Chapter 6 Mixing of Scalar Gluonium and Quark Mesons 6.1 Introduction The research in this chapter is based upon the publication: The publication above (Ref. [59]) explores mixing between scalar $^{(}$J PC = 0 ++ ) glueballs and quark mesons. As described in Chapter 1, glueballs (or gluonia) are hadrons that are composed entirely of gluons. The scalar glueball is predicted to be the lightest glueball, with a mass in the range of approximately 1 . 0 − 1 . 7 GeV. The heavy quarkonium-like states have masses in the range 3 . 8 − 4 . 7 GeV, therefore the research in this chapter is not directly relevant to the heavy quarkonium-like states. Rather, the research in this chapter is related to the problem of the light scalar mesons. Below 2 . 0 GeV, there are too many hadrons with J PC = 0 ++ to be explained in terms of conventional mesons. It is widely suspected that some of these supernumerary states could be exotic hadrons, with the scalar glueball among them. The research in this chapter considers the possibility that some of the light scalars could be mixtures of a glueball and a conventional quark meson. Refs. [87, 96] review the current experimental and theoretical status of glueballs. 92 • D. Harnett, R.T. Kleiv, K. Moats and T.G. Steele, Near-maximal mixing of scalar gluonium and quark mesons: a Gaussian sum-rule analysis, Nucl. Phys. A850 (2011) 110.