# Quarkonium Decay Matrix Elements from Quenched Lattice QCD

## TL;DR

This paper computes long-distance decay matrix elements for charmonium and bottomonium states using quenched lattice QCD, including the first QCD-based calculation of the color-octet contribution to P-wave decay.

## Contribution

It provides the first first-principles QCD calculation of the color-octet contribution to P-wave decay and relates lattice results to continuum theory at one-loop order.

## Key findings

- Calculated decay matrix elements for S- and P-wave states.
- First QCD-based calculation of color-octet contribution to P-wave decay.
- Established relations between lattice and continuum matrix elements.

## Abstract

We calculate the long-distance matrix elements for the decays of the lowest-lying S- and P-wave states of charmonium and bottomonium in quenched lattice QCD, using a nonrelativistic formulation for the heavy quarks. (The short-distance coefficients are known from perturbation theory.) In particular, we present the first calculation from QCD first principles of the color-octet contribution to P-wave decay---a contribution that is absent in potential models. We also give the relations between the lattice matrix elements and their continuum counterparts through one-loop order in perturbation theory.