The electromagnetic Sigma-to-Lambda transition form factors with coupled-channel effects in the space-like region

TL;DR

This paper models Sigma-to-Lambda electromagnetic transition form factors in the space-like region using dispersion theory and coupled-channel effects, highlighting the impact of the KbarK channel and uncertainties in chiral perturbation theory.

Contribution

It introduces a coupled-channel approach incorporating KbarK effects into the Sigma-to-Lambda transition form factors using dispersion theory and chiral perturbation theory.

Findings

The electric form factor shifts significantly with KbarK inclusion.

The magnetic form factor is weakly affected by KbarK effects.

Uncertainties are quantified via bootstrap sampling.

Abstract

Using dispersion theory, the electromagnetic Sigma-to-Lambda transition form factors are expressed as the product of the pion electromagnetic form factor and the $\Sigma\bar{\Lambda}\to\pi\pi$ scattering amplitudes with the latter estimated from SU(3) chiral perturbation theory including the baryon decuplet as explicit degrees of freedom. The contribution of the $K\bar{K}$ channel is also taken into account and the $\pi\pi$-$K\bar{K}$ coupled-channel effect is included by means of a two-channel Muskhelishvili-Omn\`{e}s representation. It is found that the electric transition form factor shows a significant shift after the inclusion of the $K\bar{K}$ channel, while the magnetic transition form factor is only weakly affected. However, the $K\bar{K}$ effect on the electric form factor is obscured by the undetermined coupling $h_A$ in the three-flavor chiral Lagrangian. The error bands of the Sigma-to-Lambda transition form factors from the uncertainties of the couplings and low-energy constant in three-flavor chiral perturbation theory are estimated by a bootstrap sampling method.