$N\bar D $ system: A challenge for $\bar {\rm P}$ANDA

Abstract

We study the $N \bar D$ system by means of a chiral constituent quark model. This model, tuned in the description of the baryon and meson spectra as well as the $NN$ interaction, provides parameter-free predictions for the charm -1 two-hadron systems. The presence of a heavy antiquark makes the interaction rather simple. We have found sharp quark-Pauli effects in some particular channels, generating repulsion, due to lacking degrees of freedom to accommodate the light quarks. Our results point to the existence of an attractive state, the $\Delta \bar D^*$ with $(T,S)=(1,5/2)$, presenting a resonance close to threshold. It would show up in the scattering of $\bar D$ mesons on nucleons as a D wave state with quantum numbers $(T)J^P=(1)5/2^-$. This resonance resembles our findings in the $\Delta\Delta$ system, that offered a plausible explanation to the cross section of double-pionic fusion reactions through the so-called {\it ABC} effect. The study of the interaction of $D$ mesons with nucleons is a goal of the $\bar {\rm P}$ANDA Collaboration at the European facility FAIR and, thus, the present theoretical study is a challenge to be tested at the future experiments.