Chiral loops and ghost states in the quenched scalar propagator

The scalar, isovector meson propagator is analyzed in quenched QCD, using the modified quenched approximation pole-shifting ansatz to study the chiral limit. In addition to the expected short-range exponential falloff characteristic of a heavy scalar meson, the propagator also exhibits a longer-range, negative metric contribution which becomes pronounced for smaller quark masses. We show that this is a quenched chiral loop effect associated with the anomalous structure of the ${\eta }^{\prime }$ propagator in quenched QCD. Both the time dependence and the quark mass dependence of this effect are well described by a chiral loop diagram corresponding to an ${\eta }^{\prime }-\pi$ intermediate state, which is light and effectively of negative norm in the quenched approximation. The relevant parameters of the effective Lagrangian describing the scalar sector of the quenched theory are determined.