QCD sum rule studies on the possible double-peak structure of the $X17$ particle

Abstract: The $X17$ particle, discovered by Krasznahorkay et al. at ATOMKI, was recently confirmed in the $\gamma \gamma$ invariant mass spectra by Abraamyan et al. at JINR. We notice with surprise and interest that the $X17$ seems to have a double-peak structure. This is in a possible coincidence with our QCD sum rule study of [arXiv:2006.01018], where we interpreted the $X17$ as a tetraquark state composed of four bare quarks ($u \bar u d \bar d$), and claimed that ``A unique feature of this tetraquark assignment is that we predict two almost degenerate states with significantly different widths''. These two different tetraquark states are described by two different chiral tetraquark currents $\bar u_L \gamma_\mu d_L~\bar d_L \gamma^\mu u_L$ and $\bar u_L \gamma_\mu d_L~\bar d_R \gamma^\mu u_R$. To verify whether the tetraquark assignment is correct or not, we replace the up and down quarks by the strange quarks, and apply the QCD sum rule method to study the other four chiral tetraquark currents $\bar u_L \gamma_\mu s_L~\bar s_L \gamma^\mu u_L$, $\bar u_L \gamma_\mu s_L~\bar s_R \gamma^\mu u_R$, $\bar d_L \gamma_\mu s_L~\bar s_L \gamma^\mu d_L$, and $\bar d_L \gamma_\mu s_L~\bar s_R \gamma^\mu d_R$. We calculate their correlation functions, and find that non-perturbative QCD effects do not contribute much to them. Our results suggest that there may exist four almost degenerate tetraquark states with masses about $236\sim296$ MeV. Each of these states is composed of four bare quarks, either $u \bar u s \bar s$ or $d \bar d s \bar s$.