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

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-Omnès 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.

arXiv comment16 pages, 10 figures

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• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints
• Baryon Form Factors