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Systematic study on production of hidden-bottom pentaquark via $γp$ and $π^{-}p$ scatterings

The production of hidden-bottom pentaquark $P_{b}$ states via $γp$ and $π^{-}p$ scatterings is studied within an effective Lagrangian approach and the vector-meson-dominance mechnism. For the $P_{b}$ production in the process $γp\rightarrow Υp$, the dipole Pomeron model is employed to calculate the background contribution, and the experimental data can be well described. For the process $π^{-}p\rightarrow Υn$, the Reggeized $t$-channel with $π$ exchange is considered as the main background for the $P_{b}$ production. Near the threshold, two-peak structure from the states $P_{b (11080)$ and $P_{b}(11125)$ can be observed if energy bin width is chosen as 0.01 GeV, and the same result is obtained in the $π^{-}p$ scattering. Moreover, by taking the branching ratio of Br$[{P_{b}\rightarrow πN}]\simeq 0.05\%$, the numerical result shows that the average value of cross section from the $P_{b}(11080)$ state produced in the $γp$ or $π^{-}p$ scattering reaches at least 0.1 nb with a bin of 0.1 GeV. Even if we reduce the branching ratio of the $P_{b}$ state into $πN$ channel by one order, the theoretical average of the cross section from $P_{b}(11080)$ production in $π^{-}p$ scattering can reach the order of 0.01 nb with a bin of 0.1 GeV, which means that the signal can still be clearly distinguished from the background. The experimental measurements and studies on the hidden-bottom pentaquark $P_{b}$ state production in the $γp $ or $π^{-}p$ scattering near-threshold energy region around $W\simeq 11$ GeV are strongly suggested, which are accessible at COMPASS and JPARC. Particularly, the result of the photoproduction suggests that it is very promising to observe the hidden-bottom pentaquark at proposed EicC facility in China.