# Lattice QCD calculation of the pion charge radius using a model-independent method

## Abstract

We use a method to calculate the hadron’s charge radius without model-dependent momentum extrapolations. The method does not require the additional quark propagator inversions on the twisted boundary conditions or the computation of the momentum derivatives of quark propagators and thus is easy to implement. We apply this method to the calculation of pion charge radius $$\langle r^2_π\rangle$$. For comparison, we also determine $$\langle r^2_π\rangle$$ with the traditional approach of computing the slope of the form factors. The new method produces results consistent with those from the traditional method and with statistical errors 1.5–1.9 times smaller. For the four gauge ensembles at the physical pion masses, the statistical errors of $$\langle r^2_π\rangle$$ range from 2.1% to 4.6% by using ≲ 50 configurations. For the ensemble at $$m_π ≈$$ 340 MeV, the statistical uncertainty is even reduced to a subpercent level.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Connecticut, Storrs, CT (United States); Argonne National Lab. (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility (ALCF)

- Sponsoring Org.:
- USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC)

- OSTI Identifier:
- 1606289

- Alternate Identifier(s):
- OSTI ID: 1802089

- Grant/Contract Number:
- SC0010339; AC02-06CH11357; 11775002

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

### Citation Formats

```
Feng, Xu, Fu, Yang, and Jin, Lu-Chang. Lattice QCD calculation of the pion charge radius using a model-independent method. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.051502.
```

```
Feng, Xu, Fu, Yang, & Jin, Lu-Chang. Lattice QCD calculation of the pion charge radius using a model-independent method. United States. https://doi.org/10.1103/PhysRevD.101.051502
```

```
Feng, Xu, Fu, Yang, and Jin, Lu-Chang. Wed .
"Lattice QCD calculation of the pion charge radius using a model-independent method". United States. https://doi.org/10.1103/PhysRevD.101.051502.
```

```
@article{osti_1606289,
```

title = {Lattice QCD calculation of the pion charge radius using a model-independent method},

author = {Feng, Xu and Fu, Yang and Jin, Lu-Chang},

abstractNote = {We use a method to calculate the hadron’s charge radius without model-dependent momentum extrapolations. The method does not require the additional quark propagator inversions on the twisted boundary conditions or the computation of the momentum derivatives of quark propagators and thus is easy to implement. We apply this method to the calculation of pion charge radius $\langle r^2_π\rangle$. For comparison, we also determine $\langle r^2_π\rangle$ with the traditional approach of computing the slope of the form factors. The new method produces results consistent with those from the traditional method and with statistical errors 1.5–1.9 times smaller. For the four gauge ensembles at the physical pion masses, the statistical errors of $\langle r^2_π\rangle$ range from 2.1% to 4.6% by using ≲ 50 configurations. For the ensemble at $m_π ≈$ 340 MeV, the statistical uncertainty is even reduced to a subpercent level.},

doi = {10.1103/PhysRevD.101.051502},

journal = {Physical Review D},

number = 5,

volume = 101,

place = {United States},

year = {2020},

month = {3}

}

https://doi.org/10.1103/PhysRevD.101.051502

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