Combining heavy quark spin and local hidden gauge symmetries in the dynamical generation of hidden charm baryons

Abstract

We present a coupled channel unitary approach to obtain states dynamically generated from the meson baryon interaction with hidden charm, using constraints of heavy quark spin symmetry. We use as basis of states, $\bar D B$, $\bar D^* B$ states, with $B$ baryon charmed states belonging to the 20 representations of SU(4) with $J^P=1/2^+,~3/2^+$. In addition we also include the $η_c N$ and $J/ψN$ states. The inclusion of these coupled channels is demanded by heavy quark spin symmetry, since in the large $m_Q$ limit the $D$ and $D^*$ states are degenerate and are obtained from each other by means of a spin rotation, under which QCD is invariant. The novelty in the work is that we use dynamics from the extrapolation of the local hidden gauge model to SU(4) and we show that this dynamics fully respects the constraints of heavy quark spin symmetry. With the full space of states demanded by the heavy quark spin symmetry and the dynamics of the local hidden gauge we look for states dynamically generated and find four basic states which are bound, corresponding to $\bar D Σ_c$, $\bar D Σ_c^*$, $\bar D^* Σ_c$ and $\bar D^* Σ_c^*$, decaying mostly into $η_c N$ and $J/ψN$. All the states appear in isospin $I=1/2$ and we find no bound states or resonances in $I=3/2$. The $\bar D Σ_c$ state appears in $J=1/2$, the $\bar D Σ_c^*$ in $J=3/2$, the $\bar D^* Σ_c$ appears nearly degenerate in $J=1/2, ~3/2$ and the $\bar D^* Σ_c^*$ appears nearly degenerate in $J=1/2, ~3/2, ~5/2$, with the peculiarity that in $J=5/2$ the state has zero width in the space of states chosen. All the states are bound with about 50 MeV with respect to the corresponding $\bar D B$ thresholds and the width, except for the $J=5/2$ state, is also of the same order of magnitude.