Towards Solving QCD in Light-Cone Quantization -- On the Spectrum of the Transverse Zero Modes for SU(2)

TL;DR

This paper explores the spectrum of transverse zero modes in a simplified SU(2) gauge theory within light-cone quantization, providing insights into non-perturbative QCD phenomena like confinement and glueball states.

Contribution

It introduces a tractable model for non-abelian gauge theories in (2+1) dimensions using discretized light-cone quantization with zero mode suppression and Fock-space truncation, leading to numerical spectra.

Findings

Color singlet states form stable bound spectra.

Glueball mass spectra are obtained numerically.

Gluon structure function shape is characterized as (x(1-x))^{1/3}.

Abstract

The formalism for a non-abelian pure gauge theory in (2+1) dimensions has recently been derived within Discretized Light-Cone Quantization, restricting to the lowest {\it transverse} momentum gluons. It is argued why this model can be a paradigm for full QCD. The physical vacuum becomes non-trivial even in light-cone quantization. The approach is brought here to tractable form by suppressing by hand both the dynamical gauge and the constraint zero mode, and by performing a Tamm-Dancoff type Fock-space truncation. Within that model the Hamiltonian is diagonalized numerically, yielding mass spectra and wavefunctions of the glue-ball states. We find that only color singlets have a stable and discrete bound state spectrum. The connection with confinement is discussed. The structure function of the gluons has a shape like $ [{x(1-x)}] ^{1\over 3} $. The existence of the continuum limit is verified by deriving a coupled set of integral equations.