English

Confinement with Perturbation Theory, after All?

High Energy Physics - Phenomenology 2015-06-22 v2

Abstract

I call attention to the possibility that QCD bound states (hadrons) could be derived using rigorous Hamiltonian, perturbative methods. Solving Gauss' law for A0A^0 with a non-vanishing boundary condition at spatial infinity gives an \order{\alpha_s^0} linear potential for color singlet qqˉq\bar q and qqqqqq states. These states are Poincar\'e and gauge covariant and thus can serve as initial states of a perturbative expansion, replacing the conventional free inin and outout states. The coupling freezes at αs(0)0.5\alpha_s(0)\simeq 0.5, allowing reasonable convergence. The \order{\alpha_s^0} bound states have a sea of qqˉq\bar q pairs, while transverse gluons contribute only at \order{\alpha_s}. Pair creation in the linear A0A^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+1D=1+1 dimensions, and some in D=3+1D=3+1.

Keywords

Cite

@article{arxiv.1409.4703,
  title  = {Confinement with Perturbation Theory, after All?},
  author = {Paul Hoyer},
  journal= {arXiv preprint arXiv:1409.4703},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-22T05:58:06.358Z