The pion vector form factor from lattice QCD and NNLO chiral perturbation theory

The pion vector form factor from lattice QCD and NNLO chiral perturbation theory

We present a comprehensive study of the electromagnetic form factor, the decay constant and the mass of the pion computed in lattice QCD with two degenerate O(*a*)-improved Wilson quarks at three different lattice spacings in the range 0.05-0.08fm and pion masses between 280 and 630MeV at *m*_{π} *L* ≥ 4. Using partially twisted boundary conditions and stochastic estimators, we obtain a dense set of precise data points for the form factor at very small momentum transfers, allowing for a model-independent extraction of the charge radius. Chiral Perturbation Theory (ChPT) augmented by terms which model lattice artefacts is then compared to the data. At next-to-leading order the effective theory fails to produce a consistent description of the full set of pion observables but describes the data well when only the decay constant and mass are considered. By contrast, using the next-to-next-to-leading order expressions to perform global fits result in a consistent description of all data. We obtain ⟨r^{2}_{π}⟩ = 0.481(33)(13)fm^{2} as our final result for the charge radius at the physical point. Our calculation also yields estimates for the pion decay constant in the chiral limit, *F*_{π}/*F* = 1.080(16)(6), the quark condensate, Σ^{1/3}_{MSbar }(2GeV) = 261(13)(1)MeV and several low-energy constants of SU(2) ChPT.

lattice qcd, nonperturbative effects, chiral lagrangians

1-37

Brandt, Bastian B.

519354d6-09ed-4ef9-8b3e-2cfc9f7761fb

Juttner, Andreas

a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247

Wittig, Hartmut

c782e4fa-6398-4cca-96e7-7651ff8cbe69

5 November 2013

Brandt, Bastian B.

519354d6-09ed-4ef9-8b3e-2cfc9f7761fb

Juttner, Andreas

a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247

Wittig, Hartmut

c782e4fa-6398-4cca-96e7-7651ff8cbe69

Brandt, Bastian B., Juttner, Andreas and Wittig, Hartmut
(2013)
The pion vector form factor from lattice QCD and NNLO chiral perturbation theory.
*Journal of High Energy Physics*, 11 (34), .
(doi:10.1007/JHEP11(2013)034).

## Abstract

We present a comprehensive study of the electromagnetic form factor, the decay constant and the mass of the pion computed in lattice QCD with two degenerate O(*a*)-improved Wilson quarks at three different lattice spacings in the range 0.05-0.08fm and pion masses between 280 and 630MeV at *m*_{π} *L* ≥ 4. Using partially twisted boundary conditions and stochastic estimators, we obtain a dense set of precise data points for the form factor at very small momentum transfers, allowing for a model-independent extraction of the charge radius. Chiral Perturbation Theory (ChPT) augmented by terms which model lattice artefacts is then compared to the data. At next-to-leading order the effective theory fails to produce a consistent description of the full set of pion observables but describes the data well when only the decay constant and mass are considered. By contrast, using the next-to-next-to-leading order expressions to perform global fits result in a consistent description of all data. We obtain ⟨r^{2}_{π}⟩ = 0.481(33)(13)fm^{2} as our final result for the charge radius at the physical point. Our calculation also yields estimates for the pion decay constant in the chiral limit, *F*_{π}/*F* = 1.080(16)(6), the quark condensate, Σ^{1/3}_{MSbar }(2GeV) = 261(13)(1)MeV and several low-energy constants of SU(2) ChPT.

Text

** 1306.2916.pdf
- Author's Original**
Text

** art%3A10.1007%2FJHEP11%282013%29034.pdf
- Version of Record**
## More information

Accepted/In Press date: 16 October 2013

Published date: 5 November 2013

Keywords:
lattice qcd, nonperturbative effects, chiral lagrangians

Organisations:
Theoretical Partical Physics Group

## Identifiers

Local EPrints ID: 393639

URI: http://eprints.soton.ac.uk/id/eprint/393639

PURE UUID: 5677776a-c381-423f-a505-4720aeaa50a8

## Catalogue record

Date deposited: 03 May 2016 08:07

Last modified: 11 Mar 2021 02:40

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## Contributors

Author:
Bastian B. Brandt

Author:
Hartmut Wittig

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