  We present a complete analysis of the Heavy Quark Effective Theory Lagrangian
at order $1/m^2$ in the leading logarithmic approximation, including effects
induced by spectator quarks. At this order new correction terms appear in the
effective Lagrangian, as four-quark operators containing both heavy and light
quark fields. We compute the coefficients of these operators to one-loop order
and in the leading-logarithmic approximation. Two of them break the heavy quark
spin symmetry and we estimate their contribution to the hyperfine splitting of
the heavy mesons in the factorization approximation. We find that they make a
positive contribution to the hyperfine splitting of about 10% of the measured
splitting in the charm case and of up to 5% in the bottom case.
