Photoproduction of the ${\Theta }^{+}$ resonance on the nucleon in a Regge model

We estimate the reaction mechanisms for the photoproduction of the ${\Theta }^{+}(1540)$ resonance on the nucleon, through $K$ and $K^{*}$ Regge exchanges. We compare the size of the cross sections for the $\gamma n\to K^{-}{\Theta }^{+}$ and $\gamma p\to {\overline{K}}^0{\Theta }^{+}$ reactions and investigate their sensitivity to the spin-parity assignments $J^P={\frac{1}{2}}^{\pm },{\frac{3}{2}}^{\pm }$ for the ${\Theta }^{+}$ resonance. The model allows one to estimate the cross sections corresponding with a given upper bound on the width of the ${\Theta }^{+}$. Within this model, the cross sections on the neutron are found to be around a factor of 5 larger than the ones on the proton, due to the presence of charged $K$ exchange for the reaction on a neutron target. Furthermore, the photon asymmetry is found to display a pronounced sensitivity to the parity of the ${\Theta }^{+}$, making it a very promising observable to help determine the quantum numbers of the ${\Theta }^{+}$ resonance.

Figure 1

The different Regge exchange contributions considered to describe the photoproduction reactions with ${\Theta }^{+}$ final state on a nucleon.

Figure 2

Regge model predictions for the $\gamma n\to K^{-}{\Theta }^{+}$ cross section at $E_{\gamma }=4\mathrm{GeV}$ for different spin-parity assignments of the ${\Theta }^{+}$. Dashed-dotted curves: gauge-invariant $K$ Regge exchange; dotted curves: $K^{*}$ Regge exchange (for the cases of $1/2^{\pm }$). To account for the range of uncertainty in the $K^{*}N\Theta$ coupling, we display the result for $K+K^{*}$ exchange for two values of the $K^{*}N\Theta$ coupling constant: $f_{K^{*}N\Theta }=+1.1$ (solid curves) and $f_{K^{*}N\Theta }=-1.1$ (dashed curves), corresponding with a width ${\Gamma }_{\Theta \to KN}=1\mathrm{MeV}$.

Figure 3

Regge model predictions for the $\gamma n\to K^{-}{\Theta }^{+}$ total cross sections for different spin-parity assignments of the ${\Theta }^{+}$ resonance. Curve conventions as in Fig. 2.

Figure 4

Regge model predictions for the $\gamma n\to K^{-}{\Theta }^{+}$ photon asymmetry at $E_{\gamma }=4\mathrm{GeV}$ for different spin-parity assignments of the ${\Theta }^{+}$. Curve conventions as in Fig. 2.

Figure 5

Regge model predictions for the $\gamma p\to {\overline{K}}^0{\Theta }^{+}$ cross section at $E_{\gamma }=4\mathrm{GeV}$ for different spin-parity assignments of the ${\Theta }^{+}$. Dotted curves: $K^{*}$ Regge exchange.

Figure 6

Regge model predictions for the $\gamma p\to {\overline{K}}^0{\Theta }^{+}$ photon asymmetry at $E_{\gamma }=4\mathrm{GeV}$ for different spin-parity assignments of the ${\Theta }^{+}$. Dotted curves: $K^{*}$ Regge exchange.

Figure 7

Regge model predictions for the $\gamma p\to {\overline{K}}^0{\Theta }^{+}$ total cross sections for different spin-parity assignments of the ${\Theta }^{+}$ resonance. Dotted curves: $K^{*}$ Regge exchange.

Figure 8

Regge model predictions for the target single spin asymmetry $T$ for the $\gamma n\to K^{-}{\Theta }^{+}$ reaction for both possible parities of the ${\Theta }^{+}$ resonance (for $J=1/2$) at $E_{\gamma }=4\mathrm{GeV}$. The model calculations correspond with the $K+K^{*}$ Regge exchanges for two values of the $K^{*}N\Theta$ coupling. Solid curves: $f_{K^{*}N\Theta }=+1.1$; dashed curves: $f_{K^{*}N\Theta }=-1.1$.

Figure 9

Regge model predictions for the recoil single spin asymmetry $P$ for the $\gamma n\to K^{-}{\Theta }^{+}$ reaction for both possible parities of the ${\Theta }^{+}$ resonance (for $J=1/2$) at $E_{\gamma }=4\mathrm{GeV}$. Curve conventions as in Fig. 8.

Figure 10

Regge model predictions for the $\gamma n\to K^{-}{\Theta }^{+}$ angular distribution for an unpolarized photon (0) for different spin-parity assignments of the ${\Theta }^{+}$ and for different decay angles ($\theta ,\varphi$), defined in the rest frame of the ${\Theta }^{+}$. Dashed-dotted curves: $K$ Regge exchange; dotted curves: $K^{*}$ Regge exchange; solid curves: $K+K^{*}$ Regge exchanges.

Figure 11

Regge model predictions for the $\gamma n\to K^{-}{\Theta }^{+}$ angular distribution for a photon linearly polarized in the reaction plane ($x$) for different spin-parity assignments of the ${\Theta }^{+}$. Curve conventions as in Fig. 10.

Figure 12

Regge model predictions for the $\gamma n\to K^{-}{\Theta }^{+}$ angular distribution for a photon linearly polarized perpendicular to the reaction plane ($y$) for different spin-parity assignments of the ${\Theta }^{+}$. Curve conventions as in Fig. 10.

Figure 13

Regge model predictions for the $\gamma n\to K^{-}{\Theta }^{+}$ angular distribution for a left-handed circularly polarized photon ($c$, left) for different spin-parity assignments of the ${\Theta }^{+}$. Curve conventions as in Fig. 10.

Figure 14

Regge model predictions for the $\gamma p\to K^0{\Theta }^{+}$ angular distribution ($c$, left) for different spin-parity assignments of the ${\Theta }^{+}$. Dotted curves: $K^{*}$ Regge exchange.

Figure 15

Regge model predictions for the $\gamma p\to {\overline{K}}^{*0}{\Theta }^{+}$ reaction for both possible parities of the ${\Theta }^{+}$ resonance. Upper panels: positive parity case; lower panels: negative parity case. Left panels: total cross section; right panels: differential cross section at $E_{\gamma }=4\mathrm{GeV}$. The model calculation corresponds with $K^0$ Regge exchange.