Spin correlations and velocity scaling in color-octet nonrelativistic QCD matrix elements

We compute spin-dependent decay matrix elements for S-wave charmonium and bottomonium in lattice nonrelativistic quantum chromodynamics (NRQCD). Particular emphasis is placed upon the color-octet matrix elements, since the corresponding production matrix elements are expected to appear in the dominant contributions to the production cross sections at large transverse momenta. We use three slightly different versions of the heavy-quark lattice Green's functions in order to minimize the contributions that scale as powers of the ultraviolet cutoff. The lattice matrix elements that we calculate obey the hierarchy that is suggested by the velocity-scaling rules of NRQCD.