Chiral loops and ghost states in the quenched scalar propagator

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 η ′ 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 η ′ -π 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.

Scalar meson in dynamical and partially quenched two-flavor QCD: Lattice results and chiral loops

“…We close this section by demonstrating that the analytical expressions for the bubble contribution (8,9) reduce to the known expressions in the fully quenched and the fully unquenched limits:…”

“…We note that the contribution of the bubble diagram (8) has no unknown parameters, since one can fix the values of M, µ 0 and m 0 from other considerations. We determine the pseudoscalar meson masses M and µ 0 = M 2 /(4m q ) from pion correlators on the same lattices.…”

“…The quenching effect, which leads to negative correlators at small quark masses, was subtracted as in [8,9]. The result is m a0 = 1.43 (10) GeV if only the leading chiral loop (one bubble) is taken into account, and m a0 = 1.04(7) GeV if next-to leading chiral corrections are included by resummation 1 .…”

“…The quenched qq correlator in the chiral limit was simulated by Bardeen et al [8,9] with Wilson fermions. The correlators were found to be negative at small quark masses, which was attributed to the similar mechanism as observed in the present partially quenched study.…”

Diquark effects in light baryon correlators from lattice QCD

“…This is best known in the situation of scalar mesons, where there is a long history of observations going back to the quenched studies of Ref. [19]. Basically, the scalar meson correlator includes a pi-eta-prime intermediate state.…”