$K^{*}\Sigma$ photoproduction off the proton target with baryon resonances

We investigate the photoproduction of $K^{*0}{\Sigma }^{+}$ and $K^{*+}{\Sigma }^0$ off the proton target, employing the effective Lagrangian approach at the tree-level Born approximation. In addition to the $(s,t,u)$-channel Born diagrams, we take into account various baryon-resonance contributions such as $D_{13}(2080)$, $S_{11}(2090)$, $G_{17}(2190)$, $D_{15}(2200)$, $S_{31}(2150)$, $G_{37}(2200)$, $F_{37}(2390)$, and ${\Sigma }^{*}(1385,3/2^{+})$ in a fully covariant manner. We present the numerical results for the energy and angular dependences for the cross sections in comparison to available experimental data. The single-polarization observables, i.e., the photon-beam (${\Sigma }_{\gamma }$), recoil ($P_y$), and target ($T_y$) baryon polarization asymmetries are computed as well for future experiments. We observe from the numerical results that the resonance contributions play a minor role in producing the strength of the cross sections, being different from the $K^{*}\Lambda$ photoproduction. In contrast, it turns out that the $\Delta (1232)$-pole contribution and $K$ exchange in the $t$ channel dominate the scattering process. On the other hand, the higher resonances influence the polarization observables such as the recoil and target asymmetries.

Figure 1

Relevant Feynman diagrams for the $\gamma N\to K^{*}\Sigma$ reactions. $N$, $N^{*}$, $\Delta$, ${\Delta }^{*}$, $Y$, and $Y^{*}$ denote the nucleon, nucleon resonances, delta, delta resonances, hyperons, and hyperon resonances, respectively, whereas $\kappa$, $K$, and $K^{*}$ stand for the strange scalar, pseudoscalar, and vector mesons, respectively. The four momenta for the initial and final states are also defined, as shown in the diagrams.

Figure 2

Total cross sections for $\gamma p\to K^{*0}{\Sigma }^{+}$ as functions of the photon energy $E_{\gamma }$ in the left panel. The black circles denote the CBELSA/TAPS data [12], whereas the open squares represent the estimated values extracted from the CLAS data [14]. The total cross sections for $\gamma p\to K^{*+}{\Sigma }^0$ are given in the right panel with the same notation.

Figure 3

$N^{*}$ and ${\Delta }^{*}$ resonance contributions to the total cross sections for $\gamma p\to K^{*0}{\Sigma }^{+}$ as functions of the photon energy $E_{\gamma }$ in the left panel and for $\gamma p\to K^{*+}{\Sigma }^0$ in the right panel with the same notation, respectively.

Figure 4

Differential cross sections for $\gamma p\to K^{*0}{\Sigma }^{+}$ as functions of $\cos \theta$ for different photon energies ($E_{\gamma }$) in the range (1.925–2.9125) GeV. The dotted curve shows the $t$-channel effects ($K$ and $\kappa$ exchanges), whereas the dot-dashed one draws the $\Delta$-pole contribution. The solid one represents the total result. The experimental data of the CBELSA/TAPS and CLAS collaborations are taken from Refs. 12, 14, respectively.

Figure 5

Differential cross sections for $\gamma p\to K^{*+}{\Sigma }^0$ as functions of $\cos \theta$ for different photon energies ($E_{\gamma }$) in the range (1.925–2.9125) GeV. The dotted curve shows the $t$-channel effects ($K$ and $\kappa$ exchanges), whereas the dot-dashed one draws the $\Delta$-pole contribution. The solid one represents the total result.

Figure 6

In the upper panel, photon-beam asymmetry ${\Sigma }_{\gamma }$ for $\gamma p\to K^{*0}{\Sigma }^{+}$ as functions of $\cos \theta$ in the range of $E_{\gamma }=(2.075–2.9125)\mathrm{GeV}$. The solid and dashed curves represent the results with and without the resonance contributions, respectively. In the lower panel, photon-beam asymmetry ${\Sigma }_{\gamma }$ for $\gamma p\to K^{*+}{\Sigma }^0$ with the same notation.

Figure 7

In the upper panel, photon-beam asymmetries ${\Sigma }_{\gamma }$ for $\gamma p\to K^{*0}{\Sigma }^{+}$ with and without $N^{*}$ and ${\Delta }^{*}$ resonances are drawn in order as functions of the photon energy $E_{\gamma }$, the scattering angle being changed from 0° to 180°. In the lower panel, those for $\gamma p\to K^{*+}{\Sigma }^0$ are shown with and without the resonance contributions, respectively.

Figure 8

Recoil asymmetries $P_y$ for $K^{*}\Sigma$ photoproduction as functions of $\cos \theta$ in the range of the photon energy $E_{\gamma }=2.075–2.9125\mathrm{GeV}$. In the upper and lower panels, $P_y$ is drawn for the $K^{*0}{\Sigma }^{+}$ and $K^{*+}{\Sigma }^0$ productions, respectively. The solid and dashed curves stand for the results with and without the $N^{*}$ and ${\Delta }^{*}$ resonances, respectively.

Figure 9

In the upper panel, recoil asymmetries $P_y$ for $\gamma p\to K^{*0}{\Sigma }^{+}$ with and without $N^{*}$ and ${\Delta }^{*}$ resonances are drawn in order as functions of the photon energy $E_{\gamma }$, the scattering angle being changed from 0° to 180°. In the lower panel, those for $\gamma p\to K^{*+}{\Sigma }^0$ are shown with and without the resonance contributions, respectively.

Figure 10

Target asymmetries $T_y$ for $K^{*}\Sigma$ photoproduction as functions of $\cos \theta$ in the range of the photon energy $E_{\gamma }=(2.075–2.9125)\mathrm{GeV}$. In the upper and lower panels, $T_y$ are drawn for the $K^{*0}{\Sigma }^{+}$ and $K^{*+}{\Sigma }^0$ productions, respectively. The solid and dashed curves stand for the results with and without the $N^{*}$ and ${\Delta }^{*}$ resonances, respectively.

Figure 11

In the upper panel, target asymmetries $T_y$ for $\gamma p\to K^{*0}{\Sigma }^{+}$ with and without $N^{*}$ and ${\Delta }^{*}$ resonances are drawn in order as functions of the photon energy $E_{\gamma }$, the scattering angle being changed from 0° to 180°. In the lower panel, those for $\gamma p\to K^{*+}{\Sigma }^0$ are shown with and without the resonance contributions, respectively.