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Manuscript Title: Relativistic three-quark bound states in separable two-quark approximation.
Authors: M. Oettel, L. van Smekal, R. Alkofer
Program title: BSE
Catalogue identifier: ADPT_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 144(2002)63
Programming language: Fortran.
Computer: Workstation DEC Aplha, LINUX PCs (AMD K7).
Operating system: True-Unixv5.0, SuSe Linux 7.1.
RAM: 10M words
Word size: 32
Peripherals: disc.
Keywords: Linear integral equations, Bethe-Salpeter equation, Nucleon model, Diquarks, Elementary particle physics, Phenomenological model.
Classification: 11.6.

Nature of problem:
Diquarks are introduced as separable correlations in the two-quark Green's function to facilitate the description of baryons as relativistic three-quark bound states. These states then emerge as solutions of Bethe-Salpeter equations for quarks and diquarks that interact via quark exchange.

Solution method:
Chebyshev polynomials are used for an expansion of the Bethe-Salpeter vertex and wave functions and an (approximative) representation of the interaction kernel and propagators. The resulting set of coupled one-dimensional integral equations for the corresponding moments of vertex and wave function is converted to a matrix equation by employing Gaussian quadrature grid points. This equation is then solved iteratively for a certain test mass of the bound state. A bisection method in the bound state mass variable is used to determine the correct mass corresponding to the chosen quark and diquark parameters.

Restrictions:
The separable quark-quark correlations are restricted to the leading covariants in the scalar and axialvector (i.e. positive parity) channels.

Additional comments:
Programming issue The program has been tested with the following compilers: DEC-f90v5.3, Lahey-Fujitsu-f95-LINUX-Expressv5.5, NagWare-f95.

Running time:
Depending on the parameters and the desired accuracy between one and ten minutes on 1.2 GHz AMD K7.