A proposal of a local modified QCD

TL;DR

This paper introduces a local, renormalizable modification of QCD that maintains gauge invariance and explores its implications for quark mass hierarchy and vacuum energy, with detailed calculations supporting its consistency.

Contribution

It presents a novel local and gauge-invariant formulation of modified QCD that could be equivalent to massless QCD, including new terms and detailed loop calculations.

Findings

Gluon self-energy is transversal and gauge invariant.

Vacuum energy is gauge parameter independent at two loops.

Potential for quark mass hierarchy generation discussed.

Abstract

A local and renormalizable version of a modified PQCD introduced in previous works is presented. The construction indicates that it could be equivalent to massless QCD. The case in which only quark condensate effects are retained is discussed in more detail. Then, the appearing auxiliary fermion fields can be integrated leading to a theory with the action of massless QCD, to which one local and gauge invariant Lagrangian term for each quark flavour is added. These terms are defined by two gluon and two quark fields, in a form curiously not harming power counting renormalizability. The gluon self-energy is evaluated in second order in the gauge coupling and all orders in the new quark couplings, and the result became transversal as required by the gauge invariance. The vacuum energy was calculated in the two loop approximation and also became gauge parameter independent. The possibilities that higher loop contributions to the vacuum energy allow the generation of a quark mass hierarchy as a flavour symmetry breaking effect are discussed. However, the decision on this issue needs the evaluation of more than two loop contributions, in which more than one type of quark loops start appearing, possibly leading to interference effects in the vacuum energy.