Mesons in Light-Front QCD$_{2+1}$: Investigation of a Bloch Effective Hamiltonian

TL;DR

This paper investigates mesons in 2+1 dimensional light-front QCD using a Bloch effective Hamiltonian, addressing infrared divergences, and exploring confinement and rotational symmetry violations.

Contribution

It introduces a numerical approach to solve the effective Hamiltonian in 2+1D light-front QCD and analyzes infrared divergence issues and confinement mechanisms.

Findings

Gaussian quadrature effectively cancels infrared divergences.

Vanishing energy denominator causes severe infrared divergences.

A reduced model exhibits logarithmic confinement and rotational symmetry violation.

Abstract

We study the meson sector of 2+1 dimensional light-front QCD using a Bloch effective Hamiltonian in the first non-trivial order. The resulting two dimensional integral equation is converted into a matrix equation and solved numerically. We investigate the efficiency of Gaussian quadrature in achieving the cancellation of linear and logarithmic light-front infrared divergences. The vanishing energy denominator problem which leads to severe infrared divergences in 2+1 dimensions is investigated in detail. Our study indicates that in the context of Fock space based effective Hamiltonian methods to tackle gauge theories in 2+1 dimensions, approaches like similarity renormalization method may be mandatory due to uncanceled infrared divergences caused by the vanishing energy denominator problem. We define and study numerically a reduced model which is relativistic, free from infrared divergences, and exhibits logarithmic confinement. The manifestation and violation of rotational symmetry as a function of the coupling are studied quantitatively.