Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems

TL;DR

This paper derives tight constraints on the scalar K pi form factor at low energies by combining unitarity bounds, phase and modulus information, and low-energy theorems, leading to precise predictions of its parameters.

Contribution

It introduces an improved unitarity bounds method incorporating phase and modulus data, providing new constraints on the form factor's low-energy parameters.

Findings

Stringent bounds on slope and curvature of the form factor.

Narrow predicted range for higher order ChPT corrections.

Enhanced understanding of low-energy K pi interactions.

Abstract

We investigate the scalar K pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t=0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher order ChPT corrections at the second Callan-Treiman point.