Vacuum condensates, effective gluon mass and color confinement in a new reformulation of QCD

TL;DR

This paper introduces a new reformulation of Yang-Mills theory that simplifies gluon interactions, enabling analysis of gluon mass generation, confinement, and glueball properties through a novel 1/N_c expansion and vacuum structure.

Contribution

It presents a reformulation of QCD eliminating gluon self-interactions with auxiliary fields, facilitating calculations of gluon mass, confinement, and glueball masses, and establishing a new 1/N_c expansion framework.

Findings

Gluons acquire a common non-zero mass through vacuum condensation.

The static potential combines Yukawa and linear potentials, indicating confinement.

The lightest scalar glueball mass is proportional to the gluon mass.

Abstract

We propose a new reformulation of Yang-Mills theory in which three- and four-gluon self-interactions are eliminated at the price of introducing a sufficient number of auxiliary fields. We discuss the validity of this reformulation in the possible applications such as dynamical gluon mass generation, color confinement and glueball mass calculation. Moreover, we set up a new $1/N_c$ color expansion in the $SU(N_c)$ Yang-Mills theory based on this reformulation. In fact, we give the Feynman rules of the $1/N_c$ expansion in the manifestly Lorentz covariant gauge. The Yang-Mills theory is defined on a non-trivial vacuum where color--singlet transverse gluon pair condensations take place by the attractive gluonic self-interactions. This vacuum condensation provides a common non-vanishing mass for all the gluons with color symmetry being preserved. It is shown that the auxiliary fields become dynamical by acquiring the kinetic term due to quantum corrections. Then the static potential between a pair of color charges is derived as a combination of the Yukawa-type potential and the linear potential with non-vanishing string tension. The mass of the lightest scalar glueball is calculated as the ratio to the gluon mass. The explicit calculations are performed as a partial resummation of the leading order diagrams for the small 't Hooft coupling.