Composite Operators in QCD

Abstract

We give a formula for the derivatives of a correlation function of composite operators with respect to the parameters (i.e., the strong fine structure constant and the quark mass) of QCD in four-dimensional euclidean space. The formula is given as spatial integration of the operator conjugate to a parameter. The operator product of a composite operator and a conjugate operator has an unintegrable part, and the formula requires divergent subtractions. By imposing consistency conditions we derive a relation between the anomalous dimensions of the composite operators and the unintegrable part of the operator product coefficients.

26 pages

References in corpus (1)

• Operator Coefficients for Composite Operators in the $({\varphi }^4{)}_4$ Theory

Cited by in corpus (19)

• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• Connections on the State-Space over Conformal Field Theories
• A Proof of Local Background Independence of Classical Closed String Field Theory
• All order I.R. finite expansion for short distance behavior of massless theories perturbed by a relevant operator
• Nearby CFT's in the operator formalism: The role of a connection
• Vacuum Expectation Values from a variational approach
• Tricritical Ising Model near criticality
• On the Short Distance Behavior of the Critical Ising Model Perturbed by a Magnetic Field
• Short distance behaviour of correlators in the 2D Ising model in a magnetic field
• Operator Coefficients for Composite Operators in the $({\varphi }^4{)}_4$ Theory
• Type-B Anomaly Matching and the 6D (2,0) Theory
• On the geometry of the theory space in the ERG formalism
• Manifestly Finite Perturbation Theory for the Short-Distance Expansion of Correlation Functions in the Two Dimensional Ising Model
• New Moduli Spaces from String Background Independence Consistency Conditions
• Operator Product Expansions in the Two-Dimensional O(N) Non-Linear Sigma Model
• Recursive construction of the operator product expansion in curved space
• The Perturbative Calculation of the Spin-Spin Correlation Function in the Two Dimensional Ising Model
• Torus Bundles, Automorphisms and T-Duality
• Towards c=0 Flows