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The Borel summation technique of infrared renormalons is applied to thelattice determination of heavy quark mass. With Borel summation a physicalheavy quark pole mass and binding energy of a heavy-light meson can be definedin a rigorous and calculable manner. A notable feature of the Borel summation,compared to the usual perturbative cancellation of IR renormalons, is anautomatic scale separation. The two approaches of handling renormalondivergence are compared in the B-meson as well as in an (imaginary) heavy-lightmeson with a mass much larger than the inverse of the lattice spacing.Comment: References and NNLO analysis added. Version to appear in Phys Rev

Constraining renormalon effects in lattice determination of heavy quark mass