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

Several $X$ and $Z_{cs}$ exotic hadrons were claimed in the LHCb's amplitude analysis on $B^+\to J/\psi \phi K^+$. The data shows that all the peaks and also dips in the spectra are located at thresholds of seemingly relevant meson-meson channels. While the LHCb analysis fitted the peaks with Breit-Wigner resonances, threshold kinematical cusps might be the cause of such structures. We thus analyze the LHCb data considering the threshold cusps. Our model 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 is different from the LHCb's spin-parity assignments ($1^+$ and $0^+$). The number of fitting parameters can be significantly reduced by considering the relevant threshold cusps. Our analysis shows that $D_s^{(*)}\bar{D}^{*}$ scattering lengths are consistent with zero. This disfavors an explanation of $Z_{cs}(4000)$ and $Z_{cs}(4220)$ as $D_s^{(*)}\bar{D}^{*}$ molecules, which is consistent with lattice QCD via the SU(3) relation.