Chromopolarizabilities of fully-heavy baryons

We compute the chromopolarizabilities of the fully heavy baryons $\Omega_{QQQ'}$ ($Q,Q'=b,c$) in the framework of potential nonrelativistic quantum chromodynamics. At leading order, the fully heavy hadrons are considered as ground chromo-Coulombic bound states. We find that the chromopolarizability $\beta_\Omega$ of a fully heavy baryon $QQQ$ is 2.6 times the chromopolarizability $\beta_\psi$ of the quarkonium $\bar{Q}Q$ with the same heavy quark flavor $Q$. This result is accurate up to the correction of the order 0.3 for $Q=b$ and provides an order-of-magnitude estimate for $Q=c$. We discuss the dependence of the ratio $\beta_\Omega/\beta_\psi$ on the heavy quark mass $m_Q$ and the strong coupling constant $\alpha_s$ as well as on the ratio of the masses $m_{Q'}/m_Q$, in the case not all quarks in the baryon are identical. Since the chromopolarizability of heavy hadrons defines the strength of their interaction at low energies mediated by soft gluons, which at long range hadronize into pairs of pions and kaons, our findings argue in favor of the existence of near-threshold states composed of pairs of fully heavy baryons.