Hadronic quarkonium decays at order v^7

TL;DR

This paper calculates higher-order imaginary parts of the NRQCD Lagrangian to improve predictions of heavy quarkonium decay widths, providing next-to-leading order corrections and new insights into P-wave and S-wave decays.

Contribution

It presents the complete next-to-leading order corrections to heavy quarkonium decay widths at order v^7, including new terms and a first-time analysis of Poincare' invariance constraints.

Findings

Confirmed previous results for S-wave decay widths.

Discovered discrepancies with prior results for P-wave decay widths.

Provided a framework for phenomenological applications of decay calculations.

Abstract

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.