Polarization observables in $\gamma N\to K\overline{K}N$

Some of the rich structure of the polarization observables recently developed for processes like $\gamma N\to \pi \pi N$ and $\gamma N\to K\overline{K}N$ are explored within the framework of a specific model for the latter process. Emphasis is placed on observables that may be accessible at existing facilities in the near future. The sensitivity of the observables to the details of the model indicate that they will be a very useful tool in differentiating among models used to describe reactions like these. Within the framework of a model for $\gamma N\to K\overline{K}N$, the sensitivity of the observables to the coupling constants of the ϕ, to the properties of the $\Lambda (1405)$, and to the existence of the ${\Theta }^{+}$ is examined.

Figure 1

“Born” diagrams: Solid unlabeled lines are nucleons; unlabeled dashed lines are kaons; and wavy lines are photons.

Figure 2

Diagrams containing vector mesons. The dotted lines represent the vector mesons.

Figure 3

Diagrams containing excited baryons. In (a)–(d), the thick solid lines may be either ${\Lambda }^{*},{\Sigma }^{*}$ or Θ, while the thin solid line is a nucleon. In diagram (d), the photon couples to the charge of the intermediate resonance: In this model, couplings to any higher electromagnetic moments of the resonance are neglected.

Figure 4

The observable $P_x^{\odot }$ shown in terms of different kinematic variables. (a) as a function of $m_{K\overline{K}}$; (b) as a function of $m_{\mathit{NK}}$; (c) as a function of $m_{N\overline{K}}$; (d) as a function of $\cos {\Theta }^{*}$.

Figure 5

The observable $I^s$, showing its sensitivity to the coupling constants $G_v^{\varphi }$ and $G_t^{\varphi }$. (a) $G_v^{\varphi }=4,\hspace{1em}{G}_t^{\varphi }=0$; (b) $G_v^{\varphi }=-4,\hspace{1em}{G}_t^{\varphi }=0$; (c) $G_v^{\varphi }=0,\hspace{1em}{G}_t^{\varphi }=4$; (d) $G_v^{\varphi }=0,\hspace{1em}{G}_t^{\varphi }=-4$. In each case, the observable is shown as a function of $m_{K\overline{K}}$.

Figure 6

The observable $P_x^{\odot }$, showing its sensitivity to the coupling constants $G_v^{\varphi }$ and $G_t^{\varphi }$. (a) $G_v^{\varphi }=4,\hspace{1em}{G}_t^{\varphi }=0$; (b) $G_v^{\varphi }=-4,\hspace{1em}{G}_t^{\varphi }=0$; (c) $G_v^{\varphi }=0,\hspace{1em}{G}_t^{\varphi }=4$; (d) $G_v^{\varphi }=0,\hspace{1em}{G}_t^{\varphi }=-4$. In each case, the observable is shown as a function of $m_{K\overline{K}}$.

Figure 7

The observable $P_x^s$, showing its sensitivity to the subthreshold resonance $\Lambda (1405)$: (a) results with the $\Lambda (1405)$ excluded in the calculation; (b) results when this state is included, with $g_{\Lambda (1405)\mathit{NK}}=5.3$; and (c) results when the coupling constant is increased from 5.3 to 8.0. All curves are shown as functions of $m_{N\overline{K}}$.

Figure 8

The observable $I^c$, showing its sensitivity to the subthreshold resonance $\Lambda (1405)$; (a) results with the $\Lambda (1405)$ excluded in the calculation; (b) results when this state is included, with $g_{\Lambda (1405)\mathit{NK}}=5.3$, and (c) results when the coupling constant is increased from 5.3 to 8.0. All curves are shown as functions of $m_{N\overline{K}}$.

Figure 9

The observable $P_y^c$, showing its sensitivity to the subthreshold resonance $\Lambda (1405)$: (a) results with the $\Lambda (1405)$ excluded in the calculation; (b) results when this state is included, with $g_{\Lambda (1405)\mathit{NK}}=5.3$; and (c) results when the coupling constant is increased from 5.3 to 8.0. All curves are shown as functions of $m_{N\overline{K}}$.

Figure 10

The observable ${\mathcal{O}}_{{\mathit{yz}}^{\text{'}}}^c$, showing its sensitivity to the subthreshold resonance $\Lambda (1405)$: (a) results with the $\Lambda (1405)$ excluded in the calculation; (b) results when this state is included, with $g_{\Lambda (1405)\mathit{NK}}=5.3$; and (c) results when the coupling constant is increased from 5.3 to 8.0. All curves are shown as functions of $m_{N\overline{K}}$.

Figure 11

The beam asymmetry $I^{\odot }$, showing its sensitivity to the exotic resonance ${\Theta }^{+}$: (a) results when the ${\Theta }^{+}$ is excluded from the calculation, (b) results when a ${\Theta }^{+}$ of positive parity is included in the calculation, and (c) results when a ${\Theta }^{+}$ of negative parity is inclu- ded in the calculation. All curves are shown as functions of $m_{\mathit{NK}}$.

Figure 12

The observable $P_x^{\odot }$, showing its sensitivity to the exotic resonance ${\Theta }^{+}$: (a) results when the ${\Theta }^{+}$ is excluded from the calculation, (b) results when a ${\Theta }^{+}$ of positive parity is included in the calculation, and (c) results when a ${\Theta }^{+}$ of negative parity is included in the calculation. All curves are shown as functions of $m_{\mathit{NK}}$.

Figure 13

The observable $P_z^{\odot }$, showing its sensitivity to the exotic resonance ${\Theta }^{+}$: (a) results when the ${\Theta }^{+}$ is excluded from the calculation, (b) results when a ${\Theta }^{+}$ of positive parity is included in the calculation, and (c) results when a ${\Theta }^{+}$ of negative parity is included in the calculation. All curves are shown as functions of $m_{\mathit{NK}}$.

Figure 14

The observables (a) $I^{\odot }$, (b) $P_x^{\odot }$, and (c)$P_z^{\odot }$, showing their sensitivities to both the exotic resonance ${\Theta }^{+}$ (with positive parity) and the nonexotic $\Lambda (1405)$. The solid curves all correspond to ${\Phi }^{*}=\pi /6$, while the dash-dotted curves are for ${\Phi }^{*}=\pi /2$. In each panel, the uppermost curves arise when the contibution of the $\Lambda (1405)$ is turned off. The lowermost curves result when $g_{\Lambda (1405)\mathit{NK}}=8.0$, while the middle curves arise when this coupling constant has a value of 5.3. All curves are shown as functions of $m_{\mathit{NK}}$.