$S$-wave $D^{(\ast )}N$ molecular states: ${\Sigma }_c(2800)$ and ${\Lambda }_c(2940{)}^{+}$?

Abstract

Theoretically, some works have proposed the hadronic resonances ${\Sigma }_c(2800)$ and ${\Lambda }_c(2940{)}^{+}$ to be $S$-wave $DN$ and $D^{\ast }N$ molecular candidates, respectively. In the framework of QCD sum rules, we investigate that whether ${\Sigma }_c(2800)$ and ${\Lambda }_c(2940{)}^{+}$ could be explained as the $S$-wave $DN$ state with $J^P={\frac{1}{2}}^{-}$ and the $S$-wave $D^{\ast }N$ state with $J^P={\frac{3}{2}}^{-}$, respectively. Technically, contributions of operators up to dimension $12$ are included in the operator product expansion (OPE). The final results are $3.64\pm0.33~\mbox{GeV}$ and $3.73\pm0.35~\mbox{GeV}$ for the $S$-wave $DN$ state of $J^P={\frac{1}{2}}^{-}$ and the $S$-wave $D^{\ast }N$ state of $J^P={\frac{3}{2}}^{-}$, respectively. They are somewhat bigger than the experimental data of ${\Sigma }_c(2800)$ and ${\Lambda }_c(2940{)}^{+}$, respectively. In view of that corresponding molecular currents are constructed from local operators of hadrons, the possibility of ${\Sigma }_c(2800)$ and ${\Lambda }_c(2940{)}^{+}$ as molecular states can not be arbitrarily excluded merely from these disagreements between molecular masses using local currents and experimental data. But then these results imply that ${\Sigma }_c(2800)$ and ${\Lambda }_c(2940{)}^{+}$ could not be compact states. This may suggest a limitation of the QCD sum rule using the local current to determine whether some state is a molecular state or not. As byproducts, masses for their bottom partners are predicted to be $6.97\pm0.34~\mbox{GeV}$ for the $S$-wave $\bar{B}N$ state of $J^P={\frac{1}{2}}^{-}$ and $6.98\pm0.34~\mbox{GeV}$ for the $S$-wave ${\bar{B}}^{\ast }N$ state of $J^P={\frac{3}{2}}^{-}$.

the version accepted for publication in Phys. Rev. D; more discussions added; 12 pages, 8 eps figures

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