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Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex

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Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex

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dc.contributor.author Freedman, Daniel Z.
dc.contributor.author Grignani, Gianluca
dc.contributor.author Rius Dionis, Nuria
dc.contributor.author Johnson, Kenneth
dc.date.accessioned 2015-03-02T13:10:02Z
dc.date.available 2015-03-02T13:10:02Z
dc.date.issued 1992
dc.identifier.citation Freedman, Daniel Z. Grignani, Gianluca Rius Dionis, Nuria Johnson, Kenneth 1992 Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex Annals of Physics 218 1 75 120
dc.identifier.uri http://hdl.handle.net/10550/42562
dc.description.abstract The conformal symmetry of the QCD Lagrangian for massless quarks is broken both by renormalization effects and the gauge fixing procedure. Renormalized primitive divergent amplitudes have the property that their form away from the overall coincident point singularity is fully determined by the bare Lagrangian, and scale dependence is restricted to δ-functions at the singularity. If gauge fixing could be ignored, one would expect these amplitudes to be conformal invariant for non-coincident points. We find that the one-loop three-gluon vertex function Γμνρ(x,y,z) is conformal invariant in this sense, if calculated in the background field formalism using the Feynman gauge for internal gluons. It is not yet clear why the expected breaking due to gauge fixing is absent. The conformal property implies that the gluon, ghost and quark loop contributions to Γμνρ are each purely numerical combinations of two universal conformal tensors Dμνρ(x,y,z) and Cμνρ(x,y,z) whose explicit form is given in the text. Only Dμνρ has an ultraviolet divergence, although Cμνρ requires a careful definition to resolve the expected ambiguity of a formally linearly divergent quantity. Regularization is straightforward and leads to a renormalized vertex function which satisfies the required Ward identity, and from which the beta-function is easily obtained. Exact conformal invariance is broken in higher-loop orders, but we outline a speculative scenario in which the perturbative structure of the vertex function is determined from a conformal invariant primitive core by interplay of the renormalization group equation and Ward identities.
dc.language.iso eng
dc.relation.ispartof Annals of Physics, 1992, vol. 218, num. 1, p. 75-120
dc.subject Física
dc.title Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex
dc.type journal article es_ES
dc.date.updated 2015-03-02T13:12:15Z
dc.identifier.doi 10.1016/0003-4916(92)90269-R
dc.identifier.idgrec 100458
dc.rights.accessRights open access es_ES

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