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Study on the possible molecular states composed of $\Lambda_c\bar D^*$, $\Sigma_c\bar D^*$, $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$ in the Bethe-Salpeter frame based on the pentaquark states $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$
High Energy Physics - Phenomenology · Submitted 1 Aug 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The conclusion that two $\Xi_c\bar D^*$ bound states exist, supports the suggestion that the observed peak of $P_{cs}(4459)$ may hide two states $P_{cs}(4455)$ and $P_{cs}(4468)$.
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The measurements on a few pentaquarks states $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$ excite our new interests about their structures. Since the masses of $P_c(4440)$ and $P_c(4457)$ are close to the threshold of $\Sigma_c\bar D^*$, in the earlier works, they were regarded as molecular states of $\Sigma_c\bar D^*$ with quantum numbers $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and $\frac{1}{2}(\frac{3}{2}^-)$, respectively. In a similar way $P_{cs}(4459)$ is naturally considered as a $\Xi_c\bar D^*$ bound state with $I=0$. Within the Bethe-Salpeter (B-S) framework we systematically study the possible bound states of $\Lambda_c\bar D^*$, $\Sigma_c\bar D^*$, $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$. Our results indicate that $\Sigma_c\bar D^*$ can form a bound state with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$, which corresponds to $P_c(4440)$. However for the $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$ system the attraction between $\Sigma_c$ and $\bar D^*$ is too weak to constitute a molecule, so $P_{c}(4457)$ may not be a bound state of $\Sigma_c\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. As $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$ systems we take into account of the mixing between $\Xi_c$ and $\Xi'_c$ and the eigenstets should include two normal bound states $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and a loosely bound state $\Xi_c\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. The conclusion that two $\Xi_c\bar D^*$ bound states exist, supports the suggestion that the observed peak of $P_{cs}(4459)$ may hide two states $P_{cs}(4455)$ and $P_{cs}(4468)$. Based on the computations we predict a bound state $\Xi_c'\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ but not that with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. Further more accurate experiments will test our approach and results.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The measurements on a few pentaquarks states $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$ excite our new interests about their structures. | background 1.00 | 0.05 | 0.01 | asserted 0.98 |
| s1 | Since the masses of $P_c(4440)$ and $P_c(4457)$ are close to the threshold of $\Sigma_c\bar D^*$, in the earlier works, they were regarded as molecular states of $\Sigma_c\bar D^*$ with quantum numbers $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and $\frac{1}{2}(\frac{3}{2}^-)$, respectively. | background 1.00 | 0.04 | 0.03 | asserted 0.94 |
| s2 | In a similar way $P_{cs}(4459)$ is naturally considered as a $\Xi_c\bar D^*$ bound state with $I=0$. | background 1.00 | 0.07 | 0.03 | asserted 0.70 |
| s3 | Within the Bethe-Salpeter (B-S) framework we systematically study the possible bound states of $\Lambda_c\bar D^*$, $\Sigma_c\bar D^*$, $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$. | contribution 0.82 | 0.93 | 0.05 | asserted 0.92 |
| s4 | Our results indicate that $\Sigma_c\bar D^*$ can form a bound state with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$, which corresponds to $P_c(4440)$. | result 0.99 | 0.94 | 0.20 | asserted 0.57 |
| s5 | However for the $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$ system the attraction between $\Sigma_c$ and $\bar D^*$ is too weak to constitute a molecule, so $P_{c}(4457)$ may not be a bound state of $\Sigma_c\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. | result 0.80 | 0.91 | 0.15 | hedged possibility 0.96 |
| s6 | As $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$ systems we take into account of the mixing between $\Xi_c$ and $\Xi'_c$ and the eigenstets should include two normal bound states $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and a loosely bound state $\Xi_c\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. | result 0.95 | 0.89 | 0.15 | asserted 0.98 |
| s7 | The conclusion that two $\Xi_c\bar D^*$ bound states exist, supports the suggestion that the observed peak of $P_{cs}(4459)$ may hide two states $P_{cs}(4455)$ and $P_{cs}(4468)$. | interpretation 0.98 | 0.65 | 0.21 | hedged possibility 0.86 |
| s8 | Based on the computations we predict a bound state $\Xi_c'\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ but not that with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. | result 1.00 | 0.94 | 0.16 | asserted 0.93 |
| s9 | Further more accurate experiments will test our approach and results. | future work 1.00 | 0.07 | 0.02 | hedged possibility 0.52 |
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The paper
Original abstract
The measurements on a few pentaquarks states $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$ excite our new interests about their structures. Since the masses of $P_c(4440)$ and $P_c(4457)$ are close to the threshold of $\Sigma_c\bar D^*$, in the earlier works, they were regarded as molecular states of $\Sigma_c\bar D^*$ with quantum numbers $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and $\frac{1}{2}(\frac{3}{2}^-)$, respectively. In a similar way $P_{cs}(4459)$ is naturally considered as a $\Xi_c\bar D^*$ bound state with $I=0$. Within the Bethe-Salpeter (B-S) framework we systematically study the possible bound states of $\Lambda_c\bar D^*$, $\Sigma_c\bar D^*$, $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$. Our results indicate that $\Sigma_c\bar D^*$ can form a bound state with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$, which corresponds to $P_c(4440)$. However for the $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$ system the attraction between $\Sigma_c$ and $\bar D^*$ is too weak to constitute a molecule, so $P_{c}(4457)$ may not be a bound state of $\Sigma_c\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. As $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$ systems we take into account of the mixing between $\Xi_c$ and $\Xi'_c$ and the eigenstets should include two normal bound states $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and a loosely bound state $\Xi_c\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. The conclusion that two $\Xi_c\bar D^*$ bound states exist, supports the suggestion that the observed peak of $P_{cs}(4459)$ may hide two states $P_{cs}(4455)$ and $P_{cs}(4468)$. Based on the computations we predict a bound state $\Xi_c'\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ but not that with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. Further more accurate experiments will test our approach and results.
