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 <r2>V,S. Numerical simulations are carried out on a 163 x 32 lattice at a lattice spacing of 0.12 fm with quark masses down to ms/6, where ms 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 ms/6 to ms/2. Chiral extrapolation based on two-loop ChPT yields <r2>V=0.409(23)(37)fm and <r2>S=0.617(79)(66)fm, which are consistent with phenomenological analysis. We also present our estimates of relevant low-energy constants.