We compute the mass of the charm quark using both quenched and dynamical
lattice QCD calculations. We examine the effects of mass dependent lattice
artifacts by comparing two different formalisms for the heavy quarks. We take
the continuum limit of the charm mass in quenched QCD by extrapolating from
three different lattice spacings. At a fixed lattice spacing, the mass of the
charm quark is compared between quenched QCD and dynamical QCD with a sea quark
mass around strange. In the continuum limit of quenched QCD, we find
m_c(m_c)=1.29(7)(13) GeV. No evidence was seen for unquenching.Comment: Added NP analysis of quenched data, corrected error in PCAC RGI mass,
updated strange quark mass discussion and references, unified notation and
corrected typos. No change in final result. Version accepted for publication
in JHE
