$\sigma$ exchange in the one-boson exchange model involving the ground state octet baryons

Abstract

Based on the one-boson-exchange framework that the $\sigma$ meson serves as an effective parameterization for the correlated scalar-isoscalar $\pi\pi$ interaction, we calculate the coupling constants of the $\sigma$ to the $\frac{1}{2}^+$ ground state light baryon octet ${\mathbb B}$ by matching the amplitude of ${\mathbb B}\bar{{\mathbb B}}\to\pi\pi\to\bar{{\mathbb B}}{\mathbb B}$ to that of ${\mathbb B}\bar{{\mathbb B}}\to\sigma\to\bar{{\mathbb B}}{\mathbb B}$. The former is calculated using a dispersion relation, supplemented with chiral perturbation theory results for the ${\mathbb B}{\mathbb B}\pi\pi$ couplings and the Muskhelishvili-Omn\` es representation for the $\pi\pi$ rescattering. Explicitly, the coupling constants are obtained as $g_{NN\sigma}=8.7_{-1.9}^{+1.7}$, $g_{\Sigma\Sigma\sigma}=3.5_{-1.3}^{+1.8}$, $g_{\Xi\Xi\sigma}=2.5_{-1.4}^{+1.5}$, and $g_{\Lambda\Lambda\sigma}=6.8_{-1.7}^{+1.5}$. These coupling constants can be used in the one-boson-exchange model calculations of the interaction of light baryons with other hadrons.