Confinement with Perturbation Theory, After All?

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 ${\mathcal{O}({\alpha_s^0})}$ linear potential for color singlet ${q \bar{q}}$ and qqq states. These states are Poincaré 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 ${\mathcal{O}({\alpha_s^0})}$ bound states have a sea of ${q \bar{q}}$ pairs, while transverse gluons contribute only at ${\mathcal{O}({\alpha_s})}$ . 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.