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 \order{α_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 \order{α_s^0} bound states have a sea of $q\bar{q}$ pairs, while transverse gluons contribute only at \order{α_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 $D=3+1$.

6 pages, 2 figures. Based on talks at Light Cone 2014 (Raleigh, NC USA, May 2014) and at the FAIR Workshop (Kolymbari, Greece, July 2014). Minor changes, this version is to be published in the journal Few-Body Systems

References in corpus (5)

• Infrared Properties of QCD from Dyson-Schwinger equations
• Non-perturbative comparison of QCD effective charges
• Determination of the effective strong coupling constant alpha_{s,g_1}(Q^2) from CLAS spin structure function data
• Towards a Born term for hadrons
• Evidence for infrared finite coupling in Sudakov resummation