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26 April 2024
 
  » arxiv » 2102.07159

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Revisiting the nature of the $P_c$ pentaquarks
Meng-Lin Du ; Vadim Baru ; Feng-Kun Guo ; Christoph Hanhart ; Ulf-G. Meißner ; José A. Oller ; Qian Wang ;
Date 14 Feb 2021
AbstractThe nature of the three narrow hidden-charm pentaquark $P_c$ states is under intense discussion since their discovery from the updated analysis of the process $Lambda_b^0 o J/psi pK^-$ by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)] by including the $Lambda_car{D}^{(*)}$ and $eta_cp$ explicitly as required by unitarity and HQSS, respectively. Three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic and inelastic channels and without the $Lambda_car D^{(*)}$ interactions, (b) scheme II, where the OPE is added to scheme I, and (c) scheme III, where the $Lambda_car D^{(*)}$ interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with $S$-wave-to-$D$-wave mixing contact terms. As a result we demonstrate that the experimental data are consistent with the interpretation of the $P_c(4312)$ and $P_c(4440)/P_c(4457)$ as $Sigma_car{D}$ and $Sigma_c ar{D}^{*}$ molecules, respectively, and that the data show clear evidence for a new narrow state, $P_c(4380)$, identified as a $Sigma_c^*ar D$ molecule, which should exist as a consequence of HQSS. However, now two solutions are found in all schemes which describe the data equally well, and thus no unambiguous conclusion about the quantum numbers of the $P_c(4440)$ and $P_c(4457)$ from data in the $J/psi p$ channel alone is possible. It is argued that one of these solutions, in which the quantum numbers of the $P_c(4440)$ and $P_c(4457)$ are $J^P=3/2^-$ and $1/2^-$, respectively, is theoretically preferred. Moreover, we demonstrate that the line shapes related to the $P_c(4440)$ and $P_c(4457)$ in the $Sigma_c^{(*)}ar{D}$ and $eta_cp$ mass distributions will allow one to pin down their quantum numbers once the data are available.
Source arXiv, 2102.07159
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