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

Abstract

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 αV = 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 αV. 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 αV as a free parameter.