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Several $X$ and $Z_{cs}$ exotic hadrons were claimed in the LHCb's amplitudeanalysis on $B^+\to J/\psi \phi K^+$. The data shows that all the peaks andalso dips in the spectra are located at thresholds of seemingly relevantmeson-meson channels. While the LHCb analysis fitted the peaks withBreit-Wigner resonances, threshold kinematical cusps might be the cause of suchstructures. We thus analyze the LHCb data considering the threshold cusps. Ourmodel is simultaneously fitted to $J/\psi \phi$, $J/\psi K^+$, and $K^+\phi$invariant mass distributions. The threshold cusps fit well all the $X$,$Z_{cs}$, and dip structures. Our analysis indicates that spin-parity of the$X(4274)$ and $X(4500)$ structures are $0^-$ and $1^-$, respectively. This isdifferent from the LHCb's spin-parity assignments ($1^+$ and $0^+$). The numberof fitting parameters can be significantly reduced by considering the relevantthreshold cusps. Our analysis shows that $D_s^{(*)}\bar{D}^{*}$ scatteringlengths are consistent with zero. This disfavors an explanation of$Z_{cs}(4000)$ and $Z_{cs}(4220)$ as $D_s^{(*)}\bar{D}^{*}$ molecules, which isconsistent with lattice QCD via the SU(3) relation.

Threshold-cusp explanation for $X$ and $Z_{cs}$ in $B^+\to J/\psi\phi K^+$