Nucleon and $\mathrm{\Delta }$ resonances in $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$ photoproduction

The most recent data on beam asymmetries $\mathrm{\Sigma }$ and beam-target asymmetries $E$ from the CLAS Collaboration, together with the previous data on differential cross sections and beam asymmetries from the CLAS and LEPS Collaborations, for the $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$ reaction are studied based on an effective Lagrangian approach in the tree-level Born approximation. The $t$-channel $K$ and $K^{*}(892)$ exchanges, the $u$-channel $\mathrm{\Sigma }$ exchange, the interaction current, and the exchanges of $N$, $\mathrm{\Delta }$, and their excited states in the $s$ channel are considered in constructing the reaction amplitudes to describe the available experimental data. The reaction mechanisms of $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$ are analyzed, and the associated resonances’ parameters are extracted. The numerical results show that the $\mathrm{\Delta }$ exchange and the $N(1710)1/2^{+}$, $N(1880)1/2^{+}$, $N(1900)3/2^{+}$, and $\mathrm{\Delta }(1920)3/2^{+}$ resonance exchanges in the $s$ channel dominate the $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$ reaction in the lower energy region, and the $t$-channel $K^{*}(892)$ exchange plays a crucial role at forward angles in the higher energy region.

Figure 1

Generic structure of the amplitude for $\gamma N\to K\mathrm{\Sigma }$. Time proceeds from left to right.

Figure 2

Differential cross sections for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$. The solid (black), dotted (red), and long-dashed (green) lines represent the results from the full calculation, the $t$-channel amplitudes [$K$ and $K^{*}(892)$ exchanges], and $s$-channel amplitudes ($N$, $N^{*}$, $\mathrm{\Delta }$, and ${\mathrm{\Delta }}^{*}$ exchanges), respectively. Data with red circles and blue triangles are taken from the CLAS Collaboration [25] and the LEPS Collaboration [14], respectively. The numbers in parentheses denote the incident energies (left number) and the corresponding center-of-mass energies of the system (right number), in MeV.

Figure 3

Photobeam asymmetries $\mathrm{\Sigma }$ for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$. The solid (black) lines represent the results from the full calculation. The dotted (red), dashed (blue), long-dashed (green), and dot-dashed (magenta) lines represent the results obtained by switching off the $t$-channel amplitudes [$K$ and $K^{*}(892)$ exchanges], $u$-channel amplitude ($\mathrm{\Sigma }$ exchange), $s$-channel amplitudes ($N$, $N^{*}$, $\mathrm{\Delta }$, and ${\mathrm{\Delta }}^{*}$ exchanges), and interaction current, respectively. Data with red circles and blue triangles are taken from the CLAS Collaboration [39] and the LEPS Collaboration [14], respectively. The numbers in parentheses denote the incident energies (left number) and the corresponding center-of-mass energies of the system (right number), in MeV.

Figure 4

Beam-target asymmetries $E$ for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$. Notations for lines are the same as Fig. 3. Data with red circles are taken from the CLAS Collaboration [40]. $E_{\gamma }$ and $W$ denote the incident energies and the corresponding center-of-mass energies of the system, respectively.

Figure 5

Predicted total cross sections for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}$ with contributions from individual terms.