Hidden charm pentaquark states and Σc(D)over-bar(*) interaction in chiral perturbation theory

In this work, we employ the heavy hadron chiral perturbation theory to calculate the Sigma(c)(D) over bar (()*()) potentials to the next-to-leading order. The contact, the one-pion exchange, and the two-pion exchange interactions are all included in the calculation along with the mass splittings between the heavy quark spin symmetry partner states. Our result shows that neglecting the heavy quark symmetry violation effect may be misleading to predict the potentials between the charmed hadrons. We perform numerical analysis with three scenarios. In the first scenario, we relate the low-energy constants (LECs) in the contact terms of Sigma(c)(D) over bar (()*()) to those of nucleon systems and reproduce the P-c(4312) and P-c(4440) as loosely bound states. In the second scenario, we vary the unknown LECs and find a small parameter region in which P-c(4312), P-c(4440) and P-c(4457)can coexist as molecular states. In the third scenario, we include the coupled-channel effect on the basis of scenario II and notice that the three P-c states can be reproduced as molecular states simultaneously in a large region of parameters. Our analytical results can be used for the chiral extrapolations in lattice QCD. With the lattice QCD results in the future as inputs, the identification of the P-c states and predictions for other systems would be more reliable.