Renormalized Wick expansion for a modified PQCD

TL;DR

This paper develops a renormalization scheme for a modified perturbative QCD that incorporates mass scales from condensates, enabling analysis of dynamical mass generation and vacuum structure.

Contribution

It introduces a new renormalization approach for a modified PQCD with mass parameters linked to condensates, allowing dimensional transmutation and vacuum analysis.

Findings

One-loop potential suggests dynamical quark condensate formation.

Mass scales $m_q$ and $m_g$ enable dimensional transmutation.

Framework accommodates massive counter-terms in massless QCD.

Abstract

The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered, by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counter-terms are allowed in this mass less theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and to masses $m_q$ and $m_g$ associated to quarks and gluons respectively. This procedure allows to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters $m_q$ and $m_g$ is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential, is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum.