Chiral and volume extrapolation of pion and kaon electromagnetic form factor within SU(3) ChPT

TL;DR

This paper computes finite volume corrections to pion and kaon electromagnetic form factors using SU(3) chiral perturbation theory, providing numerical estimates relevant for lattice QCD simulations.

Contribution

It introduces a new form of the hadronic matrix element suitable for finite volume calculations and compares finite volume effects for pion and kaon form factors.

Findings

Finite volume correction for pion form factor: 0.0041 at q^2 = -0.1358

Finite volume correction for kaon form factor: 0.0029 at q^2 = -0.1357

Finite volume effects depend on lattice size and meson mass.

Abstract

We calculate the pion and kaon electromagnetic form factors in finite volume for a generic momentum transfer in space-like region, using SU(3) chiral perturbation theory. To this end, we first find the hadronic matrix element in a new form which is suitable for our calculation in finite volume. We present our numerical findings for the chiral behavior and finite volume corrections and compare these for pion and kaon form factors. As a result, for the pion electromagnetic form factor we find the finite volume correction $\Delta F^{\pi}_{em} = 0.0041$ at momentum transfer $q^2 = -0.1358$ and for the kaon form factor $\Delta F^{K}_{em} = 0.0029$ at $q^2 = -0.1357$ with $m_{\pi} = 0.3128$ and $L = 2.6 fm$ as the linear size of the lattice.