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

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 ⟨r²_π⟩ = 0.481(33)(13)fm² 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.

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ORCID for Andreas Juttner: orcid.org/0000-0002-3978-0927

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