QCD sum rule study of the $d^{*}\left(2380\right)$

We systematically construct $I\left(J^P\right)=0\left(3^{+}\right)$ six-quark local interpolating currents without derivative operators. We discuss the best choice of operator and select three $\Delta \text{−}\Delta$-like operators to perform QCD sum rule analyses to calculate the mass of the $d^{*}\left(2380\right)$. The mass extracted from this analysis is $M_{d^{*}}=2.4\pm 0.2$ GeV, consistent with the $d^{*}\left(2380\right)$ mass observed by the WASA detector at COSY. We also obtain a sum rule lower mass bound $M_{d^{*}}>2.25$ GeV. We also consider the effect of mixing of singlet dibaryon fields with the same quantum numbers, and perform the QCD sum rule analysis of the mixed interpolating current and extract the mass of the $d^{*}\left(2380\right)$ and its lower mass bound. With optimized mixing parameters, we find that the mixed current does not change the numerical result significantly.

Figure 1

The variation of $M_{d^{*}}$ with respect to the threshold value $s_0$ (left) for $M_B^2=3,4,7,12,30,50 {\mathrm{GeV}}^2$, and the Borel mass $M_B$ (right) for $s_0=5.5$ (dotted), $6.0$ (solid), and $6.5 {\mathrm{GeV}}^2$ (dashed). The current $J_1^{{\alpha }_1{\alpha }_2{\alpha }_3}$ is used. The curves start to merge when $M_B^2$ is around $50 {\mathrm{GeV}}^2$, so we can not obtain a mass below 2.25 GeV.

Figure 2

The variation of $M_{d^{*}}$ with respect to the threshold value $s_0$ and the Borel mass $M_B$. The current $J_2^{{\alpha }_1{\alpha }_2{\alpha }_3}$ is used here.