Study of $\Lambda _c$ $\Lambda _c$ dibaryon and $\Lambda _c$ ${\bar{\Lambda }}_c$ baryonium states via QCD sum rules

Abstract

In this article, we construct the six-quark currents with the $J^P=0^+$, $0^-$, $1^+$ and $1^-$ to study the $\Lambda _c$ $\Lambda _c$ dibaryon and $\Lambda _c$ ${\bar{\Lambda }}_c$ baryonium states via QCD sum rules. We consider the vacuum condensates up to dimension 16 and truncation of the order ${\mathcal {O}}(\alpha _s^k )$ with $k\le 3$. The predicted masses are $5.11_{-0.12}^{+0.15}$ GeV, $4.66_{-0.06}^{+0.10}$ GeV, $4.99_{-0.09}^{+0.10}$ GeV $4.68^{+0.08}_{-0.08}$ GeV for the $J^P=0^+$, $0^-$, $1^+$ and $1^-$ states, respectively, which can be confronted to the experimental data in the future considering the high integrated luminosity at the center-of-mass energy about $4.8\,\mathrm {GeV}$ at the BESIII. We find the terms with $\frac{3}{2}< k \le 3$ do play a tiny role, and we can ignore these terms safely in the QCD sum rules.