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Mariana Kirchbach

Autonomous University of San Luis Potosi, Mexico
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Baryon Spectroscopy from an Exactly Solvable Quark Confinement Potential of QCD Traits

The two-body potential predicted by Lattice QCD
is known to be a linear combination of a
Coulomb- and a linear potentials. This so called Cornell
potential has been of frequent use not only in charmonium spectroscopy
but also in the spectroscopy of baryons when considered as
quark-di-quark systems.
We first make the point that the Cornell potential allows for an
extension toward an exactly solvable trigonometric potential of O(4)
symmetry. Next we apply the new potential in the calculation of
the respective spectra of nucleon and the Delta, considered
as quark-diquark systems.
We observe that both spectra are reproduced pretty well and that
none of the non-strange resonances observed so far drops
out of the systematic provided by the trigonometric potential
(modulo the hybrid Delta (1600)).
Moreover, the number of the missing resonances is significantly
reduced.
We calculate the proton electric form-factor in terms of a closed
expression and find that it follows data with amazing accuracy.
We conclude that the complicated quark-gluon dynamics results
in a simple exactly solvable trigonometric two-body potential
which represents a promising point of departure for more sophisticated
studies of baryon properties.

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