Pion form factors from lattice QCD with exact chiral symmetry

TL;DR

This paper uses lattice QCD with exact chiral symmetry to calculate pion form factors and radii, comparing results with chiral perturbation theory and highlighting the importance of two-loop contributions.

Contribution

It provides the first lattice QCD calculation of pion form factors with exact chiral symmetry and includes disconnected diagrams, improving the understanding of chiral behavior.

Findings

Two-loop ChPT is necessary to describe the radii at M_ er 290 MeV.

Calculated vector radius <r^2>_V = 0.409(23)(37) fm^2.

Calculated scalar radius <r^2>_S = 0.617(79)(66) fm^2.

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}. For a direct comparison with chiral perturbation theory (ChPT), chiral symmetry is exactly preserved by employing the overlap quark action. We utilize the all-to-all quark propagator in order to calculate the scalar form factor including the contributions of disconnected diagrams. A detailed comparison with ChPT reveals that two-loop contributions are important to describe the chiral behavior of the radii in our region of the pion mass M_\pi \gtrsim 290 MeV. From chiral extrapolation based on two-loop ChPT, we obtain <r^2>_V = 0.409(23)(37) fm^2 and <r^2>_S = 0.617(79)(66) fm^2, which are consistent with phenomenological analyses.