Mesons in Light-Front QCD$_{2+1}$: Investigation of a Bloch Effective Hamiltonian
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.
Cite
@article{arxiv.hep-th/0107188,
title = {Mesons in Light-Front QCD$_{2+1}$: Investigation of a Bloch Effective Hamiltonian},
author = {Dipankar Chakrabarti and A. Harindranath},
journal= {arXiv preprint arXiv:hep-th/0107188},
year = {2010}
}
Comments
Accepted for publication in Physical Review D