In a chromomagnetic model, we analyse the properties of the newly observed $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ states. We estimate the masses of the $(uud)_{ 8_c}(c\bar{ c})_{ 8_c}$ and $(uds)_{ 8_c}(c\bar{ c})_{ 8_c}$ pentaquark states by considering the isospin breaking effects. Their values are determined by calculating mass distances from the $\Sigma_c^{ ++}D^-$ and $\Xi_c^{ \prime+}D^-$ thresholds, respectively. It is found that the isospin breaking effects on the spectrum are small. From the uncertainty consideration and the rearrangement decay properties in a simple model, we find that it is possible to assign the $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ as $J^P=3/2^-$, $1/2^-$, and $3/2^-$ pentaquark states, respectively. The assignment in the molecule picture can be different, in particular for the $P_c(4312)^+$. The information from open-charm channels, e.g. ${ \cal B}[P_c\to\Sigma_c^{ ++}D^-]/{ \cal B}[P_c\to J/\psi p]$, will play an important role in distinguishing the inner structures of the $P_c$ states. Discussions and predictions based on the calculations are also given.
Categories: hep-ph hep-ex hep-lat nucl-th
