Exact treatment of confinement in the semirelativistic Faddeev approach to three-quark problems

ORAL

Abstract

The spin=1/2 elementary particles, the baryons, are mostly described as three-quark configurations. The quarks obey relativistic quantum mechanics. Their mutual interaction is modeled by infinitely rising potentials whose short-range nature is mediated by the exchange of Goldstone bosons. We solve the relativistic three-quark problem by using the Faddeev method. In the Faddeev method we break the wave function into components, and the components satisfies somewhat better integral equations. Nevertheless, the solution was not possible without approximating and violating the asymptotically rising potential. In this work we overcome this problem. We devised an approximation method, which allows the exact calculation of the Green's operator of an asymptotically rising potential with semirelativistic kinetic energy operator by using matrix continued fractions.

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Authors

  • Joseph Day

    California State University Long Beach

  • Joseph McEwen

    California State University Long Beach

  • Arnulfo Gonzalez

    California State University Long Beach

  • Zoltan Papp

    California State University Long Beach

  • Joshua Lusk

    University of New Mexico, Gallup Campus, Sciprint.org, Institute of Gravitation and Cosmology, Moscow, Russia, CSU Long Beach, California State University - East Bay, LLNL, UC Santa Cruz, University of California, Berkeley, Loma Linda Medical University, Northern Illinois University, Santa Cruz Institute for Particle Physics, Dr, Pr, California State University Long Beach, California Polytechnic State University, Department of Physics, California State University, Fresno, NPS, UC-Davis, University of California-Davis, University of California Riverside, Rutgers University, Pomona College, Department of Physics, Imperial College London, Materials Research Laboratory, UC Santa Barbara, Naval Postgraduate School, Whittier College, Cardiff University, Cardiff, Wales - Cardiff School of Biosciences, University of California, Davis - Electrical and Computer Engineering, University of California, Davis - Neurosurgery, Materials Department, University of California, Santa Barbara, CA 93106-5050, Queen's University, Belfast, Rutherford Appleton Laboratory, Technical University of Darmstadt, University of York, University of California, Los Angeles, Kohat University of Science and Technology, Lawrence Livermore National Laboratory, Imperial College, The Blackett Laboratory, University of Strathclyde, University of Oxford, UC Berkeley, UC Berkeley, SLAC, Gesellschaft f\"ur Schwerionenforschung GSI, University of Washington, Seattle, LLNL and XIA LLC, University of Graz, University of California, Davis, Naval Surface Warfare Center-Indian Head Division