  Motivated by recent preliminary results from the SLD Collaboration on the
measurement of angle-dependent B-Bbar energy correlations in Z^0 -> b bbar
events, we propose a class of observables that can be computed as a power
expansion in the strong coupling constant alpha_s, of order alpha_s at the Born
level and that can be used for a precision measurement of alpha_s(M_Z). We
compute their next-to-leading order O(alpha_s^2) corrections in the strong
coupling constant, including exactly quark-mass effects. We show that, in the
theoretical evaluation of these quantities, large logarithms of the ratio of
the mass of the final quark over the centre-of-mass energy cancel out. Thus,
these variables have a well-behaved perturbative expansion in alpha_s(M_Z). We
study the theoretical uncertainties due to the renormalization-scale dependence
and the quark-mass scheme and we address the question of which mass scheme is
more appropriate for these variables.
