Photo-production of lowest ${\mathrm{\Sigma }}_{1\mathrm{/}{2}^{-}}^{\ast }$ state within the Regge-effective Lagrangian approach

Since the lowest ${\mathrm{\Sigma }}^{\ast }$ state, with quantum numbers spin-parity $J^P=1\mathrm{/}{2}^{-}$, is far from established experimentally and theoretically, we have performed a theoretical study on the ${\mathrm{\Sigma }}_{1\mathrm{/}{2}^{-}}^{\ast }$ photo-production within the Regge-effective Lagrangian approach. Taking into account that the ${\mathrm{\Sigma }}_{1\mathrm{/}{2}^{-}}^{\ast }$ couples to the $\bar{K}N$ channel, we have considered the contributions from the $t$-channel $K$ exchange diagram. Moreover, these contributions from $t$-channel $K^{\ast }$ exchange, $s$-channel nucleon pole, $u$-channel $\mathrm{\Sigma }$ exchange, and the contact term, are considered. The differential and total cross sections of the process $\gamma n\to K^{+}{\mathrm{\Sigma }}_{1\mathrm{/}{2}^{-}}^{\ast -}$ are predicted with our model parameters. The results should be helpful to search for the ${\mathrm{\Sigma }}_{1\mathrm{/}{2}^{-}}^{\ast }$ state experimentally in future.