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

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

Figure 1

$B_s^0\to J/\psi p\overline{p}$ mechanisms considered in this work: (a) one-loop; (b) direct decay. Diagrams with charge-conjugated intermediate and final states are also considered.

Figure 2

Possible quark diagrams for (a),(b) $B_s^0\to Y_c\overline{p}{\overline{D}}^{(*)}$ and (c) $B_s^0\to J/\psi p\overline{p}$; $q=u$ or $d$.

Figure 3

$J/\psi p$ and $J/\psi \overline{p}$ invariant mass distributions for $B_s^0\to J/\psi p\overline{p}$. (a) Comparison with the LHCb data [65]. The red solid (blue dashed) curve is from the full model with (without) the $Y_c{\overline{D}}^{(*)}$ single-channel scattering amplitudes, augmented by experimental background (green histogram) [65] and smeared with the bin width. The dotted vertical lines indicate thresholds for, from left to right, ${\mathrm{\Lambda }}_c^{+}{\overline{D}}^0$, ${\mathrm{\Lambda }}_c^{+}{\overline{D}}^{*0}$, and ${\mathrm{\Sigma }}_c(2455{)}^{++}{D}^{-}$, respectively. The black crosses (cyan circles) are the $J/\psi p$ ($J/\psi \overline{p}$) data and are shifted by $-2\mathrm{MeV}$ ($+2\mathrm{MeV}$) along the $M_{J/\psi p(\overline{p})}$ axis for better visibility. (b) Contribution from each mechanism. The blue dashed, green dotted, and magenta dash-dotted curves are from the ${\mathrm{\Sigma }}_c\overline{D}$, ${\mathrm{\Lambda }}_c{\overline{D}}^{*}$, and ${\mathrm{\Lambda }}_c\overline{D}$ one-loop mechanisms, respectively; the corresponding charge-conjugate ${\overline{Y}}_c{D}^{(*)}$ one-loop is also included in each. The brown dash-two-dotted curve is from the direct decay mechanism. These contributions are coherently summed to give the red solid curve. The curves are not smeared.

Figure 4

(a) $p\overline{p}$ invariant mass and (b) proton helicity angle distributions for $B_s^0\to J/\psi p\overline{p}$. The other features are the same as Fig. 3.