Coupling constants of the $\sigma$ meson to the ground state octet baryons

Author:

Bing Wu, Xiong-Hui Cao, Xiang-Kun Dong, Feng-Kun Guo

Keyword:

High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph)

journal:

date:

2023-12-02 00:00:00

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 $g_{NN\sigma}=8.7_{-1.1-1.3}^{+1.3+1.1}$, $g_{\Sigma\Sigma\sigma}=3.6_{-1.1-0.4}^{+1.8+0.4}$, $g_{\Xi\Xi\sigma}=2.5_{-1.3-0.6}^{+1.4+0.5}$, and $g_{\Lambda\Lambda\sigma}=6.8_{-1.0-1.4}^{+1.0+1.1}$. These coupling constants can be used in the one-boson-exchange model calculations of the interaction of light baryons with other hadrons.

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