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

Xuan Luo (Anhui University)Satoshi X. Nakamura (Univ. of ScienceTechnology of China)
Jul 2022
摘要
Recent LHCb's amplitude analysis on $B^+\to J/\psi \phi K^+$ suggests theexistence of exotic $X$ and $Z_{cs}$ hadrons, based on an assumption thatBreit-Wigner resonances describe all the peak structures. However, all thepeaks and also dips in the spectra are located at relevant meson-mesonthresholds where threshold kinematical cusps might cause such structures. Thispoints to the importance of an independent amplitude analysis with dueconsideration of the kinematical effects, and this is what we do in this work.Our model fits well $J/\psi \phi$, $J/\psi K^+$, and $K^+\phi$ invariant massdistributions simultaneously, demonstrating that all the $X$, $Z_{cs}$, and dipstructures 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's. Ourmodel has 29 fitting parameters which is about one-fifth of the LHCb's, whichmight indicate the importance of considering all relevant threshold cusps. TheLHCb data requires $D_s^{(*)}\bar{D}^{*}$ scattering lengths in our model to beconsistent with zero, disfavoring $D_s^{(*)}\bar{D}^{*}$ moleculeinterpretations of $Z_{cs}(4000)$ and $Z_{cs}(4220)$ and, via the SU(3)relation, being consistent with previous Lattice QCD results.
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