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

TL;DR

This paper develops a coupled channel approach respecting heavy quark spin symmetry to dynamically generate hidden charm baryons, predicting four bound states with specific quantum numbers and decay properties.

Contribution

It introduces a novel application of the local hidden gauge model extrapolated to SU(4), fully respecting heavy quark spin symmetry, to predict hidden charm baryon states.

Findings

Four bound states generated with about 50 MeV binding energy.

States decay mainly into $ar D B$ channels, specifically $ar D ightarrow ar D ext{ and } ar D^*$.

No bound states found in isospin 3/2 channel.

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 $\eta_c N$ and $J/\psi N$ 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 $\bar D \Sigma_c$, $\bar D \Sigma_c^*$, $\bar D^* \Sigma_c$ and $\bar D^* \Sigma_c^*$, decaying mostly into $\eta_c N$ and $J/\psi N$. All the states appear in isospin $I=1/2$ and we find no bound states or resonances in $I=3/2$. The $\bar D \Sigma_c$ state appears in $J=1/2$, the $\bar D \Sigma_c^*$ in $J=3/2$, the $\bar D^* \Sigma_c$ appears nearly degenerate in $J=1/2, ~3/2$ and the $\bar D^* \Sigma_c^*$ 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.