NLO Production and Decay of Quarkonium

TL;DR

The paper delivers a comprehensive NLO QCD treatment of both production and decay of heavy quarkonia within NRQCD, including colour-singlet and colour-octet channels. It extends covariant projection techniques to D=4-2ε, carefully handles soft and collinear emissions, and demonstrates IR/UV cancellations through standard QCD methods and NRQCD factorization. The work provides extensive, state-specific results for both decay widths and hadroproduction cross sections, including new calculations for several P-wave and S-wave states and cross-checks with the threshold-expansion method. The findings refine theoretical predictions for quarkonium observables and clarify the role of NRQCD matrix elements in universal, process-independent descriptions of quarkonium dynamics.

Abstract

We present a calculation of next-to-leading-order (NLO) QCD corrections to total hadronic production cross sections and to light-hadron-decay rates of heavy quarkonium states. Both colour-singlet and colour-octet contributions are included. We discuss in detail the use of covariant projectors in dimensional regularization, the structure of soft-gluon emission and the overall finiteness of radiative corrections. We compare our approach with the NLO version of the threshold-expansion technique recently introduced by Braaten and Chen. Most of the results presented here are new. Others represent the first independent reevaluation of calculations already known in the literature. In this case a comparison with previous findings is reported.

Figures (8)

• Figure 1: Diagrammatic representation of factorization in parton + parton $\to H + X$ .
• Figure 2: Diagrams for the $\hbox{$q \overline q$}$ and $gg$ Born amplitudes.
• Figure 3: Feynman diagrams contributing to the one-loop corrections to the processes $Q \overline Q[^3P_0^{[1,8]}] \to gg$, $Q \overline Q[^3P_2^{[1,8]}] \to gg$ and $Q \overline Q[^1S_0^{[1,8]}] \to gg$.
• Figure 4: Feynman diagrams contributing to the one-loop corrections to the process $\hbox{$q \overline q$}\to Q \overline Q[^3S_1^{[8]}]$.
• Figure 5: Diagrams for NLO corrections to the NRQCD matrix elements.