# SU(2) Low-Energy Constants from Mixed-Action Lattice QCD

## Abstract

An analysis of the pion mass and pion decay constant is performed using mixed-action Lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n_f = 2+1 MILC configurations. Calculations were performed at two lattice spacings of b~0.125 fm and b~0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1 <= m_l / m_s <= 0.6, while pion masses are in the range 235 < m_\pi < 680 MeV. A two-flavor chiral perturbation theory analysis of the Lattice QCD calculations constrains the Gasser-Leutwyler coefficients bar{l}_3 and bar{l}_4 to be bar{l}_3 = 4.04(40)(+73-55) and bar{l}_4 = 4.30(51)(+84-60). All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give f_\pi / f =more »

- Authors:

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

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

- OSTI Identifier:
- 1054907

- Report Number(s):
- JLAB-THY-11-1380; DOE/OR/23177-1644; arXiv:1108.1380

- DOE Contract Number:
- AC05-06OR23177

- Resource Type:
- Journal Article

- Journal Name:
- Phys Rev D

- Additional Journal Information:
- Journal Volume: 86; Journal Issue: 09

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Silas Beane, William Detmold, Parikshit Junnarkar, T.C. Luu, Konstantinos Orginos, Assumpta Parreno, Martin Savage, Aaron Torok, Andre Walker-Loud.
```*SU(2) Low-Energy Constants from Mixed-Action Lattice QCD*. United States: N. p., 2012.
Web. doi:10.1103/PhysRevD.86.094509.

```
Silas Beane, William Detmold, Parikshit Junnarkar, T.C. Luu, Konstantinos Orginos, Assumpta Parreno, Martin Savage, Aaron Torok, Andre Walker-Loud.
```*SU(2) Low-Energy Constants from Mixed-Action Lattice QCD*. United States. doi:10.1103/PhysRevD.86.094509.

```
Silas Beane, William Detmold, Parikshit Junnarkar, T.C. Luu, Konstantinos Orginos, Assumpta Parreno, Martin Savage, Aaron Torok, Andre Walker-Loud. Thu .
"SU(2) Low-Energy Constants from Mixed-Action Lattice QCD". United States. doi:10.1103/PhysRevD.86.094509.
```

```
@article{osti_1054907,
```

title = {SU(2) Low-Energy Constants from Mixed-Action Lattice QCD},

author = {Silas Beane, William Detmold, Parikshit Junnarkar, T.C. Luu, Konstantinos Orginos, Assumpta Parreno, Martin Savage, Aaron Torok, Andre Walker-Loud},

abstractNote = {An analysis of the pion mass and pion decay constant is performed using mixed-action Lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n_f = 2+1 MILC configurations. Calculations were performed at two lattice spacings of b~0.125 fm and b~0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1 <= m_l / m_s <= 0.6, while pion masses are in the range 235 < m_\pi < 680 MeV. A two-flavor chiral perturbation theory analysis of the Lattice QCD calculations constrains the Gasser-Leutwyler coefficients bar{l}_3 and bar{l}_4 to be bar{l}_3 = 4.04(40)(+73-55) and bar{l}_4 = 4.30(51)(+84-60). All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give f_\pi / f = 1.062(26)(+42-40) where f is the decay constant in the chiral limit. The most recent scale setting by the MILC Collaboration yields a postdiction of f_\pi = 128.2(3.6)(+4.4-6.0)(+1.2-3.3) MeV at the physical pion mass.},

doi = {10.1103/PhysRevD.86.094509},

journal = {Phys Rev D},

number = 09,

volume = 86,

place = {United States},

year = {2012},

month = {11}

}