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 alpha V = F/(F + D) not equal 1, there is an additional interaction: the exchange of a rho meson between a Lambda and a sigma 0 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 alpha 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 alpha V as a free parameter.