  In this work, we report on a theoretical study of possible pentaquark states
$\Lambda^0_b(5912)$ and $\Lambda^0_b(5920)$ in the
$\gamma{}p\to{}\Lambda_b^{0(*)}B^+$ 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
$\gamma{}p\to{}\Lambda_b^{0(*)}B^+$ are evaluated. Our calculation indicates
that the cross section for $\gamma{}p\to{}\Lambda_b^{0}(5912)B^{+}$ and
$\gamma{}p\to{}\Lambda_b^{0}(5920)B^{+}$ 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.
