Algebraic Approach to the Hypercoulomb Problem

E. Santopinto, M. Giannini and F. Iachello
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E. Santopinto: Universita’ di Genova, Dipartimento di Fisica
M. Giannini: Universita’ di Genova, Dipartimento di Fisica
F. Iachello: Yale University New Haven, Center for Theoretical Physics, Sloane Laboratory

A chapter in Symmetries in Science VIII, 1995, pp 445-452 from Springer

Abstract: Abstract The low-lying states of baryons are thought to be mainly composed of three-quarks configurations. Although for light (u,d) quarks a construction of the quark-quark interaction is very difficult, it has been suggested that a good fraction of this interaction is of three-body character [1], and that, in addition, it can be well approximated by a hypercentral potential, i.e. an interaction that is invariant under rotations in the six dimensional space spanned by the intrinsic coordinates of the three-body problem. This suggestion arose from a study of the flux tube configurations of Fig. 1 for heavy-quark baryons. However, in general, the fact that QCD is a non-abelian gauge theory leads to gluon-gluon couplings which, in turn, produce three-body forces, as shown in Fig. 2. One is thus led to the conclusion that three-body forces can be a very important part of the quark interactions and this is particularly so for baryons composed of light quarks where the coupling constant αs is large.

Keywords: Casimir Operator; Algebraic Solution; Hyperspherical Harmonic; Quark Interaction; Coulomb Problem (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4615-1915-7_32

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