Abstract
In situations where the low-lying eigenmodes of the Dirac operator are suppressed one observed degeneracies of some meson masses. Based on these results a hidden symmetry was conjectured, which is not a symmetry of the Lagrangian but emerges in the quantization process. We show here how the difference between classes of meson propagators is governed by the low modes and shrinks when they disappear.
Highlights
We find explicitly in an analytic calculation that some propagator identities emerge if the low-lying eigenmodes of the Dirac operator are suppressed
It is well known that the difference of the susceptibilities of, e.g., the propagator of the isovector scalar meson operator and of the isovector pseudoscalar operator are weighted by an eigenvalues density factor, that approaches a delta function in the zero mass limit
We studied the role of low-lying eigenmodes of the Dirac operator in meson propagators
Summary
It was found that in certain situations a symmetry emerges that relates vector and scalar meson propagators but that is no symmetry of the action. That symmetry was observed in lattice QCD when low-lying eigenmodes of the Dirac operator are suppressed either artificially by removing the eigenmodes from the quenched quark propagators [1,2,3,4,5] or naturally in the high temperature phase [6,7] either due to a gap or because another rapid decrease toward zero eigenvalues. It is well known that the difference of the susceptibilities of, e.g., the propagator of the isovector scalar meson operator and of the isovector pseudoscalar operator are weighted by an eigenvalues density factor (on top of the generic eigenvalue density), that approaches a delta function in the zero mass limit. We show here that this property applies to a large set of (scalar, pseudoscalar, vector and axial vector) meson propagator pairs and discuss the conditions for the CS symmetry
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