Abstract
To all orders of perturbation theory, the renormalization of the topological charge density in dimensionally regularized QCD is shown to require no more than an additive renormalization proportional to the divergence of the flavour-singlet axial current. The proof is based on the standard BRS analysis of the QCD vertex functional in the background gauge and exploits the special algebraic properties of the charge density through the Stora–Zumino chain of descent equations.
Highlights
All known consistent forms of dimensional regularization of QCD break chiral symmetry and the symmetry is only recovered after renormalization and removal of the regularization
The background field technique permits the theory to be probed with greater respect for the gauge symmetry than is the case when probed in conventional ways [11,12,13,14]
The source terms (4.1) are such that the application of the BRS variation to the sum of terms is equivalent to a change of the source fields. This property is shared by the further source terms introduced below and eventually ensures that the BRS symmetry turns into a symmetry of the vertex functional
Summary
All known consistent forms of dimensional regularization of QCD break chiral symmetry and the symmetry is only recovered after renormalization and removal of the regularization. In QCD this technical difficulty can be bypassed by representing such fields through totally antisymmetric tensor fields [1,2] Using this representation, the renormalization of the axial quark densities, the axial currents and the chiral anomaly has been worked out to high order in the gauge coupling [2,3,4,5]. 3. The symmetries of the QCD vertex functional in presence of a background gauge field and the sources for the descendants of the charge density are discussed. The symmetries of the QCD vertex functional in presence of a background gauge field and the sources for the descendants of the charge density are discussed These strongly constrain the form of the divergent parts of the vertex functional and, as shown, eventually exclude a multiplicative renormalization of the charge density. The paper ends with some comments on the axial anomaly and a few concluding remarks
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