# Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

## Abstract

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g — 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1/L ^{2} where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. Here, we have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.

- Authors:

- Univ. of Connecticut, Storrs, CT (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
- Columbia Univ., New York, NY (United States)
- Nagoya Univ., Nagoya (Japan)
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1408711

- Alternate Identifier(s):
- OSTI ID: 1375827

- Report Number(s):
- BNL-114451-2017-JA

Journal ID: ISSN 2470-0010; PRVDAQ; KA2041012; TRN: US1703307

- Grant/Contract Number:
- SC0012704; AC02-06CH11357; FG02-92ER40716; SC0011941

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 96; 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; g-2; muon; quark; lattice; QCD; magnetic; hadronic

### Citation Formats

```
Blum, Thomas, Christ, Norman, Hayakawa, Masashi, Izubuchi, Taku, Jin, Luchang, Jung, Chulwoo, and Lehner, Christoph.
```*Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.034515.

```
Blum, Thomas, Christ, Norman, Hayakawa, Masashi, Izubuchi, Taku, Jin, Luchang, Jung, Chulwoo, & Lehner, Christoph.
```*Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment*. United States. doi:10.1103/PhysRevD.96.034515.

```
Blum, Thomas, Christ, Norman, Hayakawa, Masashi, Izubuchi, Taku, Jin, Luchang, Jung, Chulwoo, and Lehner, Christoph. Tue .
"Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment". United States.
doi:10.1103/PhysRevD.96.034515. https://www.osti.gov/servlets/purl/1408711.
```

```
@article{osti_1408711,
```

title = {Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment},

author = {Blum, Thomas and Christ, Norman and Hayakawa, Masashi and Izubuchi, Taku and Jin, Luchang and Jung, Chulwoo and Lehner, Christoph},

abstractNote = {In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g — 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1/L2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. Here, we have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.},

doi = {10.1103/PhysRevD.96.034515},

journal = {Physical Review D},

number = 3,

volume = 96,

place = {United States},

year = {Tue Aug 22 00:00:00 EDT 2017},

month = {Tue Aug 22 00:00:00 EDT 2017}

}

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