Scale anomaly and the scalars

We investigate the properties of a possible low-lying scalar glueball as well as the ordinary scalar-quark states using an effective chiral Lagrangian which satisfies the trace anomaly and U(1${)}_{\mathrm{A}}$ anomaly of QCD. An interesting mass bound for the lightest particle in the scalar-singlet channel is discussed. Detailed arguments against the existence of a very light (less than 400 MeV) scalar glueball are presented. It is shown that the introduction of a derivative-coupling term in the usual type of linear σ model cures the problem of excessively large widths for the ordinary (nonet) scalar mesons. In fact, chiral symmetry enables one to nicely correlate the widths of the entire scalar nonet. It is noted that the same derivative-coupling term allows a heavy (1–2 GeV) scalar glueball to have sufficiently narrow width to permit its observation as an ordinary resonance, in contrast with a recent claim. Our model can naturally explain the unusually large partial width for the ηη’ mode of the glueball candidate G(1590). A symmetrical ansatz for the anomaly terms is suggested which enables one to successfully calculate the η’ mass as the ratio of gluon condensate to pion-decay constant. In addition, the theoretically interesting limit where the glueball becomes a true dilaton is formulated in a new and illustrative way.