Production of ${\mathrm{\Theta }}^{+}$ in $\gamma +D\to \mathrm{\Lambda }+{\mathrm{\Theta }}^{+}$ and $\gamma +D\to \mathrm{\Sigma }+{\mathrm{\Theta }}^{+}$ reactions

The $\gamma +D\to \mathrm{\Lambda }+{\mathrm{\Theta }}^{+}$ and $\gamma +D\to \mathrm{\Sigma }+{\mathrm{\Theta }}^{+}$ reactions can be used to determine the width of ${\mathrm{\Theta }}^{+}$ almost model independently. We calculate the differential cross sections of the $\gamma +D\to \mathrm{\Lambda }+{\mathrm{\Theta }}^{+}$, $\gamma +D\to \mathrm{\Sigma }+{\mathrm{\Theta }}^{+}$ and relevant background reactions in the photon energy range $1.2⩽E_{\gamma }⩽2.6\mathrm{GeV}$. We determine the most favorable kinematic conditions and observables for the experimental studies of ${\mathrm{\Theta }}^{+}$ in the considered processes. We argue that a comparison of the $\gamma +D\to \mathrm{\Lambda }+{\mathrm{\Theta }}^{+}$ and $\gamma +D\to \mathrm{\Sigma }+{\mathrm{\Theta }}^{+}$ cross sections should unambiguously determine isospin of ${\mathrm{\Theta }}^{+}$.

Figure 1

Two graphs of $\gamma +D\to \mathrm{\Lambda }\left(\mathrm{\Sigma }\right)+{\mathrm{\Theta }}^{+}$.

Figure 2

The differential cross section $d{\sigma }^{p+n}∕dt$, which includes both $\gamma +p\to \mathrm{\Lambda }\left(\mathrm{\Sigma }\right)+K^{+}$ and $\gamma +n\to \mathrm{\Lambda }\left(\mathrm{\Sigma }\right)+K^0$ amplitudes and their interference, as a function of the momentum transfer squared $t$ from $\gamma$ to $\mathrm{\Lambda }$ (solid curves). The $\gamma +p\to \mathrm{\Lambda }\left(\mathrm{\Sigma }\right)+K^{+}$ cross section $d{\sigma }^p∕dt$ is given by the dashed curves. The upper panels correspond to $\mathrm{\Lambda }$ production, the lower panels correspond to $\mathrm{\Sigma }$ production.

Figure 3

The nuclear suppression factor $S\left(t\right)$.

Figure 4

The $\gamma +D\to \mathrm{\Lambda }+{\mathrm{\Theta }}^{+}$ differential cross section as a function of the momentum transfer $t$ at different photon energies, $E_{\gamma }=1.2$, 1.6, 2, and $2.6\mathrm{GeV}$. The total width of ${\mathrm{\Theta }}^{+}$ is assumed ${\mathrm{\Gamma }}^{\mathrm{tot}}=5\mathrm{MeV}$. In order to use a different width of ${\mathrm{\Theta }}^{+}$, ${\overline{\mathrm{\Gamma }}}^{\mathrm{tot}}$, the curves in this figure should be scaled by the factor ${\overline{\mathrm{\Gamma }}}^{\mathrm{tot}}∕{\mathrm{\Gamma }}^{\mathrm{tot}}$.

Figure 5

The $\gamma +D\to \mathrm{\Sigma }+{\mathrm{\Theta }}^{+}$ differential cross section as a function of momentum transfer $t$ at different photon energies, $E_{\gamma }=1.2$, 1.6, 2, and $2.6\mathrm{GeV}$. The total width of ${\mathrm{\Theta }}^{+}$ is assumed ${\mathrm{\Gamma }}^{\mathrm{tot}}=5\mathrm{MeV}$. In order to use a different width of ${\mathrm{\Theta }}^{+}$, ${\overline{\mathrm{\Gamma }}}^{\mathrm{tot}}$, the curves in this figure should be scaled by the factor ${\overline{\mathrm{\Gamma }}}^{\mathrm{tot}}∕{\mathrm{\Gamma }}^{\mathrm{tot}}$.

Figure 6

${\mathrm{\Theta }}^{+}$ with isospin-1. The $\gamma +D\to \mathrm{\Sigma }+{\mathrm{\Theta }}^{+}$ (upper panels) and $\gamma +D\to {\mathrm{\Sigma }}^0+{\mathrm{\Theta }}^{+}$ (lower panels) differential cross sections as functions of the momentum transfer $t$ at different photon energies, $E_{\gamma }=1.2$ and $1.6\mathrm{GeV}$. It is assumed that ${\mathrm{\Gamma }}^{\mathrm{tot}}=5\mathrm{MeV}$.

Figure 7

The dominant background reaction.

Figure 8

The $\gamma +D\to \mathrm{\Lambda }\left(\mathrm{\Sigma }\right)+n+K^{+}$ double differential cross sections as functions of $t$ at different spectator momenta $p_s$. The solid curves represent the signal plus interference cross section; the dashed-dotted curves give the interference cross section; the dashed curves give the purely background cross section. The total width of ${\mathrm{\Theta }}^{+}$ is assumed ${\mathrm{\Gamma }}^{\mathrm{tot}}=5\mathrm{MeV}$; the photon energy $E_{\gamma }=1.2\mathrm{GeV}$.

Figure 9

The $\gamma +D\to \mathrm{\Lambda }\left(\mathrm{\Sigma }\right)+n+K^{+}$ triple differential cross sections as functions of the proton-kaon invariant mass squared at $E_{\gamma }=1.2\mathrm{GeV}$, $t=-0.1{\mathrm{GeV}}^2$, and $p_s=300\mathrm{MeV}∕c$. The solid curves represent the signal plus interference cross section, the dashed curves give the purely background cross section.