$S$-wave $D^{(*)}N$ molecular states: $Σ_{c}(2800)$ and $Λ_{c}(2940)^{+}$?

Theoretically, some works have proposed the hadronic resonances $Σ_{c}(2800)$ and $Λ_{c}(2940)^{+}$ to be $S$-wave $DN$ and $D^{*}N$ molecular candidates, respectively. In the framework of QCD sum rules, we investigate that whether $Σ_{c}(2800)$ and $Λ_{c}(2940)^{+}$ could be explained as the $S$-wave $DN$ state with $J^{P}=\frac{1}{2}^{-}$ and the $S$-wave $D^{*}N$ 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 $D^{*}N$ state of $J^{P}=\frac{3}{2}^{-}$, respectively. They are somewhat bigger than the experimental data of $Σ_{c}(2800)$ and $Λ_{c}(2940)^{+}$, respectively. In view of that corresponding molecular currents are constructed from local operators of hadrons, the possibility of $Σ_c(2800)$ and $Λ_{c}(2940)^{+}$ 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 $Σ_{c}(2800)$ and $Λ_{c}(2940)^{+}$ 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 $\bar{B}^{*}N$ state of $J^{P}=\frac{3}{2}^{-}$.

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