Heavy quarkonium and nonperturbative corrections

We analyze the possible existence of nonperturbative contributions in heavy bar QQ systems (bar Q and Q need not have the same flavor) which cannot be expressed in terms of local condensates. Starting from QCD, with well-defined approximations and splitting properly the fields into large and small momentum components, we derive an effective Lagrangian where hard gluons (in the nonrelativistic approximation) have been integrated out. The large momentum contributions (which are dominant) are calculated using Coulomb-type states. In addition to the usual condensate corrections, we see the possibility of new nonperturbative contributions. We parametrize them in terms of two low momentum correlators with Coulomb bound state energy insertions En. We realize that the heavy quark effective Lagrangian can be used in these correlators. We calculate the corrections that they give rise to in the decay constant, the bound state energy, and the matrix elements of bilinear currents at zero recoil. We study the cutoff dependence of the new contributions and we see that it matches perfectly with that of the large momentum contributions. We consider two situations in detail, (i) En>ΛQCD(MQ→∞) and (ii) En<ΛQCD, and briefly discuss the expected size of the new contributions in Υ, J/ψ, and Bc* systems. copyright 1996 The American Physical Society