Abstract
We perform a systematic study on the interactions of the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems within the framework of chiral effective field theory. We introduce the contact term, one-pion-exchange and two-pion-exchange contributions to describe the short-, long-, and intermediate-range interactions. The low energy constants of the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems are estimated from the $N\overline{N}$ scattering data by introducing a quark level Lagrangian. With three solutions of LECs, all the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems with isospin $I=1/2$ can form bound states, in which different inputs of LECs may lead to distinguishable mass spectra. In addition, we also investigate the interactions of the charmed-bottom ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{\overline{B}}^{(*)}$, ${\mathrm{\ensuremath{\Sigma}}}_{b}^{(*)}{D}^{(*)}$, and ${\mathrm{\ensuremath{\Sigma}}}_{b}^{(*)}{\overline{B}}^{(*)}$ systems. Among the obtained bound states, the bindings become deeper when the reduced masses of the corresponding systems are heavier.
Highlights
The existence of the qqqqqpentaquarks are proposed by Gell-Mann and Zweig [1,2,3] at the birth of the quark model in 1964
In Refs. [18,53,54], we proposed an approach which can relate the contact effective potentials derived at the hadron level to those derived at the quark level, so that the low energy constants (LECs) can be determined from the quark model
Inspired by the recently observed Pc [10] and Pcs [14] pentaquarks, we perform a systematic study on the interactions of the ΣðcÃÞDðÃÞ systems to explore the possible Pcc states
Summary
The existence of the qqqqqpentaquarks are proposed by Gell-Mann and Zweig [1,2,3] at the birth of the quark model in 1964. Based on the compact pentaquark configuration, the mass spectra of the pentaquarks with QQqqq (Q 1⁄4 b, c, and q 1⁄4 u, d, s) quark components were estimated systematically in the framework of the color-magnetic interaction model [28]. The chiral quark model [30] and QCD sum rule [31] were exploited to analyze the doubly charmed pentaquark states. Qualitatively capture some features of the double-charm pentaquarks from above works, while a systematic study of the ΣðcÃÞDðÃÞ systems is still absent. In the framework of heavy hadron chiral effective theory, we consider the one-pion-exchange, two-pion-exchange, and contact contributions to account for the long-, intermediate-, and short-range interactions of the ΣðcÃÞDðÃÞ systems, respectively. Some supplemental materials for loop diagrams and the results for charmed-bottom systems are given in the Appendixes A and B, respectively
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