Coherent ${\Theta }^{+}$ and $\Lambda (1520)$ photoproduction off the deuteron

We analyze coherent ${\Theta }^{+}\Lambda (1520)$ photoproduction in the $\gamma d$ interaction near the threshold. We demonstrate that the effect of the coherent production becomes manifest in a comparison of the ${\mathit{nK}}^{+}$ invariant mass distribution when the ${\mathit{pK}}^{-}$ system is on the $\Lambda (1520)$ mass. Our model calculations indicate a sizable contribution of resonant and nonresonant background processes in the $\gamma d\to \mathit{np}{K}^{+}{K}^{-}$ reaction that generally exceeds the contribution of the coherent resonance channel. However, we find that coherent ${\Theta }^{+}\Lambda (1520)$ photoproduction is enhanced relative to the background processes in the forward hemisphere of ${\mathit{pK}}^{-}$ pair photoproduction. Moreover, the coherence effect does not depend on the ${\Theta }^{+}$ photoproduction amplitude and is defined by the probabilities of $\Lambda (1520)$ photoproduction and the ${\Theta }^{+}\to \mathit{NK}$ transition. Therefore, this effect may be used as an independent method for studying the production mechanism and properties of ${\Theta }^{+}$.

Figure 1

Tree level diagrams for the reaction $\gamma N\to {\Theta }^{+}\overline{K}\to \mathit{NK}\overline{K}$.

Figure 2

Differential cross section of the reaction $\gamma n\to {\Theta }^{+}{K}^{-}$ (a) and $\gamma p\to {\Theta }^{+}{\overline{K}}^0$ (b) at $E_{\gamma }=2$ GeV. The label “Born” corresponds to the coherent sum of the $t,s,u$-exchange diagrams and the contact term, shown in Fig. 1a, 1b, 1c, 1d, respectively. Solid curves indicate the total of all contributions. The contribution of $K^{*}$ exchange is indicated and shown as dashed-dotted curves that almost overlap the solid curves.

Figure 3

Tree level diagrams for the reaction $\gamma N\to {\Lambda }^{*}K\to \mathit{NK}\overline{K}$.

Figure 4

Differential cross section of the reaction $\gamma p\to {\Lambda }^{+}{K}^{+}$ at $E_{\gamma }=3.7$ GeV. Experimental data from Ref. 32.

Figure 5

Total cross section of the reaction $\gamma p\to {\Lambda }^{*}{K}^{+}$ as a function of the photon energy. The experimental data are taken from Ref. 32. The dot-dashed curve is the fit of this data $\sigma \simeq 6.55\hspace{1em}{E}_{\gamma }^{-2.1}$ (μb). The long-dashed curve represents the cross section when the amplitude is taken to be constant. The solid curves corresponds to the amplitude of Eq. (12). The signs ± corresponds to the sign of ${\alpha }_{{\Lambda }^{*}}$. The dashed curve describes the extrapolation of the effective Lagrangian model to the high energy region.

Figure 6

(a) Differential cross section of the $\gamma p\to {\Lambda }^{*}{K}^{+}$ reaction at $E_{\gamma }=2$ GeV. The notation “Born” corresponds to the coherent sum of the $t,s$-exchange diagram and the contact term, shown in Figs. 3a, 3b, and 3d, respectively. (b) Differential cross section of the $\gamma n\to {\Lambda }^{*}{K}^0$ reaction (solid curve) and $\gamma p\to {\Lambda }^{*}{K}^{+}$ reaction (dashed and dot-dashed curves). The symbol ± indicates the sign of ${\alpha }_{{\Lambda }^{*}}$.

Figure 7

Tree level diagrams for the reaction $\gamma d\to {\Lambda }^{*}{\Theta }^{+}$. The exchange of charged and neutral mesons are shown in (a), (b) and in (c), (d), respectively.

Figure 8

Diagrammatic representation of cutting (indicated by crosses) in the loop diagrams.

Figure 9

Differential cross section of the $\gamma d\to {\Lambda }^{*}{\Theta }^{+}$ reaction. The notation $\gamma d\to {\Lambda }^{*}({\Theta }^{+})$ and $\gamma d\to {\Theta }^{+}({\Lambda }^{*})$ corresponds to the diagrams in Fig. 7a, 7c and in 7b, 7d, respectively.

Figure 10

Tree level diagrams for background processes. (a)–(d) noncoherent spectator channels; (e), (f) coherent semiresonant background processes.

Figure 11

Background processes for the $\gamma p\to p{K}^{+}{K}^{-}$ reaction: (a) vector meson contribution; (b) virtual $\Lambda (1405)$ excitation.

Figure 12

The ${\mathit{pK}}^{-}$ invariant mass distribution in the $\gamma p\to {\mathit{pK}}^{+}{K}^{-}$ reaction at $E_{\gamma }=2$ GeV. The resonance channel, vector meson, and $\Lambda (1405)$ contributions are shown by the inner solid, long dashed, and dashed curves, respectively.

