Asymptotic freedom using a gluon mass as a regulator

TL;DR

This paper explores a new regularization scheme for QCD Hamiltonians using a gluon mass, aiming to better understand asymptotic freedom and the dependence of the coupling on regularization methods.

Contribution

It introduces a gluon mass regulator within the RGPEP framework, providing an alternative approach to study asymptotic freedom in QCD.

Findings

Demonstrates a regulated Hamiltonian with a gluon mass

Shows the running coupling's dependence on regularization functions

Extends the method to include virtual fermion contributions

Abstract

Front-Form Hamiltonian dynamics provides a framework in which QCD's vacuum is simple and states are boost invariant. However, canonical expressions are divergent and must be regulated in order to establish well-defined eigenvalue problems. The Renormalization Group Procedure for Effective Particles (RGPEP) provides a systematic way of finding counterterms and obtaining regulated Hamiltonians. Among its achievements is the description of asymptotic freedom, with a running coupling constant defined as the coefficient in front of the three gluon-vertex operators in the regulated Hamiltonian. However, the obtained results need a deeper understanding, since the coupling exhibits a finite dependence on the regularization functions, at least at the third-order term in the perturbative expansion. Here we present a similar derivation using a different regularization scheme based on massive gluons. The procedure can be extended to incorporate contributions from virtual fermions.