Reciprocal Bootstrap Relationship of the Octet Baryon and the Decuplet Baryon

Abstract

The reciprocal bootstrap relationship of the octet of ${\left(\mathrm{½}\right)}^{+}$ baryons and the decuplet of ${\left(\frac{3}{2}\right)}^{+}$ baryons is studied making use of the static approximation. If we regard the octet baryon as a $B_8{\Pi }_8$ bound state due to octet and decuplet baryon exchange, we obtain ${\gamma }_{10}\approx 7d^2$ and $\frac{d}{f}\approx 2.2$, where ${\gamma }_{10}$ is the ${\overline{B}}_{10}{B}_8{\Pi }_8$ coupling constant and $d$ and $f$ are the $d$ and $f$ coupling constants of ${\overline{B}}_8{B}_8{\Pi }_8$ coupling. If octet vector meson exchange processes are included and if we assume the vector theory (gauge theory) of strong interactions, we obtain ${\gamma }_{10}<7\mathrm{}{d}^2$ and $\frac{d}{f}<2.2\mathrm{}$. If we regard the decuplet baryon as a $B_8{\Pi }_8$ bound state due to octet baryon exchange, we obtain ${\gamma }_{10}\approx 4d^2$ for the ratio $\frac{d}{f}=2.2\mathrm{}$.