Confinement with Perturbation Theory, after All?

TL;DR

This paper explores deriving QCD bound states using a Hamiltonian perturbative approach with a non-zero boundary condition, resulting in a linear potential and finite-width excited states, challenging conventional non-perturbative methods.

Contribution

It introduces a perturbative framework for QCD bound states with a linear potential derived from boundary conditions, enabling a new perspective on confinement and hadron structure.

Findings

Linear potential emerges at order α_s^0 from boundary conditions.

Bound states exhibit a sea of qar q pairs and finite widths.

Some analytical results verified in 1+1 and 3+1 dimensions.

Abstract

I call attention to the possibility that QCD bound states (hadrons) could be derived using rigorous Hamiltonian, perturbative methods. Solving Gauss' law for $A^0$ with a non-vanishing boundary condition at spatial infinity gives an \order{\alpha_s^0} linear potential for color singlet $q\bar q$ and $qqq$ states. These states are Poincar\'e and gauge covariant and thus can serve as initial states of a perturbative expansion, replacing the conventional free $in$ and $out$ states. The coupling freezes at $\alpha_s(0)\simeq 0.5$, allowing reasonable convergence. The \order{\alpha_s^0} bound states have a sea of $q\bar q$ pairs, while transverse gluons contribute only at \order{\alpha_s}. Pair creation in the linear $A^0$ potential leads to string breaking and hadron loop corrections. These corrections give finite widths to excited states, as required by unitarity. Several of these features have been verified analytically in $D=1+1$ dimensions, and some in $D=3+1$.