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Published: 2011

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A short review of current efforts to determine the highly excited state spectrum of QCD, and in particular baryons, using lattice QCD techniques is presented. The determination of the highly excited spectrum of QCD is a major theoretical and experimental challenge. The experimental investigation of the excited baryon spectrum has been a long-standing element of the hadronic-physics program, an important component of which is the search for so-called 'missing resonances', baryonic states predicted by the quark model based on three constituent quarks but which have not yet been observed experimentally. Should such states not be found, it may indicate that the baryon spectrum can be modeled with fewer effective degrees of freedom, such as in quark-diquark models. In the past decade, there has been an extensive program to collect data on electromagnetic production of one and two mesons at Jefferson Lab, MIT-Bates, LEGS, MAMI, ELSA, and GRAAL. To analyze these data, and thereby refine our knowledge of the baryon spectrum, a variety of physics analysis models have been developed at Bonn, George Washington University, Jefferson Laboratory and Mainz. To provide a theoretical determination and interpretation of the spectrum, ab initio computations within lattice QCD have been used. Historically, the calculation of the masses of the lowest-lying states, for both baryons and mesons, has been a benchmark calculation of this discretized, finite-volume computational approach, where the aim is well-understood control over the various systematic errors that enter into a calculation; for a recent review. However, there is now increasing effort aimed at calculating the excited states of the theory, with several groups presenting investigations of the low-lying excited baryon spectrum, using a variety of discretizations, numbers of quark flavors, interpolating operators, and fitting methodologies. Some aspects of these calculations remain unresolved and are the subject of intense effort, notably the ordering of the Roper resonance in the low-lying Nucleon spectrum.