Pion form factors from two-flavor lattice QCD with exact chiral symmetry

Abstract

We calculate pion vector and scalar form factors in two-flavor lattice QCD and study the chiral behavior of the vector and scalar radii $⟨{r}^{2}{⟩}_{V,S}$. Numerical simulations are carried out on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at a lattice spacing of 0.12 fm with quark masses down to $\ensuremath{\sim}{m}_{s}/6$, where ${m}_{s}$ is the physical strange quark mass. Chiral symmetry, which is essential for a direct comparison with chiral perturbation theory (ChPT), is exactly preserved in our calculation at finite lattice spacing by employing the overlap quark action. We utilize the so-called all-to-all quark propagator in order to calculate the scalar form factor including the contributions of disconnected diagrams and to improve statistical accuracy of the form factors. A detailed comparison with ChPT reveals that the next-to-next-to-leading-order contributions to the radii are essential to describe their chiral behavior in the region of quark mass from ${m}_{s}/6$ to ${m}_{s}/2$. Chiral extrapolation based on two-loop ChPT yields $⟨{r}^{2}{⟩}_{V}=0.409(23)(37)\text{ }\text{ }{\mathrm{fm}}^{2}$ and $⟨{r}^{2}{⟩}_{S}=0.617(79)(66)\text{ }\text{ }{\mathrm{fm}}^{2}$, which are consistent with phenomenological analysis. We also present our estimates of relevant low-energy constants.