Feasibility study of the $K^{+}d\to K^{0}pp$ reaction for the "${\Theta }^{+}$" pentaquark

Abstract

We investigate theoretically the $K^{0}p$ invariant mass spectrum of the $K^{+}d\to K^{0}pp$ reaction and scrutinize how the signal of the "${\Theta }^{+}$" pentaquark, if it exists, emerges in the $K^{0}p$ spectrum. The most prominent advantage of this reaction is that we can clearly judge whether the "${\Theta }^{+}$" exists or not as a direct-formation production without significant backgrounds, in contrast to other reactions such as photoproduction and $\pi$-induced productions. We show that while the impulse or single-step scattering process can cover the "${\Theta }^{+}$" energy region with an initial kaon momentum $k_{\mathrm{lab}}\approx 0.40\mathrm{GeV}/c$ in the laboratory frame, the contributions from double-step processes may have a potential possibility to reach the "${\Theta }^{+}$" energy region with a higher kaon momentum $k_{\mathrm{lab}}\sim 1\mathrm{GeV}/c$. Assuming that the full decay width of the "${\Theta }^{+}$" is around $0.5\mathrm{MeV}$, we predict that the magnitude of the peak corresponding to the "${\Theta }^{+}$" is around a few hundred $\mu \mathrm{b}$ to $1\mathrm{mb}$ with the momentum of the kaon beam $k_{\mathrm{lab}}\approx 0.40\mathrm{GeV}/c$ while it is around $\lesssim 1\mu \mathrm{b}$ with $k_{\mathrm{lab}}\approx 0.85\mathrm{GeV}/c$. Thus, the "${\Theta }^{+}$" peak is more likely to be seen at $k_{\mathrm{lab}}\approx 0.40\mathrm{GeV}/c$ than at $k_{\mathrm{lab}}\approx 0.85\mathrm{GeV}/c$.

Comments: 14 pages. 11 figures. Three more figures are included and the text was revised