Investigating charmed hybrid baryons via QCD sum rules

Motivated by recent interpretations of the $\eta_1(1855)$ and $X(2370)$ as a hybrid meson and a glueball, respectively, the possible existence of hybrid baryons has become a subject of considerable interest. In this letter, we investigate charmed hybrid baryons using the QCD sum rule method within the framework of heavy quark effective theory. We construct twenty-eight interpolating currents for charmed hybrid baryons, seven of which are employed in QCD sum rule analyses of nineteen states with quark-gluon configurations $qqcg$, $qscg$, and $sscg$ ($q = u/d$). The masses of the lowest-lying charmed hybrid baryons in the $SU(3)$ flavor $\mathbf{6}_F$ representation are calculated to be $M_{\Sigma_{cg}(1/2^+)} = 3.46^{+0.33}_{-0.21}~\rm{GeV}$, $M_{\Xi^\prime_{cg}(1/2^+)} = 3.60^{+0.48}_{-0.16}~\rm{GeV}$, and $M_{\Omega_{cg}(1/2^+)} = 3.77^{+0.31}_{-0.16}~\rm{GeV}$. We propose that future experiments search for these states via their $P$-wave decay channels $ND^{(*)}$, $\Lambda D^{(*)}$, and $\Xi D^{(*)}$, respectively. Such investigations would provide valuable insight into the role of gluonic excitations in hadron structure.