Hadronic quarkonium decays at order v

We compute the complete imaginary part of the NRQCD Lagrangian at order 1/M4 in the heavy-quark mass expansion, which includes center of mass operators, and at order αs in the matching coefficients. We also compute the imaginary part of the NRQCD Lagrangian at order 1/M6 and at order αs that contributes to the S-wave and P-wave inclusive decay widths of heavy quarkonium into light hadrons at order v7 in the heavy-quark velocity expansion. If we count αs(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 Poincaré 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.