$\sigma$ 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-Omnès 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.

Comments: 26 pages, 9 figures