Quarkonium Decay Matrix Elements from Quenched Lattice QCD

TL;DR

This work presents the first calculation from QCD first principles of the color-octet contribution to decay{emdash}a contribution that is absent in potential models and gives the relations between the lattice matrix elements and their continuum counterparts through one-loop order in perturbation theory.

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.

Figures (1)

• Figure 1: Lattice calculation of matrix element of 4-fermion operator. The large discs represent the sources and sinks; the smaller discs represent the 4-fermion and point source operators. The lines are the nonrelativistic quark propagators.