Scaling Properties of $S$-wave Level Density for Heavy Quarkonium from QCD Sum Rules

In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives an expression, relating the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of a heavy quark $Q$ and meson $(Q\bar{q})$ and the number of heavy quarkonium levels below the threshold of $(Q\bar{Q})\to (Q\bar{q})+(\bar{Q}q)$ decay.