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The exotic resonant state $P_{c}^{\pm}(4312)$, $P_{c}^{\pm}(4440)$, and$P_{c}^{\pm}(4457)$ are studied by using the dynamically constrained phasespace coalescence DCPC model and PACIAE model in $pp$ collisions at$\sqrt{s}=7$, 13TeV, respectively. We consider exotic state$P_{c}^{\pm}(4312)$, $P_{c}^{\pm}(4440)$ and $P_{c}^{\pm}(4457)$ to be threekinds of possible structures, i.e. pentaquark state, the nucleus-like state,and the molecular state based on $P_c^\pm \to J/\psi{p}{(\bar p)}$ bound state.The yield, the transverse momentum distribution and the rapidity distributionof $P_{c}$ with three different structures are all predicted. The resultsindicated that the yield is on the order of $10^{-6}$, which might providereference for experimental research.

A study on the exotic state ${P_{c}(4312),P_{c}(4440),P_{c}(4457)}$ in $pp$ collisions at $\sqrt{s}=7$, 13 TeV