, Robert
- The European Physical Journal C, Vol. 71, Issue 5

##
Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD

journal, April 2016

- Chakraborty, Bipasha; Davies, C. T. H.; Koponen, J.
- Physical Review D, Vol. 93, Issue 7

Works referencing / citing this record:

##
Electromagnetic finite-size effects to the hadronic vacuum polarization

journal, July 2019

- Bijnens, J.; Harrison, J.; Hermansson-Truedsson, N.
- Physical Review D, Vol. 100, Issue 1

##
Light-quark contribution to the leading hadronic vacuum polarization term of the muon $g-2$ from twisted-mass fermions

journal, December 2018

- Giusti, D.; Sanfilippo, F.; Simula, S.
- Physical Review D, Vol. 98, Issue 11