Conformal symmetry and differential regularization of the three-gluon vertex

Journal Article · Sat Aug 15 00:00:00 EDT 1992 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(92)90269-R· OSTI ID:5638540

Freedman, D Z ^[1]; Grignani, G; Johnson, K; Rius, N ^[1]

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1. Massachusetts Institute of Technology, Cambridge, MA (United States)

The conformal symmetry of the quantum chromodynamics Lagrangian for massless quarks is broken 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 [delta]-functions at the singularity. If gauge fixing could be ignored, one would expect these amplitudes to be conformal invariant for non-coincident points. The authors find that the one-loop three-gluon vertex function [Gamma][sub [mu][nu][rho]](x,y,z) is conformal invariant in this sense, if calculated in the background field formalism using the Feynman gauge for internal gluons. The conformal property implies that the gluon, ghost, and quark loop contributions to [Gamma][sub [mu][nu][rho]] are each purely numerical combinations of two universal conformal tensors D[sub [mu][nu][rho]](x, y, z) and C[sub [mu][nu][rho]](x, y, z). 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. The authors 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. Other results include: (1) The linear deviation from the Feynman gauge is not conformal invariant, and a separate computation using symbolic manipulation confirms that among D[sub [mu]]b[sub [mu]] background gauges, only the Feynman gauge is conformal invariant. (2) The conventional gluon vertex function is not conformal invariant because the Slavnov-Taylor identity it satisfies is more complicated than the simple Ward identity for the background vertex, and a superposition of D[sub [mu]v[nu][rho]] and C[sub [mu][nu][rho]] necessarily satisfies a Ward identity. 19 refs., 3 figs.

• DOE Contract Number: AC02-76ER03069
• OSTI ID: 5638540
• Journal Information: Annals of Physics (New York); (United States), Vol. 218:1; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CORRELATION FUNCTIONS
CONFORMAL INVARIANCE
ORTHOGONAL TRANSFORMATIONS
QUANTUM CHROMODYNAMICS
GLUONS
LAGRANGIAN FUNCTION
RENORMALIZATION
SYMMETRY
WARD IDENTITY
BOSONS
ELEMENTARY PARTICLES
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
POSTULATED PARTICLES
QUANTUM FIELD THEORY
TRANSFORMATIONS
662230* - Quantum Chromodynamics- (1992-)