Determination of the renormalized heavy-quark mass in Lattice QCD

We study on the lattice the correlator of heavy-quark currents in the vicinity of vanishing momentum. The renormalized charmed quark mass, the renormalized strong coupling constant and gluon condensate can be defined in terms of the derivatives of that correlator at zero momentum. We analyze quenched Monte-Carlo data on a small lattice $8^3*16$ for $\beta=6$. We generalize dispersion relations to the lattice theory in a simple way and use them successfully to fit the correlator at both small and large distances. We fit the short-distance part of the correlator with the relevant expressions of perturbative QCD on the lattice and obtain the value of the renormalized quark mass $m_c^{\bar{MS}}(m_c)\,=\,1.20(4)\,GeV$.