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

TL;DR

The study addresses the nature of the X(4140) by computing its strong decay width to $J/\psi\phi$ under the hypothesis that X(4140) is a $J^{PC}=1^{++}$ axialvector tetraquark of the $[sc]_S[\bar{s}\bar{c}]_A+[sc]_A[\bar{s}\bar{c}]_S$ configuration. Using light-cone QCD sum rules, the authors analyze the three-point correlator $\Pi_{\alpha\beta}(p,q)$, introduce condensate-driven inputs and higher-state contaminations via $C_{\psi'}$ and $C_{X'}$, project to a scalar function, and apply a rigorous quark–hadron duality to derive a stable sum rule for the hadronic coupling $g_{XJ/\psi\phi}$ with a Borel parameter $T^2$. They obtain $g_{XJ/\psi\phi}=2.88\pm0.21$ and compute the width $\Gamma(X(4140)\to J/\psi\phi)=145\pm21$ MeV, which aligns well with the experimental measurement $162\pm21^{+24}_{-49}$ MeV from LHCb. The results bolster the axialvector tetraquark interpretation of X(4140) and demonstrate the effectiveness of the employed duality-enabled light-cone sum-rule framework for diagnosing the nature of exotic states, with prospects for applying the method to other decay channels.

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 $X(4140)\rightarrow J/ψφ$ 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 $Γ(X(4140)\rightarrow J/ψφ)=145\pm21\, \text{MeV}$, which is in excellent agreement with 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.

Figures (1)

• Figure 1: The hadronic coupling constant $g_{XJ/\psi \phi}$ with variation of the Borel parameter $T^2$.