Abstract
Recently Grinstein, Jora, and Polosa have studied a theory of large-$N$ scalar quantum chromodynamics in one-space one-time dimension. This theory admits a Bethe-Salpeter equation describing the discrete spectrum of quark-antiquark bound states. They consider gauge fields in the adjoint representation of $SU(N)$ and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark-antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge-invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front 't Hooft gauge.
Highlights
It is widely perceived that heavy states such as the X, Y, Z states have an exotic structure as tetra-quark states or diquark–antidiquark states (Q Q ) [6,7,13,14,15,16,17,18,19,20,21,22,23,24], but even some light scalar mesons could be identified as diquark–antidiquark or tetra-quark systems [25,26,27,28,29,30]
Grinstein et al [30] have studied a model of large-N scalar quantum chromodynamics (QCD) [25,26,27,28,29,30] in one space and one time dimension. Their model admits [30] a Bethe–Salpeter equation describing the discrete spectrum of qqbound states [25,26,27,28,29,30]
The gauge fields have been considered in the adjoint representation of SU (N ) and the scalar fields in the fundamental representation
Summary
Various possibilities for understanding hadron structure beyond the usual mesons and baryons [6,7,8] have been considered in the literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. This work constitutes a part of our bigger project, which involves a study of some aspects related to the spontaneous symmetry breaking as well as to a study of its DLCQ using the coherent state formalism [44–52], in the LF Hamiltonian approach to study the two- and three-body relativistic bound state problems [44–52] In this sense one could think that the theory under consideration could perhaps provide a good basic field theoretic framework for a study of a large class of diquark–antidiquark or the tetra-quark states [4,5,6,7,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31], which have been investigated in various experiments.
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