Abstract
In this work, we employ the heavy hadron chiral perturbation theory (HHChPT) to calculate the $\Sigma_c\bar{D}^{(*)}$ potentials to the next-to-leading order. The contact, the one-pion exchange and the two-pion exchange interactions are included. Besides, the mass splittings between the heavy quark spin symmetry (HQSS) multiplets are kept in calculations. Our result shows that neglecting the heavy quark symmetry (HQS) 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 $\Sigma_c\bar{D}^{(*)}$ 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.
Highlights
The multiquark state has been a very important topic in hadron physics for a long time
Our result shows that neglecting the heavy quark symmetry violation effect may be misleading to predict the potentials between the charmed hadrons
In scenario II, we will assume the three structures observed in LHCb corresponding to three molecular states and check whether they can coexist in our framework
Summary
The multiquark state has been a very important topic in hadron physics for a long time (for recent reviews, see Refs. [1,2,3,4,5]). A new state Pcð4312Þ was observed with 7.3σ significance, and these three states are all measured to be narrow The masses of these resonances lie below the thresholds of ΣcDand ΣcD Ã, respectively. The deutron was well established as a hadronic molecular state in the framework of the OBE model [29]. The impacts of the HQS breaking effect on the heavy molecular states are rarely estimated. We derive the potentials between Σc and DðÃÞ in the framework of the heavy hadron chiral perturbation theory (HHCPT). In Appendix B, we present the loop integral functions we used
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