Nuclear Physics A 754 (2005) 248c–260c Baryon resonances and pentaquarks on the lattice ✩ F.X. Lee a,b,∗, C. Bennhold a a Center for Nuclear Studies, George Washington University, Washington, DC 20052, USA b Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA Received 17 December 2004; accepted 22 December 2004 Available online 21 January 2005 Abstract We review recent progress in computing excited baryons and pentaquarks in lattice QCD. 2004 Elsevier B.V. All rights reserved. 1. QCD primer Quantum Chromodynamics (QCD) is widely accepted as the fundamental theory of the strong interaction. The QCD Lagrangian density can be written down simply in one line (in Euclidean space) 1 L = Tr F F µν +¯q γ µD + m q, (1) QCD 2 µν µ q where Fµν = ∂Aµ − ∂Aν + g[Aµ,Aν] is the gluon field strength tensor and Dµ = ∂µ + gAµ is the covariant derivative which provides the interaction between the gluon and quark terms. The action of QCD is the integral of the Lagrangian density over space– 4 time: SQCD = LQCD d x. QCD is a highly non-linear relativistic quantum field theory. It is well known that the theory has chiral symmetry in the mq = 0 limit and the symmetry is spontaneously broken in the vacuum. At high energies, it exhibits asymptotic freedom, ✩ Based on plenary talk by F.X. Lee at HYP2003, JLab. * Corresponding author. E-mail address:
[email protected] (F.X. Lee). 0375-9474/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2004.12.072 F.X.