The residual mass in lattice heavy quark effective theory to alpha(3) order

We determine to order alpha (3) in the quenched approximation the so-called residual mass in the lattice regularisation of the Heavy Quark Effective T heory. We follow a gauge-invariant strategy which exploits the fact that th is mass term dominates the exponential decrease of perturbative Wilson loop s at large perimeters. Our computational tool is Numerical Stochastic Pertu rbation Theory. The new coefficient we compute is crucial to improve the de termination of the ((MS) over bar) mass of the b-quark from lattice simulat ions of the Heavy Quark Effective Theory.