Two-body strong decays and experimental search channels of the predicted compact isovector hidden-charm-singly-strange pentaquark states $P_{cs}^{+}(uusc\bar{c})$

A QCD sum-rule analysis of diquark-diquark-antiquark currents with valence content $uusc\bar{c}$, with the light quarks $uus$ arranged in two flavor octets, predicts a spectrum of 18 compact isovector ($I=1$) hidden-charm-singly-strange pentaquark states $P_{cs}^{+}$ with $IJ^{P}=1\,\frac{1}{2}^{-}$, $1\,\frac{3}{2}^{-}$ and $1\,\frac{5}{2}^{-}$ and masses between 4.35 and 4.59 GeV, together with their pole residues — but leaves their two-body strong-decay widths uncalculated, the consequences of $\mathbf{8}_{1}$–$\mathbf{8}_{2}$ octet mixing unresolved, and the proposed experimental search chains $\Sigma_{b}^{+}\to P_{cs}^{+}\phi\to J/\psi\Sigma^{+}\phi$ and $\Xi_{b}^{0}\to P_{cs}^{+}K^{-}\to J/\psi\Sigma^{+}K^{-}$ unperformed. The problem is to compute the partial decay widths and channel hierarchy of this predicted spectrum into the possible two-body channels ($\eta_{c}\Sigma$, $J/\psi\Sigma$, $\bar{D}\Xi_{c}$, $\bar{D}^{*}\Xi_{c}$, $\bar{D}_{s}\Sigma_{c}^{(*)}$, $\bar{D}_{s}^{*}\Sigma_{c}^{(*)}$), treating the octet mixing, and thereby to identify the ideal experimental search channels that would test the compact-pentaquark picture against the molecular interpretation of the observed $P_{c}$ and $P_{cs}$ candidates.

Background

Exotic hadrons — states that cannot be reduced to a quark-antiquark pair (meson) or three quarks (baryon) — moved from speculation to spectroscopy when the LHCb collaboration observed narrow peaks in the $J/\psi p$ invariant-mass spectrum, established as the hidden-charm pentaquark candidates $P_{c}(4312)^{+}$, $P_{c}(4380)^{+}$, $P_{c}(4440)^{+}$ and $P_{c}(4457)^{+}$; hidden charm means the valence content includes a $c\bar{c}$ pair, here accompanied by light quarks $uud$. Pentaquark candidates with hidden charm and one strange quark (minimal content $udsc\bar{c}$) were then reported by LHCb in the $J/\psi\Lambda$ channel: the candidates $P_{cs}(4459)^{0}$ (evidence in $\Xi_{b}^{-}\to J/\psi\Lambda K^{-}$ decays) and $P_{cs}(4338)^{0}$ (observation in $B^{-}\to J/\psi\Lambda\bar{p}$ decays), with corroborating 3.3$\sigma$ evidence for the $P_{cs}(4459)^{0}$ state from Belle in $\Upsilon(1S,2S)$ decays, plus a further structure $P_{c}(4337)^{+}$ in $B_{s}^{0}\to J/\psi p\bar{p}$. All observed $P_{c}$ and $P_{cs}$ candidates are isoscalar or isospin-$1/2$ in their light-quark content, where isospin is the approximate $SU(2)$ symmetry interchanging $u$ and $d$ quarks. Two competing pictures coexist: compact pentaquarks, most notably in the diquark-diquark-antiquark configuration, where a diquark is a correlated color-$\bar{3}$ quark pair and the state is built from two diquarks plus the $\bar{c}$ antiquark; and loose meson-baryon molecules such as $\bar{D}^{(*)}\Sigma_{c}^{(*)}$ or $\bar{D}^{(*)}\Xi_{c}$, described by color-singlet-singlet currents. The two pictures predict different spectra and, crucially, different hierarchies of two-body decay widths, so decay data discriminate between them.

QCD sum rules are a standard nonperturbative method connecting QCD to hadrons: a two-point correlation function of a local interpolating current is computed in the operator product expansion (OPE, an expansion in quark and gluon vacuum condensates of increasing mass dimension) and matched, after a Borel transform that suppresses continuum contributions, to a hadronic pole representation. This yields the mass and the pole residue $\lambda$ — the current-hadron coupling, defined for example by $\langle 0|J(0)|P(p)\rangle=\lambda\,U(p)$ with $U$ the pentaquark spinor — while a three-point (current-current-hadron) correlation function with two Borel parameters yields hadronic coupling constants and hence partial decay widths.

