Exploring the chiral regime of QCD in the interacting instanton liquid model

Abstract

The Interacting Instanton Liquid Model is used to explore the role of instanton induced dynamics in hadron structure. To support the validity of this model in the chiral regime, the quark mass dependencies of several properties are shown to agree with chiral perturbation theory, including the density of eigenmodes of the Dirac operator and the masses of the pion and nucleon. A quark mass m * = 80 MeV emerging naturally from the model is shown to specify the mass scale above which the fermion determinant is suppressed, the zero modes become subdominant, and the density of quasi-zero modes become independent of the quark mass.

Instanton fermionic zero mode at finite temperature and chemical potential

“…On the other hand, chiral symmetry breaking can be related to a finite density of quasi-zero mode through the Bank-Casher formula [3] qq = −πρ(λ = 0), where ρ is the density of modes with eigenvalue λ. The distribution of near-zero mode predicted by the Instanton Liquid Model, where a dilute and globally topologically neutral ensemble of pseudoparticle is considered, perfectly agrees with the phenomenological expectation and with calculations in Chiral Perturbation Theory [4][5][6].…”

Electromagnetic form factors of the pion and kaon from the instanton vacuum

“…We have verified that the charge normalization condition beyond the chiral limit [F K ð0Þ] is also satisfied by Eqs. (50) and (52), replacing M by m þ M and with the model value for the kaon decay constant F K . However, we note that the value of the F K in the present work, compared to the empirical value F K ¼ 113 MeV, turns out to be underestimated: F K % 108 MeV.…”

Quantum interactions between nonperturbative vacuum fields

“…For example, instantons have been shown to play an important role in the breaking of chiral symmetry [1] and instanton models [2] have been successfully used to predict physical properties of light hadrons (see e.g. [3,4] and references therein). Similarly, vacuum fields made from monopoles [5], center-vortices [6], merons [7], and, recently, regular gauge instantons [8] have been shown to generate an area law for the Wilson loop, hence to produce color confinement.…”