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

Abstract

Phenomenological Richardson potential has built in asymptotic freedom (AF in short) and confinement, with only one parameter $\text{La}$ 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 $\text{La}$ and ${\text{La}}^{\prime }$ 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 (${\text{D}}^{++}$) and the triple s - quark system (${\text{Om}}^{-}$) and found good values for $\text{La}=100MeV$ and ${\text{La}}^{\prime }=350MeV$. So we believe that the modified Richardson potential should have AF scale $\text{La}=100MeV$ and the confinement scale ${\text{La}}^{\prime }=350MeV$.

Comments: Accepted for publication in Nuclear Physics A