Instanton liquid properties from lattice QCD

Abstract

We examined the instanton contribution to the QCD configurations generated from lattice QCD for N F = 0, N F = 2 + 1 and N F = 2 + 1 + 1 dynamical quark flavors from two different and complementary approaches. First via the use of Gradient flow, we computed instanton liquid properties using an algorithm to localize instantons in the gauge field configurations and studied their evolution with flow time. Then, the analysis of the running at low momenta of gluon Green's functions serves as an independent confirmation of the instanton density which can also be derived without the use of the Gradient flow.

Small size instanton contributions to the quark quasi-PDF and matching kernel

“…The matching kernel coefficient develops into a trans-series [25] since at weak coupling √ κ ∼ e −π/αs . As we noted earlier, cooled lattice simulations of the QCD vacuum suggest κ ≈ 1/10 (regime of chiral symmetry breaking with large size instantons [15]) and κ ≈ 1 (regime of short distance physics with small size instantons [16]). For both estimates, the small size instanton contribution in (65) is sizable in comparison to the perturbative one.…”

“…Previous lattice simulations using cooling methods support these observations, see [15] for a review. A more recent lattice simulation aimed at extracting the running gauge coupling constant with momentum [16], through a pertinent ratio of 2-and 3-point gluonic functions, has suggested a larger instanton density with κ ≈ 1. This observation at large running momenta, points at the effects from the smaller size instanton-anti-instanton configurations which are likely to affect short distance physics such as the running of the coupling, with negligible effects on the longer range mechanism of chiral symmetry breaking.…”

“…To project onto the left-or right-handed Dirac spinors in (16), it is sufficient to keep only the terms proportional to P ± in the LSZ reduced quark propagators (10)(11)(12), with the result…”

Instanton-induced effects in interquark forces, light-front wave functions and formfactors

“…The "molecular component" was also shown to be important at high baryonic densities, where it contributes to quark pairing and color superconductivity [14]. Close ĪI pairs has been qualitatively studied in recent work in [15] which studied their evolution during cooling, see Fig. 3.…”

Mass sum rule of hadrons in the QCD instanton vacuum

“…Since the first one-instanton contribution in (32) is composed of self-dual fields it vanishes. So we are left with only the two and higher multi-instanton contributions.…”