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We present a comparative study of the charmed baryon$-$nucleon interaction based on different theoretical approaches. For this purpose, we make use of i) a constituent quark model tuned in the light-flavor baryon$-$baryon interaction and the hadron spectra, ii) existing results in the literature based both on hadronic and quark-level descriptions, iii) (2+1)-flavor lattice QCD results of the HAL QCD Collaboration at unphysical pion masses and their effective field theory extrapolation to the physical pion mass. There is a general qualitative agreement among the different available approaches to the charmed baryon$-$nucleon interaction. Different from hadronic models based on one-boson exchange potentials, quark$-$model based results point to soft interactions without two-body bound states. They also support a negligible channel coupling, due either to tensor forces or to transitions between different physical channels, $Lambda_c N - Sigma_c N$. Short-range gluon and quark-exchange dynamics generate a slightly larger repulsion in the $^1S_0$ than in the $^3S_1$ $Lambda_c N$ partial wave. A similar asymmetry between the attraction in the two $S$ waves of the $Lambda_c N$ interaction also appears in hadronic approaches. A comparative detailed study of Pauli suppressed partial waves, as the $^1S_0 (I=1/2)$ and $^3S_1 (I=3/2)$ $Sigma_c N$ channels, would help to disentangle the short-range dynamics of two-baryon systems containing heavy flavors. The possible existence of charmed hypernuclei is discussed.
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Stimulated by the new experimental LHCb findings associated with the $Omega_c$ states, some of which we have described in a previous work as being dynamically generated through meson-baryon interaction, we have extended this approach to make predictions for new $Xi_{cc}$ molecular states in the $C=2$, $S=0$ and $I=1/2$ sector. These states manifest themselves as poles in the solution of the Bethe-Salpeter equation in coupled channels. The kernels of this equation were obtained using the Lagrangians coming from the hidden local gauge symmetry, where the interactions are dominated by the exchange of light vector mesons. The extension of this approach to the heavy sector stems from the realization that the dominant interaction corresponds to having the heavy quarks as spectators, which implies the preservation of the heavy quark symmetry. As a result, we get several states: two states from the pseudoscalar meson-baryon interaction with $J^P=1/2^-$, and masses around $4080$ and $4090$ MeV, and one at $4150$ MeV for $J^P=3/2^-$. Furthermore, from the vector meson-baryon interaction we get three states degenerate with $J^P=1/2^-$ and $3/2^-$ from $4220$ MeV to $4330$ MeV, and two more states around $4280$ MeV and $4410$ MeV, degenerate with $J^P=1/2^-,, 3/2^-$ and $5/2^-$.
The challenges with the molecular model of the multiquark systems are the identification of the hadronic molecules and the interaction between two color neutral hadrons. We study the di-hadronic molecular systems with proposed interaction potential as s-wave one boson exchange potential along with Screen Yukawa-like potential, and arrived with the proposal that within hadronic molecule the two color neutral hadrons experience the dipole-like interaction. The present study is the continuation of our previous study cite{arxiv-Rathaud-penta}. With the proposed interaction potential, the mass spectra of $Sigma_{s}K^{*}$, $Sigma_{c}K^{*}$, $Sigma_{b}K^{*}$, $Sigma_{s}D^{*}$, $Sigma_{c}D^{*}$, $Sigma_{b}D^{*}$, $Sigma_{s}B^{*}$, $Sigma_{c}B^{*}$, $Sigma_{b}B^{*}$, $Xi_{s}K^{*}$, $Xi_{c}K^{*}$, $Xi_{b}K^{*}$, $Xi_{s}D^{*}$, $Xi_{c}D^{*}$, $Xi_{b}D^{*}$, $Xi_{s}B^{*}$, $Xi_{c}B^{*}$, $Xi_{b}B^{*}$ meson-baryon molecules are predicted. The Weinberg compositeness theorem which provides clue for the compositeness of the state is used for determination of the scattering length and effective range. The present study predict $P_{c}(4450)$ pentaquark sate as $Sigma_{c}D^{*}$ molecule with $I(J^{P})=frac{1}{2}(frac{3}{2}^{-})$. The formalism also predicts some very interesting open as well as hidden flavour near threshold molecular pentaquark states.
This is an update of the two articles [H.Y. Cheng, Int. J. Mod. Phys. A {bf 24} (Suppl. 1), 593 (2009); Front. Phys. {bf 10}, 101406 (2015)] in which charmed baryon physics around 2007 and 2015, respectively, were reviewed. In this review we emphasize the experimental progress and the theoretical development since 2015.
We study two- and three-baryon systems with two units of charm looking for possible bound states or resonances. All two-baryon interactions are consistently derived from a constituent quark model tuned in the light-flavor hadron phenomenology: spectra and interactions. The presence of the heavy quarks makes the two-body interactions simpler than in the light-flavor sector. Our results show a narrow two-body resonance with quantum numbers $(I,J^P)=(0,0^+)$. It is located 6.2 MeV below the $Sigma_cSigma_c$ threshold and has a width of 4.7 MeV. The foregoing two-body state contributes to generate a $N Sigma_cSigma_c$ resonance with quantum numbers $(I,J^P)=(1/2,1/2^+)$ and a separation energy of 0.2 MeV.
Charm spectroscopy has studied under a string model. Charmed baryons are composed of diquark and charm quark which are connected by a constant tension. In a diquark picture, the quantum numbers $J^P$ of confirmed baryons are well assigned. We give energy predictions for the first and second orbital excitations. We see some correspondences with the experimental data. Meanwhile, we have obtained diquark masses in the background of charm quark which satisfy a splitting relation based on spin-spin interaction.
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