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

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 16³×32 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) fm² and ⟨r²⟩S=0.617(79)(66) fm², which are consistent with phenomenological analysis. We also present our estimates of relevant low-energy constants.