  We compute the complete imaginary part of the NRQCD Lagrangian at order 1/M^4
in the heavy-quark mass expansion, which includes center of mass operators, and
at order alpha_s^2 in the matching coefficients. We also compute the imaginary
part of the NRQCD Lagrangian at order 1/M^6 and at order alpha_s^2 that
contributes to the S-wave and P-wave inclusive decay widths of heavy quarkonium
into light hadrons at order v^7 in the heavy-quark velocity expansion. If we
count alpha_s(M) ~ v^2, the calculation provides the complete next-to-leading
order corrections to the P-wave hadronic widths, and in the original NRQCD
power counting, the complete next-to-leading order corrections to the vector
S-wave widths, and part of the next-to-next-to leading order corrections to the
pseudoscalar S-wave widths. In the S-wave case, we confirm previous findings
and add new terms in a more conservative power counting. In the P-wave case,
our results are in disagreement with previous ones. Constraints induced by
Poincare' invariance on the NRQCD four-fermion sector are studied for the first
time and provide an additional check of the calculation. Perspectives for
phenomenological applications are discussed.
