A closer look at the Yukawa interaction from a symmetry group perspective

I investigate the use of the SU(3) Clebsch-Gordan coefficients in light of the relations of completeness and closure. I show that in the case of α_V = F/(F + D) ≠ 1, there is an additional interaction: the exchange of a ρ meson between a Λ and a Σ⁰ hyperon that only affects the symmetric coupling. I then calculate these additional coupling constants and show that this recovers the completeness and closure of the SU(3) Clebsch-Gordan coefficients for all values of α_V. Besides, it increases the symmetry of the theory, now we can group the baryon octet into four doublets. Finally, I add the new coupling constants to study numerical results in the hyperon onset in dense nuclear matter assuming α_V as a free parameter.