Nonstrange and other flavor partners of the exotic ${\Theta }^{+}$ baryon

Given presently known empirical information about the exotic ${\Theta }^{+}$ baryon, we analyze possible properties of its $\text{SU}{\left(3\right)}_F$ partners, paying special attention to the nonstrange member of the antidecuplet $N^{*}$. The modified partial wave analysis presents two candidate masses, $1680\text{MeV}$ and $1730\text{MeV}$. In both cases the $N^{*}$ should be highly inelastic. The theoretical analysis, based on the soliton picture and assumption of ${\Gamma }_{{\Theta }^{+}}<5\text{MeV}$, shows that most probably ${\Gamma }_{N^{*}}<30\text{MeV}$. Similar analysis for ${\Xi }_{3∕2}$ predicts its width to be not more than about $10\text{MeV}$. Our results suggest several directions for experimental studies that may clarify properties of the antidecuplet baryons, and structure of their mixing with other baryons.

Figure 1

Tentative unitary antidecuplet with ${\Theta }^{+}$. Isotopic multi-plet (constant values of the charge) shown by solid (dashed) lines.

Figure 2

Change of overall ${\chi }^2$ due to insertion of a resonance into $P_{11}$ for $M_R=1660-1760\text{MeV}$ with ${\Gamma }_{tot}=0.1$, 0.3, 0.5, 0.7, and $0.9\text{MeV}$ (top panel) and 1, 3, 5, 7, and $9\text{MeV}$ (bottom panel), and ${\Gamma }_{el}∕{\Gamma }_{tot}=0.1$ (left column), 0.2 (middle column), and 0.4 (right column) using $\pi N$ PWA 25. The curves are given to guide the eye. Vertical arrows indicate $M_R=1680$ and $1730\text{MeV}$.

Figure 3

Change of overall ${\chi }^2$ due to insertion of resonances into $S_{11}$ (top panel) and $P_{13}$ (bottom panel) for $M_R=1660–1760\text{MeV}$ with ${\Gamma }_{tot}=0.1$, 0.3, 0.5, 0.7, and $0.9\text{MeV}$ and ${\Gamma }_{el}∕{\Gamma }_{tot}=0.1$ (left column) and 0.2 (right column). Notation as in Fig. 2.