Heavy Mesons in a Random Instanton Gas

We analyze the correlation function of a meson with one heavy and one light quark in inverse powers of the heavy quark mass $m_Q$ using a succession of Foldy-Wouthuysen-type transformations prior to radiative corrections. We evaluate the correlator to order $m_Q^0$ in a random and dilute gas of instantons, using the planar approximation. We show, in leading order in the density, that the heavy quark mass is shifted to the order $m_Q^0$ and that the induced interaction between the heavy and light quarks is attractive. We also find it to be an order of magnitude smaller than the 't Hooft interaction between two light quarks. The shift in the heavy quark mass is related to the perimeter law of large Wilson loops. The relevance of these results for general hadronic correlators with heavy quarks is discussed.