A model finding a new Richardson potential with different scales for confinement and asymptotic freedom, by fitting the properties of ${\D}^{++}$ and ${\Om}^{-}$

Abstract

Phenomenological Richardson potential has built in asymptotic freedom (AF in short) and confinement, with only one parameter $\La$ in the potential. But it is known that the scales of AF and confinement are not the same. In the present work a relativistic mean field calculation for baryons is tried out with two parameters $\La$ and $\La^\prime$ for AF and confinement respectively .To test the two parameter potential we calculate the energies and the magnetic moments, of the triple u - quark system (${\D}^{++}$) and the triple s - quark system (${\Om}^{-}$) and found good values for $\La=100 MeV$ and $\La^\prime ~= 350 MeV$. So we believe that the modified Richardson potential should have AF scale $\La ~= 100 MeV$ and the confinement scale $\La^\prime ~= 350 MeV$.