Lattice calculation of pion form factors with overlap fermions

Abstract

We present a precise calculation of the pion form factor using overlap fermions on seven ensembles of ($2+1$)-flavor domain-wall configurations with pion masses varying from 139 to $340\text{ }\text{ }\mathrm{MeV}$. Taking advantage of the fast Fourier transform and other techniques to access many combinations of source and sink momenta, we find the pion mean square charge radius to be $⟨{r}_{\ensuremath{\pi}}^{2}⟩=0.430(5)(13)\text{ }\text{ }{\mathrm{fm}}^{2}$, which agrees well with the experimental result, and includes the systematic uncertainties from chiral extrapolation, lattice spacing and finite-volume dependence. We also find that $⟨{r}_{\ensuremath{\pi}}^{2}⟩$ depends on both the valence and sea quark masses strongly and predicts the pion form factor up to ${Q}^{2}=1.0\text{ }\text{ }{\mathrm{GeV}}^{2}$, which agrees with experiments very well.