Investigating the parity of the exotic ${ϴ}^{+}$ baryon from kaon photoproduction

Based on the hadronic model with the gauge prescription suggested by Ohta and Haberzettl, we investigate the possibility of determining the parity state of the ${ϴ}^{+}$ baryon using photon induced processes, $\gamma n\to K^{-}{ϴ}^{+}$ and $\gamma p\to {\overline{K}}^0{ϴ}^{+}$. The total and differential cross sections are simulated in two versions of pseudovector (PV) and pseudoscalar (PS) coupling schemes and the results are reported both on the positive and negative parity states of the ${ϴ}^{+}$ baryon. It is found that in both coupling schemes the total cross sections from the neutron target are in general larger than those from the proton target, regardless of the ${ϴ}^{+}$ parity. The cross sections of the ${ϴ}^{+}$ production however depend largely on the value of the ${ϴ}^{+}$ decay width which is not yet well established. Moreover, there is a wide theoretical uncertainty associated with the different assumption on the gauge prescription in model calculations. We discuss these points by comparing theoretical predictions with the existing experimental data. Our analysis suggests that the observation of the angular distribution rather than just the total cross section in the photoproduction process may be a useful tool to distinguish the parity of the ${ϴ}^{+}$ baryon.

Figure 1

Tree level diagrams for $\gamma N\to K{ϴ}^{+}$ reaction. Diagrams (a), (b), and (c) denote the $s$-, $u$-, and $t$-channel pole terms with hadron form factors depicted as the blob at each vertex. The diagram (d) is the Kroll-Ruderman (KR) term; it is absent for pseudoscalar couplings with bare vertices. The last diagram (e) corresponds to the contact interaction term required to restore gauge invariance of the Born amplitude. It is depicted as a large blob to distinguish from the KR term.

Figure 2

Cross sections for $\gamma n\to K^{-}{ϴ}^{+}$ and for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$ when the ${ϴ}^{+}$ has positive parity. The PV coupling scheme is displayed in the left column and the PS scheme is in the right column. Given the coupling constant $g_{KNϴ}=2.2$, dependence of the cross sections with $\Lambda =1.8$ and $1.2\mathrm{GeV}$ are shown. The dotted lines are the results of the Born amplitude with ${\kappa }_{ϴ}=0$ and cutoff $\Lambda =1.2\mathrm{GeV}$. The solid lines are the results of the Born amplitude with ${\kappa }_{ϴ}=0$ and cutoff $\Lambda =1.8\mathrm{GeV}$. The dot-dashed lines are the Born contributions with ${\kappa }_{ϴ}=0.7$ and $\Lambda =1.8\mathrm{GeV}$. The dot-dot-dashed lines with ${\kappa }_{ϴ}=-0.7$ and $\Lambda =1.8\mathrm{GeV}$.

Figure 3

Energy and angle dependence of the subtraction function $\widehat{F}$ for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$. The functional form of $\widehat{F}$ is given by Eq. (6). The solid line is for $\Lambda =1.8\mathrm{GeV}$. The dotted line and the dashed line are for $\Lambda =1.2$ and $0.8\mathrm{GeV}$, respectively. Note that $\widehat{F}=1$ at $E_{\gamma }=0$ below the threshold of the reaction regardless of $\Lambda$ values.

Figure 4

Diagrams for $t$-channel $K*$ and $K_1$ exchanges in the $\gamma N\to K{ϴ}^{+}$ process.

