In this work, we report on a theoretical study of possible pentaquark states $Lambda^0_b(5912)$ and $Lambda^0_b(5920)$ in the $gamma{}pto{}Lambda_b^{0(*)}B^+$ reactions within an effective Lagrangian approach. In addition to the contributions from the $s$-channel nucleon pole and $t$-channel $bar{B}^{{*}-}$ exchange, the contact term contribution are also included. Our theoretical approach is based on the chiral unitary theory where the $Lambda^0_b(5912)$ and $Lambda^0_b(5920)$ resonances are dynamically generated. Within the coupling constants of the $Lambda^0_b(5912)$ and $Lambda^0_b(5920)$ to $bar{B}p$ and $bar{B}^{*}p$ channels obtained from chiral unitary theory, the total and differential cross sections of the $gamma{}pto{}Lambda_b^{0(*)}B^+$ are evaluated. Our calculation indicates that the cross section for $gamma{}pto{}Lambda_b^{0}(5912)B^{+}$ and $gamma{}pto{}Lambda_b^{0}(5920)B^{+}$ reactions are of the order of 0.0164 nb and 0.00527 nb,respectively. If measured in future experiments, such as Electron-Ion Collider in China (EicC) or US(US-EIC), the predicted total cross sections and specific features of the angular distributions can be used to test the (molecular) nature of the $Lambda^0_b(5912)$ and $Lambda^0_b(5920)$ that they may be pentaquark states.
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