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

Abstract

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 ${\alpha }_V=F/(F+D)\ne$ 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, once 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.

Comments: 16 pages, published version