Analysis of the strong decay $X(4140)\rightarrow J/\psi \phi$ via the light-cone QCD sum rules

Abstract

In this article, we take the $X(4140)$ as the axialvector tetraquark state with the symbolic quark structure $[sc]_S[\bar{s}\bar{c}]_A+[sc]_A[\bar{s}\bar{c}]_S$, and calculate the width of the two-body strong decay $X(4140)\rightarrow J/\psi \phi$ within the framework of the light-cone sum rules. Different from the traditional light-cone sum rules, at the phenomenological side, we introduce parameters $C$ to eliminate the contaminations from the higher resonances and continuum states, and match the hadron side with the QCD side of the correlation function based on rigorous quark-hadron duality to obtain the stable QCD sum rules. Then we obtain the decay width $\Gamma(X(4140)\rightarrow J/\psi \phi)=145\pm21\, \text{MeV}$, which is reasonable according to the experimental data $162\pm21^{+24}_{-49 } \,\text{MeV}$ from the LHCb collaboration. The numerical result supports the possibility that the $X(4140)$ could be the $[sc]_S[\bar{s}\bar{c}]_A+[sc]_A[\bar{s}\bar{c}]_S$ type axialvector tetraquark state.