$J/\psi N$ interactions revisited and ${\mathrm{\Lambda }}_b^0\to J/\psi K^{-}({\pi }^{-})p$ decays

Recently LHCb experiments confirmed the findings of the two $P_c$ states in the ${\mathrm{\Lambda }}_b^0\to J/\psi p{\pi }^{-}$ decays. In the present work, we investigate both the ${\mathrm{\Lambda }}_b^0\to J/\psi K^{-}p$ and the ${\mathrm{\Lambda }}_b^0\to J/\psi p{\pi }^{-}$ decays, continuing the investigations of our former works on the interactions of $J/\psi N$ with its coupled channels by considering the s-/u-channel contributions, which are nontrivial in our results. We obtain consistent results with the previous works and the line shape of the $J/\psi N$ invariant mass distribution, which is analogous to the LHCb experiments, and favor the $P_c(4450)$ state as a ${\overline{D}}^{*}{\mathrm{\Sigma }}_c$ bound state in our theoretical model.

Figure 1

Results of the modulus squared of the amplitudes. Left: $J=1/2,I=1/2$ sector. Right: $J=3/2,I=1/2$ sector.

Figure 2

The diagrams of the s-channel (a) and u-channel (b) contributions.

Figure 3

Results of the modulus squared of the amplitudes with all the contributions from s/u channels. Left: $J=1/2,I=1/2$ sector. Right: $J=3/2,I=1/2$ sector.

Figure 4

The diagrams for the ${\mathrm{\Lambda }}_b^0\to J/\psi K^{-}({\pi }^{-})p$ decays: (a) direct $J/\psi K^{-}({\pi }^{-})p$ vertex decays at tree level; (b) final state interactions of $J/\psi p$.

Figure 5

Results of the $J/\psi p$ invariant mass distribution in the $J=1/2$ sector: upper-left panel for the ${\mathrm{\Lambda }}_b^0\to J/\psi K^{-}p$ decays and upper-right for the ${\mathrm{\Lambda }}_b^0\to J/\psi {\pi }^{-}p$ decays. The experimental results are shown in the lower panels accordingly [4, 39] and compared with the theoretical ones (solid and red lines).

Figure 6

Results of the $J/\psi p$ invariant mass distribution in the $J=3/2$ sector: Left panel for the ${\mathrm{\Lambda }}_b^0\to J/\psi K^{-}p$ decays, right for the ${\mathrm{\Lambda }}_b^0\to J/\psi {\pi }^{-}p$ decays. The solid (green) lines are evaluated with full Eq. (31), labeled as 1+GT, and the dashed (red) ones without the tree-level contributions, labeled as GT.