Hadrons as QCD Bound States

TL;DR

This paper discusses a perturbative approach to bound states in QCD, inspired by QED atom calculations, emphasizing a gauge choice that simplifies the expansion around valence states and the determination of the confining potential.

Contribution

It introduces a bound state perturbation theory framework for QCD using temporal gauge, enabling a systematic expansion around valence states and deriving the confining potential from Gauss' law.

Findings

Applicable in any frame for hadrons in QCD

Determines the confining potential up to a universal scale

Connects bound state wave functions with perturbative expansions

Abstract

Bound state perturbation theory is well established for QED atoms. Today the hyperfine splitting of Positronium is known to $O(\alpha^7\log\alpha)$. Whereas standard expansions of scattering amplitudes start from free states, bound states are expanded around eigenstates of the Hamiltonian including a binding potential. The eigenstate wave functions have all powers of $\alpha$, requiring a choice in the ordering of the perturbative expansion. Temporal $(A^0=0)$ gauge permits an expansion starting from valence Fock states, bound by their instantaneous gauge field. This formulation is applicable in any frame and seems promising even for hadrons in QCD. The $O(\alpha_s^0)$ confining potential is determined (up to a universal scale) by a homogeneous solution of Gauss' law.