  We determine to order alpha^3 in the quenched approximation the so-called
residual mass in the lattice regularisation of the Heavy Quark Effective
Theory. We follow a gauge-invariant strategy which exploits the fact that this
mass term dominates the exponential decrease of perturbative Wilson loops at
large perimeters. Our computational tool is Numerical Stochastic Perturbation
Theory. The new coefficient we compute is crucial to improve the determination
of the (MS bar) mass of the b-quark from lattice simulations of the Heavy Quark
Effective Theory.
