Letter
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$X$ and $Z_{c s}$ in $B^{+} \to J / ψ ϕ K^{+}$ as $s$ -wave threshold cusps and alternative spin-parity assignments to $X (4274)$ and $X (4500)$

Xuan Luo ¹ and Satoshi X. Nakamura ^2,3,*

¹School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, People’s Republic of China
²University of Science and Technology of China, Hefei 230026, People’s Republic of China
³State Key Laboratory of Particle Detection and Electronics (IHEP-USTC), Hefei 230036, People’s Republic of China

^*satoshi@ustc.edu.cn

Phys. Rev. D 107, L011504 – Published 27 January, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L011504

Abstract

Recent LHCb amplitude analysis on $B^{+} \to J / ψ ϕ K^{+}$ suggests the existence of exotic $X$ and $Z_{c s}$ hadrons, based on an assumption that Breit-Wigner resonances describe all the peak structures. However, all the peaks and also dips in the spectra are located at relevant meson-meson thresholds where threshold kinematical cusps might cause such structures. This points to the importance of an independent amplitude analysis with due consideration of the kinematical effects, and this is what we do in this work. Our model fits well $J / ψ ϕ$ , $J / ψ K^{+}$ , and $K^{+} ϕ$ invariant mass distributions simultaneously, demonstrating that all the $X$ , $Z_{c s}$ , and dip structures can be well described with the ordinary $s$ -wave threshold cusps. Spin-parity of the $X (4274)$ and $X (4500)$ structures are respectively $0^{-}$ and $1^{-}$ from our model, as opposed to $1^{+}$ and $0^{+}$ from the LHCb model. With all relevant threshold cusps considered, the number of fitting parameters seems to be significantly reduced. The LHCb data requires $D_{s}^{(*)} {\bar{D}}^{*}$ scattering lengths in our model to be consistent with zero, disfavoring $D_{s}^{(*)} {\bar{D}}^{*}$ molecule interpretations of $Z_{c s} (4000)$ and $Z_{c s} (4220)$ and, via the SU(3) relation, being consistent with previous lattice QCD results.

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Phys. Rev. D 107, L011504– Published 27 January, 2023

Vol. 107, Iss. 1 — 1 January 2023

Received 8 August 2022
Accepted 23 December 2022

DOI: https://doi.org/10.1103/PhysRevD.107.L011504

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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$X$ and $Z_{c s}$ in $B^{+} \to J / ψ ϕ K^{+}$ as $s$ -wave threshold cusps and alternative spin-parity assignments to $X (4274)$ and $X (4500)$

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X and Zcs in B+→J/ψϕK+ as s-wave threshold cusps and alternative spin-parity assignments to X(4274) and X(4500)

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (53)

$X$ and $Z_{c s}$ in $B^{+} \to J / ψ ϕ K^{+}$ as $s$ -wave threshold cusps and alternative spin-parity assignments to $X (4274)$ and $X (4500)$