Glueball matrix elements: a lattice calculation and applications

TL;DR

This paper calculates glueball matrix elements using lattice gauge theory, providing insights into glueball properties and their role in meson phenomenology, with implications for identifying glue-rich states.

Contribution

It presents the first lattice calculation of glueball matrix elements and applies these results to phenomenological models of meson decays and glueball identification.

Findings

Scalar matrix element suggests a larger glueball decay rate than observed.

Glueball masses and related parameters are precisely determined in the continuum.

Glueball components are likely diluted among scalar mesons.

Abstract

We compute the matrix elements of the energy-momentum tensor between glueball states and the vacuum in SU(3) lattice gauge theory and extrapolate them to the continuum. These matrix elements may play an important phenomenological role in identifying glue-rich mesons. Based on a relation derived long ago by the ITEP group for J/psi radiative decays, the scalar matrix element leads to a branching ratio for the glueball that is at least three times larger than the experimentally observed branching ratio for the f_0 mesons above 1GeV. This suggests that the glueball component must be diluted quite strongly among the known scalar mesons. Finally we review the current best continuum determination of the scalar and tensor glueball masses, the deconfining temperature, the string tension and the Lambda parameter, all in units of the Sommer reference scale, using calculations based on the Wilson action.