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\nand study the chiral behavior of the vector and scalar radii <r^2>_{V,S}.\nNumerical simulations are carried out on a 16^3 x 32 lattice at a lattice\nspacing of 0.12 fm with quark masses down to \\sim m_s/6, where m_s is the\nphysical strange quark mass. Chiral symmetry, which is essential for a direct\ncomparison with chiral perturbation theory (ChPT), is exactly preserved in our\ncalculation at finite lattice spacing by employing the overlap quark action. We\nutilize the so-called all-to-all quark propagator in order to calculate the\nscalar form factor including the contributions of disconnected diagrams and to\nimprove statistical accuracy of the form factors. A detailed comparison with\nChPT reveals that the next-to-next-to-leading-order contributions to the radii\nare essential to describe their chiral behavior in the region of quark mass\nfrom m_s/6 to m_s/2. Chiral extrapolation based on two-loop ChPT yields\n<r^2>_V=0.409(23)(37)fm and <r^2>_S=0.617(79)(66)fm, which are consistent with\nphenomenological analysis. We also present our estimates of relevant low-energy\nconstants.\n