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

Abstract

The LHCb Collaboration announced two pentaquark-like structures in the $J/\psi p$ 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 ${\chi }_{c1}p$ to $J/\psi p$: First, it is located exactly at the ${\chi }_{c1}p$ threshold. Second, the mass of the four-star well-established $\Lambda (1890)$ is such that a leading Landau singularity from a triangle diagram can coincidentally appear at the ${\chi }_{c1}p$ threshold, and third, there is a narrow structure at the ${\chi }_{c1}p$ threshold but not at the ${\chi }_{c0}p$ and ${\chi }_{c2}p$ thresholds. In order to check whether that structure corresponds to a real exotic resonance, one has to measure the process ${\Lambda }_b^0\to K^{-}{\chi }_{c1}p$. If the $P_c(4450)$ structure exists in the ${\chi }_{c1}p$ 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 ${\rm Y}(1S)\to J/\psi p\bar{p}$: a narrow structure at 4.45 GeV but not at the ${\chi }_{c0}p$ and ${\chi }_{c2}p$ thresholds would exclude the possibility of a pure kinematical effect.

arXiv comment9 pages, 4 figures. Version published in PRD as a Rapid Communication

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