Spin correlations and velocity-scaling in color-octet NRQCD matrix elements

TL;DR

This paper calculates spin-dependent decay matrix elements for S-wave quarkonium states in lattice NRQCD, focusing on color-octet contributions relevant for high transverse momentum production, and confirms the expected velocity-scaling hierarchy.

Contribution

It provides the first lattice QCD computation of spin-dependent color-octet matrix elements for S-wave quarkonia, verifying velocity-scaling rules.

Findings

Lattice matrix elements follow the predicted velocity-scaling hierarchy.

Color-octet matrix elements are computed with minimized ultraviolet cutoff effects.

Results support the dominance of color-octet mechanisms at high transverse momentum.

Abstract

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.