Abstract
We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji$^\prime s$ invariant mass decomposition of the energy momentum tensor together with the trace anomaly, to discuss the mass budget of the nucleon and pion in the QCD instanton vacuum. A measure of the gluon condensate in the nucleon, is a measure of the compressibility of the QCD instanton vacuum as a dilute topological liquid.
Highlights
A remarkable feature of QCD is that in the chiral limit, it is a scale free theory
The typical hadronic scale is 1 fm, but where does it come from? The answer appears to be from a subtle quantum effect referred to as dimensional transmutation and related to the quantum breaking of the conformal symmetry of QCD
We briefly review the salient aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry in Sec
Summary
A remarkable feature of QCD is that in the chiral limit, it is a scale free theory. Yet, all hadrons are massive, composing most of the visible mass in the universe. The QCD vacuum as a topological liquid of instantons and anti-instantons, offers by far the most compelling nonperturbative description that is analytically tractable in the continuum, thanks to its QCD semiclassical origin and diluteness [1,2,3]. Other candidates based on center vortices and monopoles, to cite a few [4], are suggested and may as well be present in addition to the instantons The latter appears to trigger the dual breaking of conformal and chiral symmetry breaking and dominate the vacuum state and its low-lying hadronic excitations.
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