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We propose a novel scenario for the peak structures, usually interpreted ashidden charm pentaquark ($P_c$) contributions, in the LHCb's $\Lambda_b^0\toJ/\psi p K^-$ data. The key idea is to utilize leading or lower-ordersingularities from double triangle mechanisms. The singularities causeanomalous threshold cusps, which are significantly more singular than theordinary ones, at the $\Sigma_c^{(*)}\bar{D}^{(*)}$ threshold. We demonstratethat the double triangle amplitudes interfere with other common mechanisms tocreate peak structure that fit well the $P_c(4312)^+$, $P_c(4380)^+$, and$P_c(4457)^+$ peaks in the data. This picture is completely different fromcommonly used ones such as hadron molecules and compact pentaquarks. Meanwhile,$P_c(4440)^+$ is included in the proposed model as a resonance with width andstrength significantly smaller than previously estimated. The proposed modelcan (partly) explain the current data for other processes where $P_c^+$ signalsare expected such as: no $P_c^+$ signals in the GlueX $J/\psi$ photoproductiondata; a possible signal only from $P_c(4440)^+$ in the LHCb's $\Lambda_b^0\toJ/\psi p \pi^-$ data.

Novel description of $P_c(4312)^+$, $P_c(4380)^+$, and $P_c(4457)^+$ with double triangle cusps