Wang and Liu (arXiv:2603.10774, published as Frontiers of Physics 22 (2027) 016201) applied the two-point method to local diquark-diquark-antiquark currents with valence content $uusc\bar{c}$, with the light quarks $uus$ arranged in two distinct flavor octets $\mathbf{8}_{1}$ and $\mathbf{8}_{2}$. These currents carry isospin $I=1$ (isovector), so the predicted states $P_{cs}^{+}$ would be charged, strangeness-$-1$ partners whose signature is a resonance in the $J/\psi\Sigma$ invariant-mass distribution, the $\Sigma$ being the $I=1$ light baryon, the isospin partner of the isoscalar $\Lambda$. Using OPE up to dimension-13 condensates and a modified energy-scale formula $\mu=\sqrt{M_{P}^{2}-(2\mathbb{M}_{c})^{2}}-\mathbb{M}_{s}$, they extracted masses and pole residues for the 18 lowest negative-parity states: 6 with $IJ^{P}=1\,\frac{1}{2}^{-}$ (masses 4.35-4.59 GeV), 7 with $1\,\frac{3}{2}^{-}$ (4.38-4.58 GeV) and 5 with $1\,\frac{5}{2}^{-}$ (4.45-4.57 GeV). The possible two-body channels and their thresholds are $\eta_{c}\Sigma$ (4173 MeV), $J/\psi\Sigma$ (4286 MeV), $\bar{D}\Xi_{c}$ (4333 MeV), $\bar{D}_{s}\Sigma_{c}$ (4423 MeV), $\bar{D}^{*}\Xi_{c}$ (4475 MeV), $\bar{D}_{s}\Sigma_{c}^{*}$ (4487 MeV), $\bar{D}_{s}^{*}\Sigma_{c}$ (4566 MeV) and $\bar{D}_{s}^{*}\Sigma_{c}^{*}$ (4630 MeV). The paper, however, stops at the mass spectrum: it explicitly defers the decay widths to future three-point sum-rule studies using the pole residues as input, notes only that $\mathbf{8}_{1}$-$\mathbf{8}_{2}$ mixing allows decays to charmonium plus a light baryon octet without resolving its quantitative consequences, and leaves the proposed experimental chains $\Sigma_{b}^{+}\to P_{cs}^{+}\phi\to J/\psi\Sigma^{+}\phi$ and $\Xi_{b}^{0}\to P_{cs}^{+}K^{-}\to J/\psi\Sigma^{+}K^{-}$ untested. Because masses alone cannot distinguish compact from molecular scenarios — the authors stress that different substructures lead to quite different branching fractions — the missing decay phenomenology is exactly the ingredient needed to make the prediction decisive.

Problem Statement

Complete the strong-decay phenomenology of the predicted compact isovector hidden-charm-singly-strange pentaquark spectrum of Wang and Liu (arXiv:2603.10774). Specifically: compute the hadronic coupling constants and two-body partial decay widths, with uncertainty budgets, for the 18 predicted $I=1$, negative-parity $uusc\bar{c}$ states (6 with $J^{P}=\frac{1}{2}^{-}$, 7 with $\frac{3}{2}^{-}$, 5 with $\frac{5}{2}^{-}$; masses 4.35-4.59 GeV) into the possible meson-baryon channels — $\eta_{c}\Sigma$, $J/\psi\Sigma$, $\bar{D}\Xi_{c}$, $\bar{D}^{*}\Xi_{c}$, $\bar{D}_{s}\Sigma_{c}$, $\bar{D}_{s}\Sigma_{c}^{*}$, $\bar{D}_{s}^{*}\Sigma_{c}$, $\bar{D}_{s}^{*}\Sigma_{c}^{*}$ — using the published pole residues as input, where each of the 18 states can decay only into the subset of these channels whose threshold lies below its own mass. The calculation must address the mixing between the two light-flavor octets $\mathbf{8}_{1}$ and $\mathbf{8}_{2}$, which controls the charmonium-plus-light-baryon-octet channels, rather than assuming it away. From the computed hierarchy, determine the dominant decay channel(s) of each state and identify the ideal experimental search channel(s) — in particular whether the proposed chains $\Sigma_{b}^{+}\to P_{cs}^{+}\phi\to J/\psi\Sigma^{+}\phi$ and $\Xi_{b}^{0}\to P_{cs}^{+}K^{-}\to J/\psi\Sigma^{+}K^{-}$, or alternative channels, are the most favorable — so that the compact diquark-diquark-antiquark scenario becomes directly testable against the molecular interpretation of the $P_{c}$ and $P_{cs}$ candidates.

