The Universal Renormalization Factors Z_1/Z_3 and Color Confinement Condition in Non-Abelian Gauge Theory

TL;DR

This paper explores the universal ratio of renormalization factors in non-Abelian gauge theory, linking it to color confinement conditions and the disappearance of massless gauge boson poles.

Contribution

It demonstrates that the ratio Z_1/Z_3 equals 1+u, connecting it to the scalar pole residue and color confinement, and discusses the related gauge symmetry restoration.

Findings

Z_1/Z_3 equals 1+u, a matter-independent ratio.

The condition 1+u=0 implies color confinement.

Disappearance of massless gauge boson pole when 1+u=0.

Abstract

The ratio Z_1/Z_3 of vertex and wave-function renormalization factors, which is universal (i.e., matter-independent), is shown to equal 1+u which gives the residue of the scalar pole $\propto p_\mu p_\nu /p^2$ of 2-point function < D_\mu c D_\nu \bar c >. This relation is interesting since 1+u=0 has been known to give a sufficient condition for color confinement. We also give an argument that, when 1+u=0 holds, it will be realized by the disappearance of the massless gauge boson pole and is related with the restoration of a certain ``local gauge symmetry" as was discussed by Hata. (Talk given at International Symposium on BRS Symmetry, Sept.~18 -- 22, 1995, Kyoto.)