Figure 13

The ${\mathit{nK}}^{+}$ invariant mass distribution in the $\gamma n\to {\mathit{nK}}^{+}{K}^{-}$ reaction at $E_{\gamma }=2$ GeV. BW indicates the Breit-Wigner ${\Theta }^{+}$ decay distribution of Eq. (25). The dashed curve corresponds to a Gaussian distribution of the ${\Theta }^{+}$ decay width $\sigma =5$ MeV.

Figure 14

(a) Invariant mass distribution function $W_{\mathit{nK}}$ as a function of $M_{{\mathit{nK}}^{+}}$ at ${\theta }_{\gamma ({\mathit{pK}}^{-})}=27.5^{°}$ and fixed values of $M_{{\mathit{pK}}^{-}}$. (b) Invariant mass distribution function $W_{\mathit{pK}}$ as a function of $M_{{\mathit{nK}}^{+}}$ at ${\theta }_{\gamma ({\mathit{pK}}^{-})}=152.5^{°}$ and fixed values of $M_{{\mathit{pK}}^{-}}$.

Figure 15

Comparison of the coherent ${\Lambda }^{*}{\Theta }^{+}$ photoproduction (solid curve) and coherent semi-resonant background (dashed curve) depicted in Fig. 10e and 10f.

Figure 16

Dependence of $\cos {\theta }_{\gamma K^{-}}$ in $\gamma p\to {\Lambda }^{*}{K}^{+}$ photoproduction and $\cos {\theta }_{\gamma K^{+}}$ in $\gamma n\to {\Theta }^{+}{K}^{-}$ photoproduction as functions of $\cos {\theta }_{\gamma {\Lambda }^{*}}$ in the $\gamma d\to {\Lambda }^{*}{\Theta }^{+}$ reaction at $E_{\gamma }=2$ GeV.

Figure 17

The ${\mathit{nK}}^{+}$ invariant mass distribution in the $\gamma d\to {\mathit{npK}}^{+}{K}^{-}$ reaction at fixed values of the ${\mathit{pK}}^{-}$ invariant mass. The angle of the ${\mathit{pK}}^{-}$ pair photoproduction in $\gamma d$ c.m.s., ${\theta }_{\gamma ({\mathit{pK}}^{-})}=27.5^{°}$ and $E_{\gamma }=2$ GeV. (a) $M_{{\mathit{pK}}^{-}}=1.52\pm 0.02$ GeV; (b) $M_{{\mathit{pK}}^{-}}=1.57\pm 0.02$ GeV, (c) $M_{{\mathit{pK}}^{-}}=1.47\pm 0.02$ GeV. The notation sp.$(\gamma p\to {\Lambda }^{*}{K}^{+})$ and sp.$(\gamma p\to \mathrm{pKK})$ corresponds to the processes depicted in Figs. 10a and 10b, respectively; $\gamma d\to {\Theta }^{+}{\mathit{pK}}^{-}$ corresponds to the coherent background shown in Fig. 10e, $\gamma d\to {\Lambda }^{*}{\Theta }^{+}$ corresponds to the coherent ${\Lambda }^{*}{\Theta }^{+}$ photoproduction (Fig. 7).

Figure 18

Summary plot of the total ${\mathit{nK}}^{+}$ invariant mass distribution in the $\gamma d\to {\mathit{npK}}^{+}{K}^{-}$ reaction at three fixed intervals of the ${\mathit{pK}}^{-}$ invariant mass with $M_0=1.52,1.57$ and $1.47$ (GeV) at ${\theta }_{\gamma ({\mathit{pK}}^{-})}=27.5^{°}$ and $E_{\gamma }=2$ GeV.

Figure 19

(a) The ${\mathit{nK}}^{+}$ invariant mass distribution in the $\gamma d\to {\mathit{npK}}^{+}{K}^{-}$ reaction at $M_0=1.52$ GeV at the forward hemisphere of ${\mathit{pK}}^{-}$ pair photoproduction and $E_{\gamma }=2$ GeV. Notation is the same as in Fig. 17. (b) Summary plot of the total ${\mathit{nK}}^{+}$ invariant mass distribution at three fixed intervals of the ${\mathit{pK}}^{-}$ invariant mass with $M_0=1.52,1.57$ and $1.47$ GeV.

Figure 20

Same as in Fig. 17 but for ${\theta }_{\gamma ({\mathit{pK}}^{-})}=152.5^{°}$. The notations sp.$(\gamma n\to {\Theta }^{+}{K}^{+})$ and sp.$(\gamma n\to \mathrm{nKK})$ corresponds to the processes depicted in Figs. 10c and 10d, respectively.

Figure 21

Same as in Fig. 18 but for ${\theta }_{\gamma ({\mathit{pK}}^{-})}=152.5^{°}$.

Figure 22

Differential cross section of ${\Lambda }^{*}{\Theta }^{+}$ photoproduction with (solid curve) and without (dashed curve) the contribution of the $\gamma p\to {\Theta }^{+}{\overline{K}}^0$ subprocess.