  X-space schemes are gauge-invariant, regulator-independent renormalization
schemes that are defined by requiring position-space correlation functions of
gauge invariant operators to be equal to their noninteracting values at
particular kinematic points. These schemes can be used to nonperturbatively
renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and
by computing matching coefficients between the X-space scheme and MSbar in the
dimensionally-regulated continuum, matrix elements calculated with LQCD can be
converted to MSbar-renormalized matrix elements. Using X-space schemes for
Heavy Quark Effective Theory (HQET) operators has the additional benefit that
appropriate ratios of position-space correlation functions cancel the power
divergent static-quark self-energy of Lattice HQET nonperturbatively. This work
presents the O($\alpha_S$) matching coefficients between X-space renormalized
four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of
charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing
between neutral mesons containing a heavy quark, such as B-Bbar mixing.
