First observation of the hidden-charm pentaquarks on lattice

Abstract

The s-wave scattering of ${\Sigma }_c\bar{D}$ and ${\Sigma }_c{\bar{D}}^{\ast }$ 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 $a\sim 0.08\mathrm{fm}$ and pion mass $M_{\pi }\sim 294\mathrm{MeV}$. The scattering amplitudes near threshold are obtained by Lüscher's finite volume method. We find bound state poles in both ${\Sigma }_c\bar{D}$ and ${\Sigma }_c{\bar{D}}^{\ast }$ channels, which are possibly related to the $P_c(4312)$ and $P_c(4440)/P_c(4457)$ pentaquarks observed in experiments. The binding energy is $6(2)(2)$MeV for ${\Sigma }_c\bar{D}$ and $7(3)(1)$MeV for ${\Sigma }_c{\bar{D}}^{\ast }$, where the first error is the statistical error and the second is the systematic error due to the lattice artifacts.

Comments: 6 pages, 3 figures