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The photoproduction of bottomonium-like states $Z_{b}(10610)$ and$Z_{b}(10650)$ via $\gamma p$ scattering is studied within an effectivLagrangian approach and the vector-meson-dominance model. The Regge model isemployed to calculate the photoproduction of $Z_{b}$ states via $t$-channelwith $\pi$ exchange.The numerical results show that the values of the totalcross-sections of $Z_{b}(10610)$ and $Z_{b}(10650)$ can reach 0.09 nb and 0.02nb, respectively, near the center of mass energy of 22 GeV. The experimentalmeasurements and studies on the photoproduction of $Z_{b}$ states near energyregion around $W\simeq 22$ GeV is suggested. Moreover, with the help ofeSTARlight and STARlight programs, one obtains the cross-sections and eventnumbers of $Z_{b}(10610)$ production in electron-ion collision (EIC) andUltraperipheral collisions (UPCs). The results show that a considerable numberof events from $Z_{b}(10610)$ can be produced on the relevant experiments ofEICs and UPCs. Also, one calculates the rates and kinematic distributions for$\gamma p\rightarrow Z_{b}n$ in $ep$ and $pA$ collisions via EICs and UPCs, andthe relevant results will provide an important reference for the RHIC, LHC,EIC-US, LHeC, and FCC experiments to search for the bottomonium-like $Z_{b}$states.

Production of the bottomonium-like states $Z_b$ states at $e$-$h$ and ultraperipheral $h$-$h$ collisions