Precise determination of the sigma pole location from a dispersive analysis

TL;DR

This paper uses recent experimental data and advanced dispersive analysis methods to precisely determine the sigma resonance pole position, improving accuracy with modified Roy-like equations and providing simple approximations for practical use.

Contribution

It introduces a refined dispersive analysis approach with modified Roy-like equations to enhance the precision of sigma resonance determination from experimental data.

Findings

Precise sigma pole position determined using dispersive methods.

Modified Roy-like equations improve accuracy around the sigma region.

Simple conformal expansion effectively approximates the results.

Abstract

We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy's equations allow us to determine the sigma resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that show a remarkable improvement in the precision around the sigma resonance region. For practical applications, these results are shown to be very well approximated by a very simple conformal expansion.