Implications of the present bound on the width of the ${\Theta }^{+}(1540)$

The recently reported ${\Theta }^{+}(1540)$ exotic baryon seems to be very narrow: $\Gamma (\Theta )<1\mathrm{M}\mathrm{e}\mathrm{V}$ according to some analyses. Using methods of low energy scattering theory, we develop expectations for the width of the $\Theta$, an elastic resonance in $KN$ scattering in a theory where the characteristic range of interactions is $\sim 1\mathrm{F}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{i}$. If the $\Theta$ is a potential scattering resonance, generated by the forces in the $KN$ channel, its width is hard to account for unless the $KN$-channel orbital angular momentum is two or greater. If the $\Theta$ is generated by dynamics in a confined channel, its coupling to the scattering channel is at least an order of magnitude less than the coupling of the $\Lambda (1520)$ unless $\ell \ge 2$. Either way, if the $\Theta$ proves to be in the $KN$ $s$- or $p$-wave, new physics must be responsible for its narrow width.

Figure 1

The width of the $\Theta$ in MeV as a function of the range of the attractive potential in Fermis with the mass of the $\Theta$ held fixed at 1540 MeV, for a square well, with (a) $\ell =1$; (b) $\ell =2$; and (c) $\ell =3$; and for a Yukawa potential and $\ell =1$, (d). Also shown is the depth of the potential (dashed line).

Figure 2

(a) The strength of the channel coupling potential responsible for the width of the $\Lambda (1520)$ in the Feshbach-Fano formalism [see Eq. (18)]. (b) Ratio of the channel coupling potential strengths for the $\Theta$ and $\Lambda (1520)$ for various assignments of the orbital angular momentum in the $\Theta$ channel.