Letter
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Pole determination of $P_{ψ s}^{Λ} (4338)$ and possible $P_{ψ s}^{Λ} (4255)$ in $B^{-} \to J / ψ Λ \bar{p}$

¹University of Science and Technology of China, Hefei 230026, People’s Republic of China
²State Key Laboratory of Particle Detection and Electronics (IHEP-USTC), Hefei 230036, People’s Republic of China
³School of Physical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing 100049, China

^*satoshi@ustc.edu.cn
^†wujiajun@ucas.ac.cn

Phys. Rev. D 108, L011501 – Published 14 July, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L011501

Abstract

The first hidden-charm pentaquark candidate with strangeness, $P_{ψ s}^{Λ} (4338)$ , was recently discovered in $B^{-} \to J / ψ Λ \bar{p}$ by the LHCb Collaboration. $P_{ψ s}^{Λ} (4338)$ shows up as a bump at the $Ξ_{c} \bar{D}$ threshold in the $J / ψ Λ$ invariant mass ( $M_{J / ψ Λ}$ ) distribution. The $M_{J / ψ Λ}$ distribution also shows a large fluctuation at the $Λ_{c} {\bar{D}}_{s}$ threshold, hinting the existence of a possible $P_{ψ s}^{Λ} (4255)$ . In this work, we determine the $P_{ψ s}^{Λ} (4338)$ and $P_{ψ s}^{Λ} (4255)$ pole positions for the first time. For this purpose, we fit a $B^{-} \to J / ψ Λ \bar{p}$ model to the $M_{J / ψ Λ}$ , $M_{J / ψ \bar{p}}$ , $M_{Λ \bar{p}}$ , and $\cos θ_{K^{*}}$ distributions from the LHCb simultaneously; $χ^{2} / ndf \sim 1.21$ . Then we extract $P_{ψ s}^{Λ}$ poles from a unitary $Ξ_{c} \bar{D} − Λ_{c} {\bar{D}}_{s}$ coupled-channel scattering amplitude built in the model. In our default fit, the $P_{ψ s}^{Λ} (4338)$ pole is found at $(4338.2 \pm 1.4) - (1.9 \pm 0.5) i MeV$ while the $P_{ψ s}^{Λ} (4255)$ pole at $4254.7 \pm 0.4 MeV$ . The $P_{ψ s}^{Λ} (4338)$ and $P_{ψ s}^{Λ} (4255)$ are mostly $Ξ_{c} \bar{D}$ bound and $Λ_{c} {\bar{D}}_{s}$ virtual states, respectively. Through our analysis, the data disfavors a hypothesis of $P_{ψ s}^{Λ} (4338)$ as merely a kinematical effect. This pole determination, which is important in its own right, sets a primary basis to study the nature of the $P_{ψ s}^{Λ}$ states.

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References (52)

