First observation of the hidden-charm pentaquarks on lattice

The s-wave scattering of ${\mathrm{\Sigma }}_c\bar{D}$ and ${\mathrm{\Sigma }}_c{\bar{D}}^{\ast }$ in the $I(J^P)=\frac{1}{2}({\frac{1}{2}}^{-})$ channel is calculated in lattice QCD using two ensembles with different volumes but the same lattice spacing $a\sim 0.08\mathrm{f}\mathrm{m}$ and pion mass $M_{\pi }\sim 294\mathrm{M}\mathrm{e}\mathrm{V}$. The scattering amplitudes near threshold are obtained by Lüscher’s finite volume method. We find bound state poles in both ${\mathrm{\Sigma }}_c\bar{D}$ and ${\mathrm{\Sigma }}_c{\bar{D}}^{\ast }$ channels, which are possibly related to the $P_c(4312)$ and $P_c(4440)\mathrm{/}{P}_c(4457)$ pentaquarks observed in experiments. The binding energy is $6(2)(2)$MeV for ${\mathrm{\Sigma }}_c\bar{D}$ and $7(3)(1)$MeV for ${\mathrm{\Sigma }}_c{\bar{D}}^{\ast }$, where the first error is the statistical error and the second is the systematic error due to the lattice artifacts.