Effective-particle approach to bound states of quarks and gluons in QCD

TL;DR

This paper introduces the RGPEP method to construct bound states in QCD by transforming the Hamiltonian to effective particles with finite size, capturing phenomena from asymptotic freedom to confinement.

Contribution

It develops a renormalization group approach for effective particles in QCD, enabling rigorous study of quark-gluon bound states across energy scales.

Findings

Derivation of the leading effective quark interaction in heavy-flavor QCD.

Demonstration that the effective Hamiltonian reproduces asymptotic freedom.

Proposal that effective gluons acquire mass, leading to confinement effects.

Abstract

A general approach to the construction of bound states in quantum field theory, called the renormalization group procedure for effective particles (RGPEP), was applied recently to single heavy-flavor QCD in order to study its utility beyond illustration of its general features. This heavy-flavor QCD is chosen as the simplest available context in which the dynamics of quark and gluon bound states can be studied with the required rigor using Minkowski-space Hamiltonian operators in the Fock space, taking the advantage of asymptotic freedom. The effective quarks and gluons differ from the point-like canonical ones by having a finite size $s$. Their size plays the role of renormalization group parameter. However, instead of integrating out high-energy degrees of freedom, our RGPEP procedure is based on a transformation of the front-form QCD Hamiltonian from its canonical form with counterterms to the renormalized, scale-dependent operator that acts in the Fock space of effective quanta of quark and gluon fields, keeping all degrees of freedom intact but accounting for them in a transformed form. We discuss different behavior of effective particles interacting at different energy scales, corresponding to different size s. Namely, we cover phenomena ranging from asymptotic freedom at highest energies down to the scales at which the formation of bound states occurs. We briefly present recent applications of the RGPEP to quarks and gluons in QCD, which have been developed using expansion in powers of the Fock-space Hamiltonian running coupling. After observing that the QCD effective Hamiltonian satisfies the requirement of producing asymptotic freedom, we derive the leading effective interaction between quarks in heavy-flavor QCD. An effective confining effect is derived as a result of assuming that the non-Abelian and non-perturbative dynamics causes effective gluons to have mass.