OPE coefficient functions in terms of composite operators only. Singlet case

TL;DR

This paper generalizes a method to compute OPE coefficient functions for singlet operators in QCD, expressing them solely via composite operators, and calculates specific gluon coefficient functions along with their renormalization properties.

Contribution

It extends the calculation of OPE coefficient functions from non-singlet to singlet cases, avoiding elementary fields and focusing on composite operators in QCD.

Findings

Derived formulas for singlet coefficient functions in terms of composite operators.

Calculated diagonal and non-diagonal gluon coefficient functions in QCD.

Analyzed the renormalization properties of these coefficient functions.

Abstract

A method for calculating coefficient functions of the operator product expansion, which was previously derived for the non-singlet case, is generalized for the singlet coefficient functions. The resulting formula defines coefficient functions entirely in terms of corresponding singlet composite operators without applying to elementary (quark and gluon) fields. Both "diagonal" and "non-diagonal" gluon coefficient functions in the product expansion of two electromagnetic currents are calculated in QCD. Their renormalization properties are studied.