Improved bounds on the radius and curvature of the K pi scalar form factor and implications to low-energy theorems

TL;DR

This paper derives tighter bounds on the scalar radius and curvature of the K pi scalar form factor using analyticity, dispersion relations, and known low-energy theorems, with implications for theoretical corrections.

Contribution

It provides improved bounds on the scalar radius and curvature of the K pi form factor, incorporating higher loop corrections and known low-energy theorems.

Findings

Bounds on scalar radius: 0.12 to 0.21 fm^2

Bounds on curvature: 0.56 to 1.47 GeV^{-4}

Correlation between radius and curvature

Abstract

We obtain stringent bounds in the < r^2 >_S^{K pi}-c plane where these are the scalar radius and the curvature parameters of the scalar pi K form factor respectively using analyticity and dispersion relation constraints, the knowledge of the form factor from the well-known Callan-Treiman point m_K^2-m_pi^2, as well as at m_pi^2-m_K^2 which we call the second Callan-Treiman point. The central values of these parameters from a recent determination are accomodated in the allowed region provided the higher loop corrections to the value of the form factor at the second Callan-Treiman point reduce the one-loop result by about 3% with F_K/F_pi=1.21. Such a variation in magnitude at the second Callan-Treiman point yields 0.12 fm^2 \lesssim < r^2>_S^{K pi} \lesssim 0.21 fm^2 and 0.56 GeV^{-4} \lesssim c \lesssim 1.47 GeV^{-4} and a strong correlation between them. A smaller value of F_K/F_pi shifts both bounds to lower values.