# A study on the correlation between poles and cuts in $\pi\pi$ scattering

## TL;DR

This paper introduces a dispersive approach to analyze elastic $\u03c0$ scattering, accurately describing experimental data, identifying resonance poles, and exploring the influence of scattering cuts on pole positions.

## Contribution

A novel dispersive method that maintains unitarity and effectively relates pole positions to scattering cuts in $\u03c0$ scattering analysis.

## Key findings

- Successfully describes experimental $\u03c0$ scattering data
- Identifies pole locations of key resonances
- Shows poles are more sensitive to the right hand cut

## Abstract

In this paper we propose a dispersive method to describe two-body scattering with unitarity imposed. This approach is applied to elastic $\pi\pi$ scattering. The amplitudes keep single-channel unitarity and describe the experimental data well, and the low-energy amplitudes are consistent with that of chiral perturbation theory. The pole locations of the $\sigma$, $f_0(980)$, $\rho(770)$ and $f_2(1270)$ and their couplings to $\pi\pi$ are obtained. A virtual state appearing in the isospin-two S-wave is confirmed. The correlations between the left (and right) hand cut and the poles are discussed. Our results show that the poles are more sensitive to the right hand cut rather than the left hand cut. The proposed method could be used to study other two-body scattering processes.