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

TL;DR

This study computes pion form factors using two-flavor lattice QCD with exact chiral symmetry, revealing the importance of higher-order chiral perturbation theory contributions for accurate chiral behavior description.

Contribution

It introduces a lattice QCD calculation employing overlap quarks and all-to-all propagators to accurately determine pion form factors and their chiral behavior, including disconnected diagrams.

Findings

Chiral extrapolation yields <r^2>_V=0.409(23)(37)fm and <r^2>_S=0.617(79)(66)fm.

Next-to-next-to-leading-order contributions are essential for describing radii.

Results are consistent with phenomenological analyses.

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 x 32 lattice at a lattice spacing of 0.12 fm with quark masses down to \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)fm and <r^2>_S=0.617(79)(66)fm, which are consistent with phenomenological analysis. We also present our estimates of relevant low-energy constants.