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

## Abstract

The quark-line disconnected diagram is a potentially important ingredient in lattice QCD calculations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. It is also a notoriously difficult one to evaluate. Here, for the first time, we give an estimate of this contribution based on lattice QCD results that have a statistically significant signal, albeit at one value of the lattice spacing and an unphysically heavy value of the u/d quark mass. We use HPQCD’s method of determining the anomalous magnetic moment by reconstructing the Adler function from time moments of the current-current correlator at zero spatial momentum. Our results lead to a total (including u, d and s quarks) quark-line disconnected contribution to a _{μ} of –0.15% of the u/d hadronic vacuum polarization contribution with an uncertainty which is 1% of that contribution.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1250189

- Alternate Identifier(s):
- OSTI ID: 1565502

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 93 Journal Issue: 7; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics

### Citation Formats

```
Chakraborty, Bipasha, Davies, C. T. H., Koponen, J., Lepage, G. P., Peardon, M. J., and Ryan, S. M.
```*Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevD.93.074509.

```
Chakraborty, Bipasha, Davies, C. T. H., Koponen, J., Lepage, G. P., Peardon, M. J., & Ryan, S. M.
```*Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD*. United States. doi:10.1103/PhysRevD.93.074509.

```
Chakraborty, Bipasha, Davies, C. T. H., Koponen, J., Lepage, G. P., Peardon, M. J., and Ryan, S. M. Fri .
"Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD". United States. doi:10.1103/PhysRevD.93.074509.
```

```
@article{osti_1250189,
```

title = {Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD},

author = {Chakraborty, Bipasha and Davies, C. T. H. and Koponen, J. and Lepage, G. P. and Peardon, M. J. and Ryan, S. M.},

abstractNote = {The quark-line disconnected diagram is a potentially important ingredient in lattice QCD calculations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. It is also a notoriously difficult one to evaluate. Here, for the first time, we give an estimate of this contribution based on lattice QCD results that have a statistically significant signal, albeit at one value of the lattice spacing and an unphysically heavy value of the u/d quark mass. We use HPQCD’s method of determining the anomalous magnetic moment by reconstructing the Adler function from time moments of the current-current correlator at zero spatial momentum. Our results lead to a total (including u, d and s quarks) quark-line disconnected contribution to aμ of –0.15% of the u/d hadronic vacuum polarization contribution with an uncertainty which is 1% of that contribution.},

doi = {10.1103/PhysRevD.93.074509},

journal = {Physical Review D},

issn = {2470-0010},

number = 7,

volume = 93,

place = {United States},

year = {2016},

month = {4}

}

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
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

##
Complete Tenth-Order QED Contribution to the Muon $g\mathbf{-}2$

journal, September 2012

- Aoyama, Tatsumi; Hayakawa, Masashi; Kinoshita, Toichiro
- Physical Review Letters, Vol. 109, Issue 11

##
( *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

##
Reevaluation of the hadronic contributions to the muon g−2 and to $\alpha (M^{2}_{Z})$

journal, January 2011

- Davier, M.; Hoecker, A.; Malaescu, B.
- The European Physical Journal C, Vol. 71, Issue 1

##
Muon $$g-2$$ g - 2 estimates: can one trust effective Lagrangians and global fits?

journal, December 2015

- Benayoun, M.; David, P.; DelBuono, L.
- The European Physical Journal C, Vol. 75, Issue 12

##
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

##
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

##
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

##
Novel quark-field creation operator construction for hadronic physics in lattice QCD

journal, September 2009

- Peardon, Michael; Bulava, John; Foley, Justin
- Physical Review D, Vol. 80, Issue 5

##
Toward the excited isoscalar meson spectrum from lattice QCD

journal, November 2013

- Dudek, Jozef J.; Edwards, Robert G.; Guo, Peng
- Physical Review D, Vol. 88, Issue 9

##
Recent developments in the comparison between theory and experiments in quantum electrodynamics

journal, May 1972

- Lautrup, B. E.; Peterman, A.; de Rafael, E.
- Physics Reports, Vol. 3, Issue 4

##
High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD

journal, September 2008

- Allison, I.; Dalgic, E.; Davies, C. T. H.
- Physical Review D, Vol. 78, Issue 5

##
High-precision $c$ and $b$ masses, and QCD coupling from current-current correlators in lattice and continuum QCD

journal, August 2010

- McNeile, C.; Davies, C. T. H.; Follana, E.
- Physical Review D, Vol. 82, Issue 3

##
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

##
Heavy quark masses from sum rules in four-loop approximation

journal, August 2007

- Kühn, Johann H.; Steinhauser, Matthias; Sturm, Christian
- Nuclear Physics B, Vol. 778, Issue 1-2

##
Review of Particle Physics

journal, July 2012

- Beringer, J.; Arguin, J. -F.; Barnett, R. M.
- Physical Review D, Vol. 86, 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

##
Quark disconnected diagrams in chiral perturbation theory

journal, November 2010

- Della Morte, Michele; Jüttner, Andreas
- Journal of High Energy Physics, Vol. 2010, Issue 11

##
First results from $2+1$ dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass

journal, February 2009

- Lin, Huey-Wen; Cohen, Saul D.; Dudek, Jozef
- Physical Review D, Vol. 79, Issue 3

##
Constrained curve fitting

journal, March 2002

- Lepage, G. P.; Clark, B.; Davies, C. T. H.
- Nuclear Physics B - Proceedings Supplements, Vol. 106-107

##
Energy dependence of the $\rho $ resonance in $\pi \pi $ elastic scattering from lattice QCD

journal, February 2013

- Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.
- Physical Review D, Vol. 87, Issue 3

##
Erratum: Energy dependence of the $\rho $ resonance in $\pi \pi $ elastic scattering from lattice QCD [Phys. Rev. D **87** , 034505 (2013)]

journal, November 2014

- Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.
- Physical Review D, Vol. 90, Issue 9

##
${V}_{us}$ from $\pi $ and $K$ decay constants in full lattice QCD with physical $u$ , $d$ , $s$ , and $c$ quarks

journal, October 2013

- Dowdall, R. J.; Davies, C. T. H.; Lepage, G. P.
- Physical Review D, Vol. 88, Issue 7

##
The Chroma Software System for Lattice QCD

journal, March 2005

- Edwards, Robert G.; Joó, Bálint
- Nuclear Physics B - Proceedings Supplements, Vol. 140

##
Solving lattice QCD systems of equations using mixed precision solvers on GPUs

journal, September 2010

- Clark, M. A.; Babich, R.; Barros, K.
- Computer Physics Communications, Vol. 181, Issue 9

Works referencing / citing this record:

##
Lattice Calculations and the Muon Anomalous Magnetic Moment

journal, May 2017

- Marinković, Marina Krstić
- Few-Body Systems, Vol. 58, Issue 4