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26 April 2024 |
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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 | Abstract: | The 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 | Services: | Forum | Review | PDF | Favorites |
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