Solving the QCD Hamiltonian for bound states

TL;DR

This paper introduces a nonperturbative flow equation method to systematically analyze bound states in QCD, leading to an effective Hamiltonian that predicts glueball masses.

Contribution

It presents a novel approach using flow equations to derive a block-diagonal QCD Hamiltonian for bound state analysis, including glueball mass predictions.

Findings

Effective Hamiltonian obtained at low energies

Predicted masses for scalar and pseudoscalar glueballs

Demonstrated perturbative renormalization in a confining background

Abstract

The systematic approach to study bound states in quantum chromodynamics is presented. The method utilizes nonperturbative flow equations in the confining background, that makes possible to perform perturbative renormalization and to bring the QCD Hamiltonian to a block-diagonal form with the number of quasiparticles conserving in each block. The effective block-diagonal Hamiltonian provides constituent description for hadron observables. The renormalized to the second order effective Hamiltonian of gluodynamics in the Coulomb gauge is obtained at low energies. The masses for scalar and pseudoscalar glueballs are predicted.