How to reveal the exotic nature of the P_c(4450)

Abstract

The LHCb Collaboration announced two pentaquark-like structures in the $J/\ddot{I}ˆp$ invariant mass distribution. We show that the current information on the narrow structure at 4.45 GeV is compatible with kinematical effects of the rescattering from $\ddot{I}{‡}_{c1}p$ to $J/\ddot{I}ˆp$: First, it is located exactly at the $\ddot{I}{‡}_{c1}p$ threshold. Second, the mass of the four-star well-established $\hat{I}›(1890)$ is such that a leading Landau singularity from a triangle diagram can coincidentally appear at the $\ddot{I}{‡}_{c1}p$ threshold, and third, there is a narrow structure at the $\ddot{I}{‡}_{c1}p$ threshold but not at the $\ddot{I}{‡}_{c0}p$ and $\ddot{I}{‡}_{c2}p$ thresholds. In order to check whether that structure corresponds to a real exotic resonance, one has to measure the process $\hat{I}{›}_b^0\to K^{-}\ddot{I}{‡}_{c1}p$. If the $P_c(4450)$ structure exists in the $\ddot{I}{‡}_{c1}p$ invariant mass distribution as well, then the structure cannot be just a kinematical effect but is a real resonance, otherwise, one cannot conclude the $P_c(4450)$ to be another exotic hadron. In addition, it is also worthwhile to measure the decay $\hat{I}\yen (1S)\to J/\ddot{I}ˆp\bar{p}$: a narrow structure at 4.45 GeV but not at the $\ddot{I}{‡}_{c0}p$ and $\ddot{I}{‡}_{c2}p$ thresholds would exclude the possibility of a pure kinematical effect.

9 pages, 4 figures. Version published in PRD as a Rapid Communication