Chiral Loops and Ghost States in the Quenched Scalar Propagator

TL;DR

This paper investigates the scalar meson propagator in quenched QCD, revealing a long-range negative contribution due to quenched chiral loops involving the eta prime and pion, and characterizes this effect with an effective Lagrangian.

Contribution

It demonstrates that the long-range negative metric component in the quenched scalar propagator arises from quenched chiral loops involving the eta prime and pion, providing a detailed analysis and parameter determination.

Findings

Negative metric contribution becomes more pronounced at smaller quark masses.

The long-range behavior is well-described by a quenched chiral loop model involving eta' and pion.

Parameters of the effective Lagrangian for the scalar sector are quantitatively determined.

Abstract

The scalar, isovector meson propagator is analyzed in quenched QCD, using the MQA 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 $\eta '$ 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 $\eta '- \pi$ 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.