Composite Operators in QCD

TL;DR

This paper derives a formula for the derivatives of correlation functions of composite operators in QCD with respect to fundamental parameters, involving operator product expansions and divergence subtractions.

Contribution

It provides a new formula linking parameter derivatives of correlation functions to integrated operator products in QCD, including divergence handling and consistency conditions.

Findings

Derived a formula for parameter derivatives of correlation functions in QCD.

Established relations between anomalous dimensions and operator product coefficients.

Addressed divergence subtraction in composite operator products.

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.