Some aspects of ${\Theta }^{+}$ parity determination in the reaction $\gamma N\to {\Theta }^{+}\overline{K}\to NK\overline{K}$

We analyze the problem of how to determine the parity of the ${\Theta }^{+}$ pentaquark in the reaction $\gamma N\to K\Theta \to \mathrm{NK}\overline{K}$, where $N=n,p$. Our model calculations indicate that the contribution of the nonresonant background of the reaction $\gamma N\to \mathrm{NK}\overline{K}$ cannot be neglected and that suggestions to determine the parity based solely on the initial-stage process $\gamma N\to K\Theta$ cannot be implemented cleanly. We discuss the various mechanisms that contribute to the background. Among the observables considered in this work, the triple spin asymmetry shows a kinematical “window” where the predictions are sensitive to the ${\Theta }^{+}$ parity and insensitive to the various reaction mechanisms considered, and thus, this observable offers a possibility of determining the parity of the ${\Theta }^{+}$.

Figure 1

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

Figure 2

Diagrams for the background process for the $\gamma N\to \mathrm{MN}\to \mathrm{NK}\overline{K}$ reaction, where M denotes the mesons $\rho ,\omega ,\varphi ,\sigma ,f_2$, and $a_2$.

Figure 3

Schematic description of the ${\Theta }^{+}$ production in (a) the $\gamma N\to \overline{K}{\Theta }^{+}$ reaction in the center-of-mass system and (b) the reaction $\gamma N\to \mathrm{NK}\overline{K}$ in the ${\Theta }^{+}$ rest frame. The notations “P” and “D” correspond to the production and decay planes, respectively.

Figure 4

The phase-space diagram for the ${\Theta }^{+}$ photoproduction at $E_{\gamma }=2$ GeV: the invariant mass $M_{K\overline{K}}$ versus $\cos \Theta$ at a fixed $\overline{K}$ production angle $(\theta ={55}^{ˆ})$. The cutoff area of the phase phase is placed between the two solid lines.

Figure 5

Cross sections for the ρ-, ω-, and ϕ-meson photoproduction. The experimental points are taken from Refs. 35, 36, 37.

Figure 6

(a) Dependence of the shape of the invariant mass distribution on the cutoff parameter ${\Lambda }_0$ in the $\gamma n\to K^{+}{K}^{-}$ reaction. (b) $K\overline{K}$ invariant mass distribution in $\gamma n\to K^{+}{K}^{-}$ taken from Ref. 1; arrows indicate the ϕ-meson cut window.

Figure 7

$K\overline{K}$ invariant-mass distribution in (a) $\gamma n\to K^{+}{K}^{-}$ and in (b) $\gamma p\to p{K}^0{\overline{K}}^0$. The arrows indicate the ϕ-meson cut window.

Figure 8

Contribution of the background processes to the differential cross section of the ${\Theta }^{+}$ photoproduction for the (a, b) $\gamma n$ and (c) $\gamma p$ reactions (a) without and (b, c) with the cut in the $K\overline{K}$ invariant mass distribution, respectively.

Figure 9

Contributions of the Born $s,t,u$ and the contact c terms in the (a, b) $\gamma p$ and (c, d) $\gamma n$ reactions, together with the t-channel $K^{*}$ exchange and the background processes. The respective cases for positive and negative ${\pi }_{\Theta }$ are depicted in (a, c) and (b, d).

Figure 10

The scale parameter α as a function of the cutoff parameters ${\Lambda }_{K^{*}}$ and ${\Lambda }_B$.

Figure 11

The cross section of the resonance ${\Theta }^{+}$ photoproduction and the background processes as a function of the $\overline{K}$-production angle for the (a, b) $\gamma p$ and (c, d) $\gamma n$ reactions and for the (a, c) positive and (b, d) negative parities of ${\Theta }^{+}$.