H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
A. Hosaka, T. Iijima, K. Miyabayashi, Y. Sakai, and S. Yasui, Exotic hadrons with heavy flavors: $X$ , $Y$ , $Z$ , and related states, Prog. Theor. Exp. Phys. 2016, 062C01 (2016).
R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Heavy-quark QCD exotica, Prog. Part. Nucl. Phys. 93, 143 (2017).
A. Esposito, A. Pilloni, and A. D. Polosa, Multiquark resonances, Phys. Rept. 668, 1 (2017).
A. Ali, J. S. Lange, and S. Stone, Exotics: Heavy pentaquarks and tetraquarks, Prog. Part. Nucl. Phys. 97, 123 (2017).
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018).
S. L. Olsen, T. Skwarnicki, and D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, 015003 (2018).
N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, The $X Y Z$ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
J.-J. Wu, R. Molina, E. Oset, and B.-S. Zou, Prediction of Narrow $N^{*}$ and $Λ^{*}$ Resonances with Hidden Charm above 4 GeV, Phys. Rev. Lett. 105, 232001 (2010).
J.-J. Wu, R. Molina, E. Oset, and B.-S. Zou, Dynamically generated $N^{*}$ and $Λ^{*}$ resonances in the hidden charm sector around 4.3 GeV, Phys. Rev. C 84, 015202 (2011).
S.-G. Yuan, K.-W. Wei, J. He, H.-S. Xu, and B.-S. Zou, Study of $q q q c \bar{c}$ five quark system with three kinds of quark-quark hyperfine interaction, Eur. Phys. J. A 48, 61 (2012).
R. Aaij et al. (LHCb Collaboration), Observation of $J / ψ p$ Resonances Consistent with Pentaquark States in $Λ_{b}^{0} \to J / ψ K^{-}$ Decays, Phys. Rev. Lett. 115, 072001 (2015).
R. Aaij et al. (LHCb Collaboration), Observation of a Narrow Pentaquark State, $P_{c} (4312)^{+}$ , and of Two-Peak Structure of the $P_{c} (4450)^{+}$ , Phys. Rev. Lett. 122, 222001 (2019).
C.-W. Xiao, J. Nieves, and E. Oset, Prediction of hidden charm strange molecular baryon states with heavy quark spin symmetry, Phys. Lett. B 799, 135051 (2019).
H.-X. Chen, L.-S. Geng, W.-H. Liang, E. Oset, E. Wang, and J.-J. Xie, Looking for a hidden-charm pentaquark state with strangeness $S = - 1$ from $Ξ_{b}^{-}$ decay into $J / ψ K^{-} Λ$ , Phys. Rev. C 93, 065203 (2016).
E. Santopinto and A. Giachino, Compact pentaquark structures, Phys. Rev. D 96, 014014 (2017).
C.-W. Shen, J.-J. Wu, and B.-S. Zou, Decay behaviors of possible $Λ_{c \bar{c}}$ states in hadronic molecule pictures, Phys. Rev. D 100, 056006 (2019).
R. Chen, J. He, and X. Liu, Possible strange hidden-charm pentaquarks from $Σ_{c}^{(*)} {\bar{D}}_{s}^{*}$ and $Ξ_{c}^{(', *)} {\bar{D}}^{*}$ interactions, Chin. Phys. C 41, 103105 (2017).
B. Wang, L. Meng, and S.-L. Zhu, Spectrum of the strange hidden charm molecular pentaquarks in chiral effective field theory, Phys. Rev. D 101, 034018 (2020).
R. Aaij et al. (LHCb Collaboration), Evidence of a $J / ψ Λ$ structure and observation of excited $Ξ^{-}$ states in the $Ξ_{b}^{-} \to J / ψ Λ K^{-}$ decay, Sci. Bull. 66, 1278 (2021).
C.-W. Xiao, J.-J. Wu, and B.-S. Zou, Molecular nature of $P_{c s} (4459)$ and its heavy quark spin partners, Phys. Rev. D 103, 054016 (2021).
F.-Z. Peng, M.-J. Yan, M. Sánchez Sánchez, and M. P. Valderrama, The $P_{c s} (4459)$ pentaquark from a combined effective field theory and phenomenological perspective, Eur. Phys. J. C 81, 666 (2021).
S. Clymton, H.-J. Kim, and H.-C. Kim, Production of hidden-charm strange pentaquarks $P_{c s}$ from the $K^{-} p \to J / ψ Λ$ reaction, Phys. Rev. D 104, 014023 (2021).
Z.-G. Wang and Q. Xin, Analysis of hidden-charm pentaquark molecular states with and without strangeness via the QCD sum rules, Chin. Phys. C 45, 123105 (2021).
J.-X. Lu, M.-Z. Liu, R.-X. Shi, and L.-S. Geng, Understanding $P_{c s} (4459)$ as a hadronic molecule in the $Ξ_{b}^{-} \to J / ψ Λ K^{-}$ decay, Phys. Rev. D 104, 034022 (2021).
M.-W. Li, Z.-W. Liu, Z.-F. Sun, and R. Chen, Magnetic moments and transition magnetic moments of $P_{c}$ and $P_{c s}$ states, Phys. Rev. D 104, 054016 (2021).
X. Hu and J. Ping, Investigation of hidden-charm pentaquarks with strangeness $S = - 1$ , Eur. Phys. J. C 82, 118 (2022).
K. Chen, R. Chen, L. Meng, B. Wang, and S.-L. Zhu, Systematics of the heavy flavor hadronic molecules, Eur. Phys. J. C 82, 581 (2022).
C. Cheng, F. Yang, and Y. Huang, Searching for strange hidden-charm pentaquark state $P_{c s} (4459)$ in $γ p \to K^{+} P_{c s} (4459)$ reaction, Phys. Rev. D 104, 116007 (2021).
