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

TL;DR

This study uses QCD sum rules to investigate whether the hadronic resonances $ ext{Σ}_c(2800)$ and $ ext{Λ}_c(2940)^+$ can be explained as $S$-wave $DN$ and $D^*N$ molecular states, finding their masses slightly larger than experimental data.

Contribution

It applies QCD sum rules with operators up to dimension 12 to analyze the molecular nature of specific charmed baryons, highlighting limitations of local current approaches.

Findings

Masses are slightly larger than experimental data.

Molecular states are unlikely to be compact states.

Predicted bottom partner masses are provided.

Abstract

Theoretically, some works have proposed the hadronic resonances $\Sigma_{c}(2800)$ and $\Lambda_{c}(2940)^{+}$ to be $S$-wave $DN$ and $D^{*}N$ 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 $D^{*}N$ 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 $\Sigma_{c}(2800)$ 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 $\bar{B}^{*}N$ state of $J^{P}=\frac{3}{2}^{-}$.