QCD Correlation Functions and the Shape of $K_{\ell 3}$ Form Factors

TL;DR

This paper uses analyticity and unitarity constraints, along with perturbative QCD calculations, to derive bounds on the shape of $K_{ ext{l}3}$ form factors, enhancing understanding of their structure.

Contribution

It compares two types of invariant amplitudes and dispersion relations, showing they produce similar bounds on $K_{ ext{l}3}$ form factor shapes.

Findings

Similar results for vector and scalar form factors from different amplitudes

Bounds consistent with experimental data

Method improves theoretical understanding of form factor shapes

Abstract

Bounds on the expansion coefficients of the strangeness changing $K\pi$ form factors were derived recently from analyticity and unitarity, using as input suitable correlation functions calculated by perturbative QCD in the Euclidian region. We investigate two types of invariant amplitudes and their corresponding dispersion relations, and show that they lead to similar results for the shape of the vector and scalar $K_{\ell 3}$ form factors.