H.-X. Chen, W. Chen, X. Liu, and X.-H. Liu, Establishing the first hidden-charm pentaquark with strangeness, Eur. Phys. J. C 81, 409 (2021).
Z.-G. Wang, Analysis of the $P_{c s} (4459)$ as the hidden-charm pentaquark state with QCD sum rules, Int. J. Mod. Phys. A 36, 2150071 (2021).
K. Azizi, Y. Sarac, and H. Sundu, Investigation of $P_{c s} (4459)^{0}$ pentaquark via its strong decay to $Λ J / Ψ$ , Phys. Rev. D 103, 094033 (2021).
R. Chen, Can the newly $P_{c s} (4459)$ be a strange hidden-charm $Ξ_{c} {\bar{D}}^{*}$ molecular pentaquarks?, Phys. Rev. D 103, 054007 (2021).
M.-Z. Liu, Y.-W. Pan, and L.-S. Geng, Can discovery of hidden charm strange pentaquark states help determine the spins of $P_{c} (4440)$ and $P_{c} (4457)$ ?, Phys. Rev. D 103, 034003 (2021).
W.-Y. Liu, W. Hao, G.-Y. Wang, Y.-Y. Wang, E. Wang, and D.-M. Li, The resonances $X (4140)$ , $X (4160)$ , and $P_{c s} (4459)$ in the decay of $Λ_{b} \to J / ψ Λ ϕ$ , Phys. Rev. D 103, 034019 (2021).
LHCb Collaboration, Observation of a $J / ψ Λ$ resonance consistent with a strange pentaquark candidate in $B^{-} \to J / ψ Λ \bar{p}$ decays, arXiv:2210.10346.
M. Karliner and J. R. Rosner, New strange pentaquarks, Phys. Rev. D 106, 036024 (2022).
F.-L. Wang and X. Liu, Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{ψ s}^{Λ} (4338)$ and $P_{c s} (4459)$ , Phys. Lett. B 835, 137583 (2022).
M.-J. Yan, F.-Z. Peng, M. S. Sánchez, and M. P. Valderrama, $P_{ψ s}^{Λ} (4338)$ pentaquark and its partners in the molecular picture, Phys. Rev. D 107, 074025 (2023).
T. J. Burns and E. S. Swanson, The LHCb state $P_{ψ s}^{Λ} (4338)$ as a triangle singularity, Phys. Lett. B 838, 137715 (2023).
F.-K. Guo, X.-H. Liu, and S. Sakai, Threshold cusps and triangle singularities in hadronic reactions, Prog. Part. Nucl. Phys. 112, 103757 (2020).
L. Meng, B. Wang, and S.-L. Zhu, The double thresholds distort the lineshapes of the $P_{ψ s}^{Λ} (4338)^{0}$ resonance, Phys. Rev. D 107, 1 (2023).
X.-K. Dong, F.-K. Guo, and B.-S. Zou, Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum, Phys. Rev. Lett. 126, 152001 (2021).
P. A. Zyla et al. (Particle Data Group), The review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
H. Kamano, S. X. Nakamura, T.-S. H. Lee, and T. Sato, Unitary coupled-channels model for three-mesons decays of heavy mesons, Phys. Rev. D 84, 114019 (2011).
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.108.L011501 for parameter values, statistical significance of the $P_{ψ s}^{Λ} (4338)$ pole, which includes Ref. [47].
O. Behnke, K. Kröninger, G. Schott, and T. Schörner-Sadenius, Data Analysis in High Energy Physics—A Practical Guide to Statistical Methods (Wiley-VCH Verlag GmbH & Co. KGaA, Germany, 2013).
S. X. Nakamura, A. Hosaka, and Y. Yamaguchi, $P_{c} (4312)^{+}$ and $P_{c} (4337)^{+}$ as interfering $Σ_{c} \bar{D}$ and $Λ_{c} {\bar{D}}^{*}$ threshold cusps, Phys. Rev. D 104, L091503 (2021).
N. Brambilla, G. Krein, J. T. Castellà, and A. Vairo, Long-range properties of $1 S$ bottomonium states, Phys. Rev. D 93, 054002 (2016).
X.-K. Dong, V. Baru, F.-K. Guo, C. Hanhart, A. Nefediev, and B.-S. Zou, Is the existence of a $J / ψ J / ψ$ bound state plausible? Sci. Bull. 66, 2462 (2021).
Y. Lyu, T. Doi, T. Hatsuda, Y. Ikeda, J. Meng, K. Sasaki, and T. Sugiura, Attractive $N − ϕ$ interaction and two-pion tail from lattice QCD near physical point, Phys. Rev. D 106, 074507 (2022).
M.-L. Du, M. Albaladejo, F.-K. Guo, and J. Nieves, Combined analysis of the $Z_{c} (3900)$ and the $Z_{c s} (3985)$ exotic states, Phys. Rev. D 105, 074018 (2022).

Phys. Rev. D 108, L011501– Published 14 July, 2023

Vol. 108, Iss. 1 — 1 July 2023

Received 30 August 2022
Revised 28 February 2023
Accepted 21 June 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L011501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Pole determination of $P_{ψ s}^{Λ} (4338)$ and possible $P_{ψ s}^{Λ} (4255)$ in $B^{-} \to J / ψ Λ \bar{p}$

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Pole determination of PψsΛ(4338) and possible PψsΛ(4255) in B−→J/ψΛp¯

Abstract

Physics Subject Headings (PhySH)

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References (52)

Pole determination of $P_{ψ s}^{Λ} (4338)$ and possible $P_{ψ s}^{Λ} (4255)$ in $B^{-} \to J / ψ Λ \bar{p}$