Deciphering the production mechanism of the LHCb $P_c$ states

Abstract: The three narrow pentaquarks $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ observed by LHCb are widely interpreted as hadronic molecules owing to their proximity to the $Σ<em>c\bar{D}<sup>{(*)}$ thresholds. However, heavy-quark spin symmetry predicts additional partner states that have not been seen experimentally, making the production mechanism in $Λ_b<sup>0$ decays particularly important in understanding their nature. We propose a novel production mechanism, which can naturally explain why only these three LHCb $P_c$ states have been clearly observed. The $P_c(4440)$ and $P_c(4457)$ are produced via the $D</em>{s1}<sup>*(2860)Λ_c(2595)\bar{D}π$ box diagram leading to $K<sup>-Σ_c\bar{D}<sup>{*}$, followed by rescattering into $K^- J/ψp$. The box diagram develops a box singularity in the vicinity of the $P_c(4457)$, as all four states in the box can go on shell. The $P_c$ states themselves are dynamically generated through the rescattering of the $S$-wave $Σ<em>c\bar{D}<sup>{(*)}$ to $J/ψp$. The $P_c(4312)$ proceeds analogously via the $D</em>{s0}(2590)Λ<em>c(2595)\bar{D}<sup>*π$ box diagram but without a box singularity. The near-invisibility of the $Σ_c<sup><em>\bar{D}^{(</em>)}$ molecular states is attributed to the suppressed production of the $Λ_c(2625)$ in $Λ_b$ weak decays, as established by the lattice QCD calculations. This mechanism naturally reproduces the data with only two production parameters, whereas previous works required 7 parameters and a finely tuned background, and provides a natural explanation for why the $Σ_c<sup><em>\bar{D}^{(</em>)}$ states are barely visible. It yields unique, falsifiable predictions, $$Γ(Λ_b^0\to P_c(4440/4457) K\to J/ψp K)/Γ(Λ_b^0\to\bar D</em>{s1}^{*(2860)Λ_c(2595))\approx} (0.2-0.4)\%$$, $$Γ(Λ<em>b^0\to P_c(4312) K\to J/ψp K)/Γ(Λ_b^0\to \bar D</em>{s0}(2590)Λ_c(2595))\approx (0.2-0.8)\%$$.