Figure 5

Cross sections for $\gamma n\to K^{-}{ϴ}^{+}$ of PV (upper left) and PS scheme (upper right). Cross sections for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$ of PV (lower left) and PS scheme (lower right) when the ${ϴ}^{+}$ has positive parity. ${\kappa }_{ϴ}=0$ in any cases for all panels. The solid lines are the contributions of the Born amplitude with $g_{K*Nϴ}=0$. The dotted lines are the sum of the Born terms and $K*$ with $g_{K*Nϴ}=1.32$. The dot-dashed lines the sum of the Born terms and $K*$ with $g_{K*Nϴ}=-1.32$. The dashed lines are the sum in total of the Born terms, $K*$ and $K_1$ with $g_{K*Nϴ}=1.32$, $g_{K_{1}Nϴ}=-0.07$ for $\gamma n\to K^{-}{ϴ}^{+}$ and $g_{K_{1}Nϴ}=-0.1$ for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$, respectively. The dot-dot-dashed lines are the sum in total of the Born terms, $K*$ and $K_1$ with $g_{K*Nϴ}=-1.32$, $g_{K_{1}Nϴ}=+0.07$ for $\gamma n\to K^{-}{ϴ}^{+}$ and $g_{K_{1}Nϴ}=+0.1$ for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$, respectively.

Figure 6

Angular distributions for $\gamma n\to K^{-}{ϴ}^{+}$ at $E_{\gamma }=1.8\mathrm{GeV}$ (upper left), $E_{\gamma }=2.5\mathrm{GeV}$ (lower left) of PV and $E_{\gamma }=1.8\mathrm{GeV}$ (upper right), $E_{\gamma }=2.5\mathrm{GeV}$ (lower right) of PS scheme when the parity of ${ϴ}^{+}$ is positive. The notations are the same as in Fig. 5.

Figure 7

Angular distributions for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$ at $E_{\gamma }=1.8\mathrm{GeV}$ (upper left), $E_{\gamma }=2.5\mathrm{GeV}$ (lower left) of PV and $E_{\gamma }=1.8\mathrm{GeV}$ (upper right), $E_{\gamma }=2.5\mathrm{GeV}$ (lower right) of PS scheme when the parity of ${ϴ}^{+}$ is positive. The notations are the same as in Fig. 5.

Figure 8

Cross sections for $\gamma n\to K^{-}{ϴ}^{+}$ of PV (upper left) and PS scheme (upper right). Cross sections for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$ of PV (lower left) and PS scheme (lower right) when the ${ϴ}^{+}$ has negative parity. ${\kappa }_{ϴ}=0$ in any cases for all panels. The solid lines are the contribution of the Born amplitude with $g_{KNϴ}=0.3$, $g_{K*Nϴ}=0$. The dotted lines are the sum of the Born amplitude and $K*$ with $g_{K*Nϴ}=0.18$. The dot-dashed lines the sum of the Born amplitude and $K*$ with $g_{K*Nϴ}=-0.18$. The dashed lines are the sum in total of the Born terms, $K*$ and $K_1$ with $g_{K*Nϴ}=0.18$, $g_{K_{1}Nϴ}=-0.1$ for $\gamma n\to K^{-}{ϴ}^{+}$ and $g_{K_{1}Nϴ}=-0.16$ for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$, respectively. The dot-dot-dashed lines are the sum in total of the Born, $K*$ and $K_1$ with $g_{K*Nϴ}=-0.18$, $g_{K_{1}Nϴ}=+0.1$ for $\gamma n\to K^{-}{ϴ}^{+}$ and $g_{K_{1}Nϴ}=+0.16$ for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$, respectively.

Figure 9

Angular distributions for $\gamma n\to K^{-}{ϴ}^{+}$ at $E_{\gamma }=1.8\mathrm{GeV}$ (upper left), $E_{\gamma }=2.5\mathrm{GeV}$ (lower left) of PV and $E_{\gamma }=1.8\mathrm{GeV}$ (upper right), $E_{\gamma }=2.5\mathrm{GeV}$ (lower right) of PS scheme with the negative parity ${ϴ}^{+}$. The notations are the same as in Fig. 8.

Figure 10

Angular distributions for $\gamma p\to {\overline{K}}^0{ϴ}^{+}$ at $E_{\gamma }=1.8\mathrm{GeV}$ (upper left), $E_{\gamma }=2.5\mathrm{GeV}$ (lower left) of PV and $E_{\gamma }=1.8\mathrm{GeV}$ (upper right), $E_{\gamma }=2.5\mathrm{GeV}$ (lower right) of PS scheme with the negative parity ${ϴ}^{+}$. The notations are the same as in Fig. 8.