Production of the pentaquark ${\Theta }^{+}$ in $np$ scattering

We study $np\to \Lambda {\Theta }^{+}$ and $np\to {\Sigma }^0{\Theta }^{+}$ processes for both of the positive and negative parities of the ${\Theta }^{+}$. Employing the effective chiral Lagrangians for the $KNY$ and $K^{*}NY$ interactions, we calculate differential cross sections as well as total cross sections for the $np\to {\Sigma }^0{\Theta }^{+}$ and $np\to \Lambda {\Theta }^{+}$ reactions. The total cross sections for the positive parity ${\Theta }^{+}$ turn out to be approximately 10 times larger than those for the negative parity ${\Theta }^{+}$ in the range of the c.m. energy $E_{\mathrm{c}.\mathrm{m}.}^{\mathrm{t}\mathrm{h}}\le E_{\mathrm{c}.\mathrm{m}.}\le 3.5\mathrm{G}\mathrm{e}\mathrm{V}$. The results are rather sensitive to the parameters of $K$ exchanges in the $t$ channel.

Figure 1

Born diagrams for the $np\to Y^0{\Theta }^{+}$ reaction.

Figure 2

The total cross sections of $np\to \Lambda {\Theta }_{+}^{+}$ with ten different combinations of the signs of the $K^{*}N\Theta$ coupling constants which are labeled by ($\mathrm{s}\mathrm{g}\mathrm{n}(g_{K^{*}N\Theta })$, $\mathrm{s}\mathrm{g}\mathrm{n}(g_{K^{*}N\Theta }^T)$). The parameter set of the Nijmegen potential with the cutoff parameter $\Lambda =1.0\mathrm{G}\mathrm{e}\mathrm{V}$ is employed.

Figure 3

The differential cross sections for the reaction $np\to \Lambda {\Theta }_{+}^{+}$ at $E_{\mathrm{c}.\mathrm{m}.}=2.7\mathrm{G}\mathrm{e}\mathrm{V}$ with five different combinations of the signs of the $K^{*}N\Theta$ coupling constants as labeled by ($\mathrm{s}\mathrm{g}\mathrm{n}(g_{K^{*}N\Theta })$, $\mathrm{s}\mathrm{g}\mathrm{n}(g_{K^{*}N\Theta }^T)$). The parameter set of the Nijmegen potential with the cutoff parameter $\Lambda =1.0\mathrm{G}\mathrm{e}\mathrm{V}$ is employed.

Figure 4

The total cross sections for the reaction $np\to {\Sigma }^0{\Theta }_{+}^{+}$. The parameter set of the Nijmegen potential with the cutoff parameter $\Lambda =1.0\mathrm{G}\mathrm{e}\mathrm{V}$ is employed. The notations are the same as in Fig. 3.

Figure 5

The total cross sections of $np\to \Lambda {\Theta }_{-}^{+}$ in the left panel (a) and $np\to {\Sigma }^0{\Theta }_{-}^{+}$ in the right panel (b). The parameter set of the Nijmegen potential with the cutoff parameter $\Lambda =1.0\mathrm{G}\mathrm{e}\mathrm{V}$ is employed. The notations are the same as in Fig. 3.

Figure 6

The total cross sections of $np\to \Lambda {\Theta }_{+}^{+}$ in the left panel (a) and $np\to {\Sigma }^0{\Theta }_{+}^{+}$ in the right panel (b). The parameter set of the Jülich-Bonn potential is employed. The notations are the same as in Fig. 3.

Figure 7

The total cross sections of $np\to \Lambda {\Theta }_{-}^{+}$ in the left panel (a) and $np\to {\Sigma }^0{\Theta }_{-}^{+}$ in the right panel (b). The parameter set of the Jülich-Bonn potential is employed. The notations are the same as in Fig. 3.