Mesons in (2+1) Dimensional Light Front QCD. II. Similarity Renormalization Approach

TL;DR

This paper explores the similarity renormalization approach in 2+1 dimensional light front QCD, demonstrating its ability to generate confining interactions and analyzing its limitations regarding rotational symmetry violations.

Contribution

It introduces the application of similarity renormalization to gauge theories, showing how it produces confining interactions and analyzing spectrum sensitivities.

Findings

Similarity approach generates linear confinement at large transverse separations.

Interaction grows as square root of longitudinal separation, causing symmetry violations.

Numerical results highlight the importance of higher order calculations.

Abstract

Recently we have studied the Bloch effective Hamiltonian approach to bound states in 2+1 dimensional gauge theories. Numerical calculations were carried out to investigate the vanishing energy denominator problem. In this work we study similarity renormalization approach to the same problem. By performing analytical calculations with a step function form for the similarity factor, we show that in addition to curing the vanishing energy denominator problem, similarity approach generates linear confining interaction for large transverse separations. However, for large longitudinal separations, the generated interaction grows only as the square root of the longitudinal separation and hence produces violations of rotational symmetry in the spectrum. We carry out numerical studies in the G{\l}azek-Wilson and Wegner formalisms and present low lying eigenvalues and wavefunctions. We investigate the sensitivity of the spectra to various parameterizations of the similarity factor and other parameters of the effective Hamiltonian, especially the scale $\sigma$. Our results illustrate the need for higher order calculations of the effective Hamiltonian in the similarity renormalization scheme.