Pion-induced production of hidden-charm pentaquarks $P_c(4312),P_c(4440)$, and $P_c(4457)$

Abstract

The production of the hidden-charm pentaquarks $P_c$ via pion-induced reaction on a proton target is investigated within an effective Lagrangian approach. Three experimentally observed states, $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$, are considered in the calculation, and the Reggeized $t$-channel meson exchange is considered as main background for the reaction ${\pi }^{-}p\to J/\psi n$. The numerical results show that the experimental data of the total cross section of the reaction ${\pi }^{-}p\to J/\psi n$ at $W\simeq 5$ GeV can be well explained by contribution of the Reggeized $t$ channel with reasonable cutoff. If the branching ratios $Br[P_c\to J/\psi N]\simeq 3\%$ and $Br[P_c\to \pi N]\simeq 0.05\%$ are taken, the average value of the cross section from the $P_c(4312)$ contribution is about 1.2 nb/100 MeV, which is consistent with existing rude data at near-threshold energies. The results indicate that the branching ratios of the $P_c$ states to the $J/\psi N$ and $\pi N$ should be small. The shape of differential cross sections shows that the Reggeized $t$-channel provides a sharp increase at extreme forward angles, while the differential cross sections from the $P_c$ states contributions are relatively flat. High-precision experimental measurements on the reaction ${\pi }^{-}p\to J/\psi n$ at near-threshold energies are suggested to confirm the LHCb hidden-charm pentaquarks as genuine states, and such experiments are also helpful to understand the origin of these resonance structures.

6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1904.11706