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

TL;DR

This study combines lattice QCD simulations and NNLO chiral perturbation theory to accurately determine the pion's electromagnetic form factor, charge radius, decay constant, and related low-energy constants.

Contribution

It provides a comprehensive analysis of pion properties using lattice QCD data and NNLO ChPT, highlighting the importance of higher-order terms for consistent descriptions.

Findings

Final pion charge radius: 0.481(33)(13) fm^2

Pion decay constant ratio: 1.080(16)(6)

Estimates of quark condensate and low-energy constants

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_pi 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_pi>=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_pi/F=1.080(16)(6), the quark condensate, Sigma^{1/3}_MSbar(2GeV)=261(13)(1)MeV and several low-energy constants of SU(2) ChPT.