High statistics study of the scalar singlet states in lattice QCD

In this thesis we present a study of the glueball spectrum in lattice QCD, using 2 + 1 flavours of Asqtad fermions and the one-loop Symanzik improved Lüscher-Weisz gauge action. The ensembles for this study have been generated with very high statistics ($N_traj\sim 20000−30000$) to enable us to resolve the notoriously noisy glueball states as accurately as possible. We introduce the theoretical construction of lattice QCD and of staggered fermions in particular before describing how one goes about generating ensembles of gauge fields for such analysis. Here we briefly present our tuning results performed using the improved RHMC algorithm used to generate the finer ensemble. We then present the methods by which one measures glueballs on the lattice before presenting our measurements and analysis for the scalar glueball. Here we discuss several complications which one may face, as we have, performing spectroscopy on the lattice. We finally present determinations of the $0^{++}$ and the excited $0^{++}$ glueball masses, as well as tentative continuum extrapolations. We have also measured the pseudoscalar and tensor glueball states on our lattices and we present these results. Where possible we present a comparison with previous lattice measurements of the glueball spectrum obtained using both dynamical quarks and the quenched approximation in order to gauge the scale of unquenching effects on the glueball spectrum. The study of the scalar glueball forms part of a wider physics project by the UKQCD collaboration which aims to study the flavour-singlet sector using 2 + 1 flavours of dynamical fermions with unprecedented statistics. We briefly present motivation and an outline of the measurements performed as part of this wider project