$P_c(4312{)}^{+}$ and $P_c(4337{)}^{+}$ as interfering ${\Sigma }_c\bar{D}$ and ${\Lambda }_c{\bar{D}}^{\ast }$ threshold cusps

Abstract

The recent LHCb data on $B_s^0\to J/\psi p\bar{p}$ revealed a new pentaquark-like $P_c(4337{)}^{+}$ structure, while finding no evidence for $P_c(4312{)}^{+}$ discovered earlier in ${\Lambda }_b^0\to J/\psi p{K}^{-}$. Though puzzling, the data actually offer an important hint to understand the nature of the pentaquark candidates. We develop a model to analyze the $B_s^0\to J/\psi p\bar{p}$ data. We find that a ${\Sigma }_c\bar{D}$ one-loop mechanism causes a threshold cusp that fits well the $P_c(4337{)}^{+}$ peak. Also, the ${\Sigma }_c\bar{D}$ and ${\Lambda }_c{\bar{D}}^{\ast }$ threshold cusps interfere with each other to reproduce an oscillating behavior in the proton helicity angle distribution. These results combined with our earlier analysis on ${\Lambda }_b^0\to J/\psi p{K}^{-}$ indicate that $P_c(4312{)}^{+}$ and $P_c(4337{)}^{+}$ are created by different interference patterns between the ${\Sigma }_c\bar{D}$ and ${\Lambda }_c{\bar{D}}^{\ast }$ (anomalous) threshold cusps. The proposed scenario consistently explains why the $P_c(4312{)}^{+}$ and $P_c(4337{)}^{+}$ peaks appear in ${\Lambda }_b^0\to J/\psi p{K}^{-}$ and $B_s^0\to J/\psi p\bar{p}$, respectively, but not vice versa or both.

Comments: 7 pages, 4 figures; (v2) published version, title changed, one paragraph added in Sec. 2, references added