Multiquark study of exotic open bottom baryonic states

We present a simultaneous study of baryon-meson systems containing a bottom degree of freedom, either as a quark or as an antiquark. This produces two different types of structures: the $NB$ system, subject to quark antisymmetry effects and whose existence would generate explicit exotic states; and the $N\overline{B}$ system, subject to the coupling to heavy baryon–light meson systems and whose existence would represent a higher Fock space component of the bottom baryon spectrum. Both systems have been studied within the framework of a full-fledged chiral constituent quark model tuned in the description of the baryon and meson spectra and the $NN$ interaction. Although the masses of the constituents are larger than its partners in the charm sector, we do not observe a proliferation of bound states. This is due to the coupled-channel mechanism that governs the dynamics for most spin-isospin channels, and requires, in order to have a bound state, several conditions that are difficult to be met at the same time. Our results point to the existence of a deep $NB$ bound state in the $(T)J^P=(2)3/2^{-}$ channel, as a consequence of the reduction of the mass difference between pseudoscalar and vector mesons when the mass of the heavy quark increases. The same effect gives rise to a resonance at threshold in the $(T)J^P=(0)1/2^{-}$ channel, the best candidate for an exotic state among the channels that do not contain a $\mathrm{\Delta }$ isobar. In the $N\overline{B}$ system, a few channels may lodge molecular or compact hadrons with a five-quark structure, being specially suited the $(T)J^P=(0)1/2^{-}$ and $(T)J^P=(1)5/2^{-}$ channels.

Figure 1

Fredholm determinant of channels: (a) $(T,J)=(1,5/2)$, (b) $(T,J)=(2,3/2)$, for $N\overline{D}$ (solid lines) and $NB$ (dashed lines) systems.

Figure 2

Comparison of the energy gaps between different thresholds contributing to a given $(T,J)$ channel in the charm and bottom sectors. Note that the energies of the charm sector are referred to the mass of the $N\overline{D}$ state while those of the bottom sector are referred to the mass of the $NB$ state.

Figure 3

Binding energy of channel $\mathrm{\Delta }\overline{D}$ $(T,J)=(2,3/2)$ as a function of the $\mathrm{\Delta }\overline{D}-\mathrm{\Delta }{\overline{D}}^{*}$ mass difference.

Figure 4

Dependence on the Gaussian parameter of the wave function of the heavy quark, ${\tilde{b}}^{\prime }$, of: (a) Binding energy of the $(T,J)=(1,5/2)$ channel; (b) Fredholm determinant at zero energy of the $(T,J)=(0,3/2)$ channel.

Figure 5

Masses and quantum numbers of $N\overline{B}$ molecular states. The dashed lines stand for the different two-hadron thresholds.

Figure 6

Diagram representing the coupling between a light baryon–bottom meson and a bottom baryon–light meson two-hadron systems.

Figure 7

Different two-body channels contributing to each set of $(T,J)$ quantum numbers as shown in Table 1.

Figure 8

Masses and quantum numbers of compact five-quark states. The dashed lines stand for the different two-hadron thresholds.