Human review
References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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Two $\Xi_c \bar{D}^{*} $ molecular states are produced with spin parities $ J^P=1/2^-$ and $3/2^- $.
Papers citing it
Cites it as background 2 papers
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Besides the compact model, there is an alternative literature in which pentaquarks are described as meson-baryon molecules [ref] .
A Simple Model of Pentaquarks · Introduction · 0.98
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In addition, several additional exotic states in the hidden-charm pentaquark sector with strange quark content are theoretically proposed in Refs. [ref] .
Hidden-charm pentaquarks with strangeness in a chiral quark model · INTRODUCTION · 0.93
What it cites · 38 sentences without a confident label
Uses data or values from 3 papers
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In Ref. [ref] we fix the value of $θ$ to be $16.27^∘$ using the data of $Γ(Ξ_cc→Ξ_c)/Γ(Ξ_cc→Ξ'_c)$ .
Revisiting the transition $\Xi^{+}_{cc}\to\Xi^{(')+}_c$ to understand the data from LHCb · the numerical results on $Ξ_cD̅^*$ and $Ξ'_cD̅^*$ · 0.81
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In the flavor $SU(3)$ symmetry and heavy quark limit, the above coupling constants are given by$g__D^*D^*σ=2g_σM_D^*,$ $g__D^*D^*P=2g/f_π,$ $g__D̅^*D̅^*V=βg_V/√(2), g'__D̅^*D̅^*V=2√(2)λg_V M_D^*$ with $g_σ=-0.76$ [ref] , $f_π=132$ MeV [ref] , $β=0.9$, $g_V=5.9$ [ref] and $λ=0.56$ GeV$^-1$ [ref] .
Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks · The effective interactions · 1.00
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In the flavor $SU(3)$ symmetry and heavy quark limit, the above coupling constants are given by$g__D^*D^*σ=2g_σM_D^*,$ $g__D^*D^*P=2g/f_π,$ $g__D̅^*D̅^*V=βg_V/√(2), g'__D̅^*D̅^*V=2√(2)λg_V M_D^*$ with $g_σ=-0.76$ [ref] , $f_π=132$ MeV [ref] , $β=0.9$, $g_V=5.9$ [ref] and $λ=0.56$ GeV$^-1$ [ref] .
Chiral Multiplets of Heavy-Light Mesons · The effective interactions · 1.00
Compares with 1 paper
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In Ref. [ref] with the coupled channel effect being taken into account for their initial results, the values of $Λ$ apparently changed and the degeneration between the two states $I(J^P)=0(1/2^-)$ and $0(3/2^-)$ disappeared.
Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^\Lambda(4338)$ and $P_{cs}(4459)$ · the numerical results on $Ξ_cD̅^*$ and $Ξ'_cD̅^*$ · 0.93
Cites as support 2 papers
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If the structure includes two states: $P_cs(4455)$ and $P_cs(4468)$ they are just corresponding to two states of $Ξ_cD̅^*$ with $I(J^P)=0(1/2^-)$ and $0(3/2^-)$, it seems the suggestion in Refs. [ref] is reasonable.
New strange pentaquarks · the numerical results on $Ξ_cD̅^*$ and $Ξ'_cD̅^*$ · 0.99
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If the structure includes two states: $P_cs(4455)$ and $P_cs(4468)$ they are just corresponding to two states of $Ξ_cD̅^*$ with $I(J^P)=0(1/2^-)$ and $0(3/2^-)$, it seems the suggestion in Refs. [ref] is reasonable.
Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^\Lambda(4338)$ and $P_{cs}(4459)$ · the numerical results on $Ξ_cD̅^*$ and $Ξ'_cD̅^*$ · 0.99
Cites as background 27 papers
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There have been many papers which address to these hidden charm pentaquark states [ref] .
A comparison between the $P_c$ and $P_{cs}$ systems · Introduction · 0.97
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There have been many papers which address to these hidden charm pentaquark states [ref] .
Possible interpretations of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ · Introduction · 0.97
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There have been many papers which address to these hidden charm pentaquark states [ref] .
Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks · Introduction · 0.97
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