Exploring the resonances $X(4140)$ and $X(4274)$ through their decay channels

Investigation of the resonances $X(4140)$ and $X(4274)$, which were recently confirmed by the LHCb Collaboration [1], is carried out by treating them as the color triplet and sextet $[cs][\bar{c}\bar {s}]$ diquark-antidiquark states with the spin-parity $J^{P}=1^{+}$, respectively. We calculate the masses and meson-current couplings of these tetraquarks in the context of QCD two-point sum rule method by taking into account the quark, gluon and mixed vacuum condensates up to eight dimensions. We also study the vertices $X(4140)J/\psi\phi$ and $X(4274)J/\psi\phi$, and evaluate corresponding strong couplings $g_{X(4140)J/\psi\phi}$ and $g_{X(4274)J/\psi\phi}$ by means of QCD light-cone sum rule method, and a technique of the soft-meson approximation. In turn, these couplings contain a required information to determine the width of the $X(4140)\to J/\psi\phi$ and $X(4274) \to J/\psi\phi$ decay channels. We compare our results for the masses and decay widths of the $X(4140)$ and $X(4274)$ resonances with the LHCb data, and alternative theoretical predictions.