Kaon semi-leptonic form factor at zero momentum transfer in finite volume

TL;DR

This paper uses Chiral Perturbation Theory to calculate the kaon semi-leptonic form factor in finite volume at various momentum transfers, providing a useful tool for lattice data extrapolation.

Contribution

It offers the first finite volume correction formulas for the kaon semi-leptonic form factor at arbitrary momentum transfer, validated against lattice data.

Findings

Finite volume effects are negligible at zero momentum transfer.

ChPT results align with lattice data within certain ranges.

The correction formulas assist in extrapolating lattice results to infinite volume.

Abstract

Using Chiral Perturbation Theory, we obtain the kaon semi-leptonic vector form factor in finite volume at a generic momentum transfer, $q^2$, up to one loop order. At first we confirm the lattice observation that the contribution of the heavy Pseudo-Goldstone boson in the finite volume corrections at zero momentum transfer is unimportant. We then evaluate the form factor at $q^2=0$ numerically and compare our results with the present lattice data. It turns out that our ChPT results are comparable with the lattice data to some extend. The formula for the finite volume corrections obtained for the form factor at momentum transfer $q^2$, provides a tool for lattice data in order to extrapolate at large lattice size.