References

1. Zhi-Gang Wang and Yang Liu, Analysis of the hidden-charm pentaquark candidates in the J/ψΣ mass spectrum via the QCD sum rules, Frontiers of Physics 22 (2027) 016201, arXiv:2603.10774, DOI:10.15302/frontphys.2027.016201, https://arxiv.org/abs/2603.10774
2. Xiu-Wu Wang and Zhi-Gang Wang, Strong decays of Pcs(4338) and its high isospin cousin via QCD sum rules, Physical Review D 110 (2024) 014008, arXiv:2404.12146, DOI:10.1103/PhysRevD.110.014008, https://arxiv.org/abs/2404.12146
3. Xiu-Wu Wang, Xin Li and Zhi-Gang Wang, Systematic study of the strong decays of the Pc states and their possible isospin cousins via the QCD sum rules, Chinese Physics C 50 (2026) 083102, arXiv:2601.14723, DOI:10.1088/1674-1137/ae66d1, https://arxiv.org/abs/2601.14723
4. Ulaş Özdem, Deciphering the nature of P_ψs^Σ pentaquarks in the light of their electromagnetic multipole moments, Journal of High Energy Physics 07 (2026) 004, arXiv:2604.12533, DOI:10.1007/JHEP07(2026)004, https://arxiv.org/abs/2604.12533
5. Zhi-Gang Wang and Yang Liu, Analysis of the hidden-charm pentaquark candidates in the J/ψΞ mass spectrum via the QCD sum rules, Nuclear Physics B 1027 (2026) 117456, arXiv:2511.13067, DOI:10.1016/j.nuclphysb.2026.117456, https://arxiv.org/abs/2511.13067
6. Zhi-Gang Wang, Analysis of the hidden-charm pentaquark candidates in the J/ψΞ* mass spectrum via the QCD sum rules, arXiv:2606.28095, https://arxiv.org/abs/2606.28095
7. Zhi-Gang Wang and Yang Liu, Analysis of the hidden-charm pentaquark candidates in the J/ψΣ* mass spectrum via the QCD sum rules, arXiv:2607.17492, https://arxiv.org/abs/2607.17492
8. Zhi-Gang Wang, Analysis of the hidden-charm pentaquark candidates in the J/ψΩ mass spectrum via the QCD sum rules, arXiv:2607.09430, https://arxiv.org/abs/2607.09430
9. Zhi-Gang Wang, Analysis of the hidden-charm pentaquark candidates in the J/ψp mass spectrum with QCD sum rules, European Physical Journal C 86 (2026) 209, arXiv:2509.05648, DOI:10.1140/epjc/s10052-026-15446-0, https://arxiv.org/abs/2509.05648
10. Zhi-Gang Wang and Qi Xin, Analysis of the hidden-charm pentaquark candidates in the J/ψΛ mass spectrum via the QCD sum rules, European Physical Journal C 86 (2026) 472, arXiv:2508.17373, DOI:10.1140/epjc/s10052-026-15680-6, https://arxiv.org/abs/2508.17373
11. LHCb Collaboration (R. Aaij et al.), Evidence of a J/ψΛ structure and observation of excited Ξ⁻ states in the Ξ_b⁻ → J/ψΛK⁻ decay, Science Bulletin 66 (2021) 1278, arXiv:2012.10380, DOI:10.1016/j.scib.2021.02.030, https://arxiv.org/abs/2012.10380
12. LHCb Collaboration (R. Aaij et al.), Observation of a J/ψΛ resonance consistent with a strange pentaquark candidate in B⁻ → J/ψΛp̄ decays, Physical Review Letters 131 (2023) 031901, arXiv:2210.10346, DOI:10.1103/PhysRevLett.131.031901, https://arxiv.org/abs/2210.10346
13. Belle Collaboration (I. Adachi et al.), Search for Pcs(4459) and Pcs(4338) in Υ(1S,2S) inclusive decays at Belle, Physical Review Letters 135 (2025) 041901, arXiv:2502.09951, DOI:10.1103/pf8m-6j69, https://arxiv.org/abs/2502.09951
14. LHCb Collaboration (R. Aaij et al.), Evidence for a new structure in the J/ψp and J/ψp̄ systems in B_s⁰ → J/ψpp̄ decays, Physical Review Letters 128 (2022) 062001, arXiv:2108.04720, DOI:10.1103/PhysRevLett.128.062001, https://arxiv.org/abs/2108.04720
15. LHCb Collaboration (R. Aaij et al.), Observation of a narrow pentaquark state, Pc(4312)⁺, and of the two-peak structure of Pc(4450)⁺, Physical Review Letters 122 (2019) 222001, arXiv:1904.03947, DOI:10.1103/PhysRevLett.122.222001, https://arxiv.org/abs/1904.03947