  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.