Figure 12

The decay distributions of (a) ${\mathrm{nK}}^{+}$ and (b) ${\mathrm{pK}}^0$ in the reactions $\gamma \to {\mathrm{nK}}^{+}{K}^{-}$ and $\gamma \to {\mathrm{pK}}^0{\overline{K}}^0$, respectively. The solid and dashed curves correspond to the positive and negative ${\Theta }^{+}$ parities, respectively. The distribution from the background is shown by the dot-dashed curve, whereas the contribution from the pure resonance channel is shown by the solid thin line. (c) The differential cross section of the background channels.

Figure 13

The beam asymmetry in $\gamma p\to {\mathrm{pK}}^0{\overline{K}}^0$ as a function of the K decay angle for ${\kappa }^{*}=0$. The results for ${\pi }_{\Theta }=+$ and ${\pi }_{\Theta }=-$ are shown in (a, b) and (c, d), respectively. The results for pseudovector (PV) and pseudoscalar (PS) couplings are displayed in (a, c) and (b, d), respectively. The symbol (±) corresponds to positive and negative $\alpha .$ The asymmetries due to the resonant channel are shown by the long dashed $(\alpha >0)$ and dashed $(\alpha <0)$ lines, respectively. The asymmetry from the background is shown by the dot-dashed curves.

Figure 14

The beam asymmetry in $\gamma p\to {\mathrm{pK}}^0{\overline{K}}^0$ as a function of the K decay angle. The result is for $\overline{\alpha }>0$ and ${\kappa }^{*}=0,\hspace{1em}\pm 0.5$. Other notations are the same as in Fig. 13.

Figure 15

The beam asymmetry in $\gamma n\to {\mathrm{nK}}^{+}{\overline{K}}^{-}$ as a function of the K decay angle. Notation is the same as in Fig. 13.

Figure 16

The beam asymmetry $\gamma n\to {\mathrm{nK}}^{+}{\overline{K}}^{-}$ for different values of ${\kappa }^{*}$ as a function of the K decay angle. Notation is the same as in Fig. 14.

Figure 17

The double target-recoil spin asymmetry $A_{\mathrm{tr}}$ in $\gamma p\to p{K}^0{\overline{K}}^0$ as a function of the K decay angle. Notation is the same as in Fig. 13.

Figure 18

The double target-recoil spin asymmetry $A_{\mathrm{tr}}$ in $\gamma p\to {\mathrm{pK}}^0{\overline{K}}^0$ as a function of the K decay angle for different values of ${\kappa }^{*}$. Notation is the same as in Fig. 14.

Figure 19

Same as in Fig. 17, for $\gamma n\to n{K}^{+}{K}^{-}$.

Figure 20

Same as Fig. 18, for $\gamma n\to {\mathrm{nK}}^{+}{K}^{-}$.

Figure 21

The triple spin asymmetry ${\Sigma }_{\mathrm{yy}}(\uparrow \uparrow )$ in $\gamma p\to {\mathrm{pK}}^0{\overline{K}}^0$ as a function of the K decay angle. Notation is the same as in Fig. 13.

Figure 22

The triple spin asymmetry ${\Sigma }_{\mathrm{yy}}(\uparrow \uparrow )$ in $\gamma p\to {\mathrm{pK}}^0{\overline{K}}^0$ as a function of the K decay angle for different values of ${\kappa }^{*}$ and negative α. Notation is the same as in Fig. 14.

Figure 23

Same as Fig. 21, for $\gamma n\to {\mathrm{nK}}^{+}{K}^{-}$.

Figure 24

Same as Fig. 22, for $\gamma n\to {\mathrm{nK}}^{+}{K}^{-}$.

Figure 25

The triple spin asymmetry ${\Sigma }_{\mathrm{yy}}(\uparrow \downarrow )$ in (a) $\gamma p\to {\mathrm{pK}}^0{\overline{K}}^0$ and (b) $\gamma n\to {\mathrm{nK}}^{+}{K}^{-}$ as a function of the $K^{+}$ decay angle for different values of ${\kappa }^{*}$ and positive $\overline{\alpha }$ and the PV-coupling scheme.