Pole position of the $a_1(1260)$ resonance in a three-body unitary framework

TL;DR

This paper analyzes the analytic structure of three-body scattering amplitudes to accurately determine the pole position of the $a_1(1260)$ resonance, providing a precise characterization of its properties.

Contribution

It introduces a method to study the analytic structure of three-body scattering amplitudes and applies it to extract the $a_1(1260)$ pole position from experimental data.

Findings

Determined the $a_1(1260)$ pole position as $ ext{Re}( oot s_0) ext{ and } ext{Im}( oot s_0)$ with uncertainties.

Provided insights into the analytic structure of three-body scattering amplitudes.

Enhanced understanding of resonance properties in the complex energy plane.

Abstract

Masses, widths, and branching ratios of hadronic resonances are quantified by their pole positions and residues with respect to transition amplitudes on the Riemann sheets of the complex energy-plane. In this study we discuss the analytic structure in the physical energy region of three-body scattering amplitudes on such manifolds. As an application, we determine the pole position of the $a_1(1260)$ meson from the ALEPH experiment by allowing for $\pi\rho$ coupled channels in S- and D-wave. We find it to be $\sqrt{s_0}=(1232^{+15+9}_{-0-11}-i266^{+0+15}_{-22-27})~\text{MeV}$.