Abstract
Classical conformal invariance of QCD in the chiral limit is broken explicitly by scale anomaly. As a result, the lightest scalar particle (scalar glueball, or dilaton) in QCD is not light, and cannot be described as a Goldstone boson. Nevertheless basing on an effective low-energy theory of broken scale invariance we argue that inside the hadrons the non-perturbative interactions of gluon fields result in the emergence of a massless dilaton excitation (which we call the "scalaron"). We demonstrate that our effective theory of broken scale invariance leads to confinement. This theory allows a dual formulation as a classical Yang-Mills theory on a curved conformal space-time background. Possible applications are discussed, including the description of strongly coupled quark-gluon plasma and the spin structure of hadrons.
Highlights
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Basing on an effective low-energy theory of broken scale invariance we argue that inside the hadrons the non-perturbative interactions of gluon fields result in the emergence of a massless dilaton excitation
We demonstrate that our effective theory of broken scale invariance leads to confinement
Summary
The invariance with respect to the scale transformation xμ → λxμ is a property of the QCD Lagrangian in the chiral limit. An elegant way to derive this effective Lagrangian has been suggested by Migdal and Shifman in [6] They noted that since the gluodynamics is conformally invariant only in four dimensions, the anomalous contribution to the divergence of the dilatation current appears — in the dimensional regularization scheme — as a residual term in the 4D limit. The energy density of the vacuum |ǫv| and the mass of the dilaton m are the parameters of the theory It is constructed in such a way that at χ = 1 (corresponding to some semihard momentum scale M0) the terms containing the effective field χ cancel implying that dynamics of the color fields is perturbative. Since at this point the dilaton potential in (2.4) vanishes, the formation of the flux tube is accompanied by the emergence of a massless dilaton excitation — the “scalaron”
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