Interpretation of axial resonances in $J/\psi -\varphi$ at the LHCb

We suggest that the $J/\psi \varphi$ structures observed by LHCb can be fitted in two tetraquak multiplets, the $S$-wave ground state and the first radial excitation, with composition $[cs][\overline{c}\overline{s}]$. When compared to the previously identified $[cq][\overline{c}\overline{q}]$ multiplet, the observed masses agree with that expected for a multiplet with $q\to s$. We propose the $X(4274)$, fitted by LHCb with a single $1^{++}$ resonance, to correspond rather to two, almost degenerate, unresolved lines with $J^{PC}=0^{++},2^{++}$. Masses of missing particles in the $1S$ and $2S$ multiplets are predicted.

Figure 1

Mass spectrum of the states in Eqs. (1)-(5) as given by a Hamiltonian of spin-spin interactions confined inside diquarks. Under this assumption $|1,1⟩$ states are degenerate; see text. The assignement of $X(4140)$ and our hypothesis on $X(4274)$ are shown.