# 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. doi: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. doi: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}

}

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

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