Renormalization of the quantum chromodynamics with massive gluons

TL;DR

This paper demonstrates the renormalization and gauge-invariance of quantum chromodynamics with massive gluons, deriving identities and showing asymptotic freedom similar to massless gluon theories.

Contribution

It establishes the renormalizability of massive gluon QCD using BRST symmetry, Ward-Takahashi identities, and one-loop calculations, extending the standard massless gluon framework.

Findings

Successful derivation of Ward-Takahashi identities for propagators and vertices.

Renormalization constants satisfy Slavnov-Taylor identities.

Effective coupling and masses exhibit asymptotic freedom.

Abstract

In our previously published papers, it was proved that the chromodynamics with massive gluons can well be set up on the gauge-invariance principle. The quantization of the chromodynamics was perfectly performed in the both of Hamiltonian and Lagrangian path-integral formalisms by using the Lagrangian undetermined multiplier method. In this paper, It is shown that the quantum theory is invariant with respect to a kind of BRST-transformations. From the BRST-invariance of the theory, the Ward-Takahashi identities satisfied by the generating functionals of full Green functions, connected Green functions and proper vertex functions are successively derived. As an application of the above Ward-Takahashi identities, the Ward-Takahashi identities obeyed by the massive gluon and ghost particle propagators and various proper vertices are derived and based on these identities, the propagators and vertices are perfectly renormalized. Especially, as a result of the renormalization, the Slavnov-Taylor identity satisfied by renormalization constants is natually deduced. To demonstrate the renormalizability of the theory, the one-loop renormalization of the theory is carried out by means of the mass-dependent momentum space subtraction scheme and the renormalization group approach, giving an exact one-loop effective coupling constant and one-loop effective gluon and quark masses which show the asymptotically free behaviors as the same as those given in the quantum chromodynamics with massless gluons.